So, the whole understanding is that surface with such a curvature we have seen in the previous lecture at least qualitatively that because of the curvature of the surface pressure gradient may be developed along it. Our objective is to have an assessment of the effect of pressure gradient. We have to keep in mind that pressure gradient for an external flow may be induced by such a curvature effect but for an internal flow when it is say flow in a pipe or a channel you automatically have a pressure gradient. So, there it is not a curvature induced pressure gradient but natural consequence of the confinement that is there and here it is the curvature that is creating the pressure gradient. Now our important objective first will be to see that what is the effect of or what is the demarcating effect of dp dx less than 0 and dp dx greater than 0 and we will look into these cases separately. So, when we say x remember we are talking about a boundary layer coordinate. So, this x need not be a rectilinear coordinate x and a rectilinear coordinate y. So, let us say that when we are talking about dp dx less than 0 maybe we are talking about any flow in this part and whenever we are talking about dp dx greater than 0 we are talking about the part in the right hand side. So, here you have dp dx less than 0 and here you have dp dx greater than 0. We will try to draw the following profiles say u versus x just the other way we will plot u versus y del u del y versus y and del 2 u del y 2 versus y. We will try to make a qualitative sketch of these. Let us first do it for dp dx less than 0. So, for dp dx less than 0 I mean we have already seen dp dx even dp dx equal to 0 we have seen for flow over a flat plate. So, the situation is quite similar even for dp dx less than 0 and what you will get is say this is how you will vary with y till you come to a condition where like when y tends to delta u will tend to u infinity something like that. Now if you want to plot du dy versus y. So, first of all at the wall what is du dy positive or negative at the wall what is du dy positive or negative positive right u is increasing with y. So, you have a positive du dy at the wall what is du dy at the first stream as y tends to infinity it tends to 0. So, maybe like this in between what should be the variation the variation is monotonic there is no separate physical behavior. What is d2u dy2 at y equal to 0 negative because du dy is decreasing with y. So, you have a negative d2u dy2 and eventually it will come down to 0 as y tends to delta. So, that is the qualitative picture and this kind of qualitative picture is general hallmark of a flow with favorable pressure gradient. So, this is favorable pressure gradient next let us consider the case of dp dx greater than 0 which we have seen is known as adverse pressure gradient. Let us try to make such plots velocity profile du dy versus y before making the plot let us try to look into the corresponding boundary layer equations. So, the boundary layer equation what you have with pressure gradient u del u del x plus v del u del y is equal to nu del 2 u del y 2 minus 1 by rho dp dx. Let us see that how we applied this for dp dx less than 0 see at the wall let us say we are interested to apply it at the wall. So, when it is at the wall u is 0 by no slip 0 by no penetration. So, basically at the wall what you have is 1 by rho dp dx. So, what we conclude out of this is that when dp dx is negative this is negative and that is what we got here. So, this has to be consistent with the governing equation this we did intuitively from our previous experience in dealing with such cases, but it agrees with the governing equation. When it comes to dp dx greater than 0 for dp dx greater than 0 you must have d 2 u dy 2 at the wall greater than 0 right. So, at the wall let us start with this diagram. So, d 2 u dy 2 is greater than 0 at the wall right. The next question is that what is d 2 u dy 2 at the far stream far far away if it has to be 0 right at the very far stream away from the wall there should be no sort of gradient like u is like u infinity constant. So, far away you must have like asymptotically d 2 u dy 2 is 0. The question is then would we have d 2 u dy 2 something like this maybe something like this or even could we have it cross the y axis somewhere there could be many possibilities that is this is one value at the wall this is the value at the far stream far far away. Think of a case could you have in between a point where u is a maximum you could in between you should have a point where u is a maximum right that means you just has attained the maximum and then maybe further it is change is very less typically just outside the boundary layer. So, when u is a maximum you have d u dy equal to 0 and what is d 2 u dy 2 negative. So, you have it is value positive somewhere it is value positive somewhere because at some point away from the wall you must have u as maximum and this is a continuous function. So, it must cross 0 somewhere right. So, the correct variations will not be these ones right try to understand this very carefully by logical reasoning that you have d 2 u dy 2 greater than 0 at the wall there must be some point away from the wall where u is a maximum d u dy is 0 and d 2 u dy 2 is negative. So, that means there is a variation from and d 2 u dy to the second derivative is a continuous function. So, it has a variation from positive to negative somewhere it must have cross the 0 right and that is why its variation should be like this. So, that means we have identified a point where you have d 2 u dy 2 maybe 0 and not the far stream but somewhere in between. See the far stream d 2 u dy 2 0 is obvious this is not something which is obvious this is not an obvious conclusion. So, now if you want to extrapolate this plot that is you want to get a d u dy variation. So, what will be the d u dy variation at the wall you have a d u dy something okay there we will see that there may be a limiting case when you may also have d u dy at the wall in the limiting sense 0 and then what happens we will see that what is that. But in a general sense d u dy at the wall is say positive then you know that at this point you will have d u dy as the maximum that is why d 2 u dy 2 is 0. So, you may have something like this.  So, now if you draw the velocity profile here at this point you have d 2 u dy 2 is 0 that means it is an inflection point that is there is no rate of change of d u dy with respect to y. So, you may have a curve may be something of this sort where the curvature changes. But what you have is the slope from by looking from 1 n is same as the so at this point if you consider the slope like this and the slope like this. So, it is may be just show it in a different way something like an essay. So, where this will come to a limit of course where it will not change any further. But this is the point where no matter we take slope from the bottom part of the curve or the top part of the curve is the same. So, that point we call as a point of inflection p i. So, the point of inflection in the velocity profile is one of the hallmarks of the dp dx greater than 0 which is not there for dp dx less than 0. This is the first thing that we are understanding. Now, next thing is that now what happens at the wall? See when you have a velocity profile of this particular shape it is highly possible that it comes to a limiting condition when d u dy is 0 at the wall just you look into this particular form. So, if you consider an extreme case of this will represent what? An extreme case of this may have a situation when like the velocity profile takes off almost in this way almost like a vertical take off. That means the with change in y u does not change. So, d u dy with such a shape of velocity profile it is possible with such a shape it is not possible. So, you may have a limiting case when d u dy with the adverse pressure gradient the d u dy at the wall may even become 0. See in a favourable case it started with greater than 0 when it is coming less and less favourable at the wall you may have d u dy equal to 0 and then if it continues in that way it may be less than 0 and less than 0 is such a case when actually u will be not in the positive direction but in the negative direction. So, reverse flow will occur to understand that let us try to draw a schematic say for flow over may be a circular shaped object or object with a curvature. So, let us say that we have an object like this. So, we are interested to draw velocity profiles at different locations at different radial locations. So, initially when the dp dx is less than 0 you see that it is a intuitive way in which the velocity profiles are there may be it maintains it like this in the process the boundary layer grows. Now when you come to the dp dx greater than 0 you will come with locations of inflection points in the velocity. So, now if you draw the velocity profile at some point you will come to a state let us say that at this point we come to a limiting condition when the velocity profile is something like this. We have just now seen that it is possible with dp dx greater than 0 that is what we learnt from this experience. So, this is a special case of course the velocity profile has an inflection point that is the first thing the second important thing is here you are having at the wall equal to 0 that is a limiting case when it is 0 at the wall and then the pressure gradient is going on getting more and more adverse then what is happening the flow may reverse in its direction. So, you might have sort of a reverse flow like this in this way you may get points. So, if you have a reverse flow we will see physically that why such a reverse flow is occurring, but if you come to a location let us say this point this point represents what this point represents a location where the velocity is 0. Similarly, you may draw such velocity profiles at all other points and you will find that there will be such points. So, if you join such points so get a locus of may be all the points where you have such cases with velocity as 0 and above that velocity is greater than 0 that means as if the wall which was the location of 0 velocity has got shifted to this new location because beyond which you are having the velocity as greater than 0 and it is maintaining its direction and here what is happening here what is happening is a local back flow that is a loss. So, to say because it does not contribute to the main energy of the flow. So, this point where this all initiates that is known as a point of separation and when this has occurred we say that the boundary layer has got separated. So, you no more have a monotonous growth of the boundary layer beyond this point and the name of this point is the point of separation. So, we call this as s this is separation point. You may have different stream lines passing through the separation point may be like this or whatever it I mean that is possible this is the stream line passing through the separation point just as an example I mean there it may be possible that you have locally recirculating flows. So, you may also have other stream lines like this because in some case you have a negative flow then you may have a positive flow like this. So, the question or the emphasis is not really that how should the stream lines look there the big emphasis is that from the till the point s the boundary layer did grow as we expected and as we discussed may be like for flow over a flat plate. Flow over a flat plate is what is the special case what is the special case dp dx equal to 0. So, when dp dx equal to 0 for flow over a flat plate where lies the point of inflection look into the governing equation dp dx equal to mu at the wall. So, if dp dx is 0 that means this is equal to 0 that means point of inflection for flow over a flat plate is at the wall at y equal to 0. So, that case is the limiting case it is saved from such a phenomenon because if you do not have a point of inflection within the flow domain this type of limiting situation does not occur where you might have the velocity gradient 0 at the wall. So, when you have the velocity gradient 0 at the wall from the point s what we have come to a conclusion that the boundary layer separation has taken place point s onwards. That means because of this type of reverse flow the boundary layer is not monotonically growing as it was doing earlier and as if it has got detached from the wall as if the new boundary that now represents the growth of whatever apparent growth of boundary layer is this one is the new one. So, the very important conclusion we get out of this is that this line sort of represents a wall that has got detached from the main wall like that. So, it is therefore considered as a flow separation or boundary layer separation when you consider the case of a boundary layer theory. So, very important restriction is that beyond this point s you cannot apply the boundary layer theory. So, when we were discussing about the boundary layer theory and its assumptions one of the important assumptions that we made is Reynolds number is large that remains, but the other important assumption is that there is no boundary layer separation because if boundary layer separation occurs from the separation point onwards the boundary layer theory is no more valid and that we have to keep in mind. So, these are the two most important fundamental assumptions behind the boundary layer theory that we have developed. Now, what happens beyond the separation point actually there is a low pressure region that is formed beyond the separation point and because of this formation of the low pressure region this low pressure region behind the separation point it is called as a wake and what is important here is to note that because of the formation of that wake or the low pressure region or the separation the symmetry in the pressure distribution around the body is disturbed. So, if there was no such separation the pressure distribution with respect to the vertical axis would have been same for the left and the right, but because it has occurred now it gives rise to a low pressure region and the pressure distribution does not remain uniform and therefore there occurs a net resultant force because of the pressure distribution that acts on the body and the pressure distribution that acts on the body it is very critical because depending on that you may have a resultant force that acts on the body. We have seen that the resultant force that acts on the body is a combination of the effect of the shear as well as the pressure gradient. The pressure gradient is absent for flow over a flat plate, but for flow with such surfaces with such curvature that effect cannot be neglected that is one of the important conclusions that we should keep in mind. Now, before moving on to the consequence of this separation let us maybe look into one example to see that how the velocity profile gets affected because of it. Let us say that we want to have an estimation of the velocity profile at the point of separation and let us say that it is given in this form u y u infinity is equal to a0 plus a1 y by delta plus a2. This is an example of assume that this is velocity profile at the inception of separation. Our objective is to find out a0 a1 a2 a3 consistent with the physical conditions. So, it is just like estimating a velocity profile or fitting a velocity profile in a polynomial form that we did for flow over a flat plate, but the boundary conditions which should be consistent with this one the boundary conditions are somewhat altered. So, what are the boundary conditions that we need to consider for this? Again there are 4 constants. So, we should consider 4 boundary conditions to specify the velocity profile completely. So, what are the boundary conditions that we should consider? Number 1, y equal to 0 u equal to 0 fine. Then at y tends to infinity or at y equal to delta here which is like tends to infinity at y equal to delta u equal to u infinity at y equal to delta you have no further change in u and fourth one at y equal to 0 this is equal to 0. This is very very important because this is the hallmark of separation at y equal to 0 you cannot apply d2 u dy2 equal to 0 that was for flow over a flat plate because dp dx was 0. Here dp dx is not 0 because you are given that the velocity profile at the inception of separation when there is a chance of separation it must be dp dx greater than 0. Now the big question is that why such a separation will occur? See when the fluid is there within the boundary layer it has some energy but because of the reduction in the velocity that is being imposed by the shear effect within the boundary layer the boundary layer tries to or the fluid in the boundary layer has a tendency to get slowed down. Now when it has a tendency to get slowed down still it has to move forward then what is that which will try to make it move forward? One is the shear interaction with the outer layer that is what it tends to make it move forward. So it has sort of it takes some energy from that and tries to retain its energy and make its forward movement and if you have dp dx less than 0 that on the top of it helps it. If dp dx is equal to 0 then also it is okay there is no extra effect from dp dx as a help but there is no extra effect also in terms of resistance. But when dp dx is greater than 0 then the pressure gradient resists the forward movement. So there is a poor fluid element which is located within the boundary layer has a tendency to get slowed down and the pressure gradient externally on the top of it tends to slow it down further and further. So it has a tendency of continuous reduction in momentum and that may give rise to shift in the direction of the velocity. So that is how you can get a back flow or a reverse flow. So the momentum in the boundary layer is not sufficient and external pressure gradient which is acting adverse to it if dp dx is greater than 0 may be just sufficient to make it flow in the reverse direction. But the question is if dp dx is greater than 0 is it necessary that it has to flow in the reverse direction. The answer is no it may not because still it might have sufficient momentum to overcome that adverse pressure gradient and somehow maintain the flow but if the pressure gradient is so adverse that it does not have enough momentum to overcome that then only it will be a reverse flow. So existence of an adverse pressure gradient is a necessary condition for boundary layer separation but it is not a sufficient condition. So you cannot say that there is an adverse pressure gradient and because of that there will be boundary layer separation. But you can definitely say that if there is no adverse pressure gradient there will be no boundary layer separation. So adverse pressure gradient is a necessary condition for boundary layer separation but not sufficient. The sufficiency will come from what is the strength of that adverse pressure gradient is it good enough to overcome the forward momentum and create a reverse flow that is the important concept that we need to learn. So what we have understood is that if you have a flow if you have a solid body in a fluid the solid body in a fluid may be subjected to different forces and these forces may come from one is the skin friction drag which we have identified for flow over a flat plate even without pressure gradient that is because of the shear plus there may be a force due to the pressure gradient. So that force due to pressure gradient may give rise to a net effect which may also be a drag force but to understand that what is the net effect is it just a drag force or something more than that we have to formally define that what are the forces which may act on a body which is immersed in a fluid. So let us do that. So we have now at least got the origin of the forces that is the pressure gradient and the shear but how we combine these to get the net force. So the resultant force on a body immersed in a fluid under motion. So do not confuse it with fluid statics it is not fluid at rest. So we are not talking about forces like buoyancy forces like that. So this is solely because of the relative motion between the fluid and the solid whatever is the force that force we want to identify. So generally the convention is that let us say you have an arbitrary shaped body let us consider a 2 dimensional flow. So what are the forces which are acting on the body? One is there is a pressure distribution around the body. The pressure distribution is not uniform. Why it is not uniform? Because for example there may be flow separation because of the flow separation after the flow separation has occurred it will be a low pressure region and that means there is asymmetric pressure distribution that is created because of flow separation. So the net effect is that the pressure distribution will be non-uniform there will be a force due to pressure distribution plus there will be a force due to the viscous shear effect. So you will have some shear effect also. Let us say that there will be some force due to shear. So you can see that even mathematically whatever we considered as tangential forces and normal components of forces those are automatically coming physically through the effect of pressure as the normal force and the effect of shear through the tangential force. The resultant force whatever if you integrate the net effect over the body you may resolve it into 2 components. What are of course you may resolve it into 2 components in many ways but what is the important convention? Let us say that this is the free stream direction. Let us say this is the u infinity direction. So the force on the body what is usually done is it is resolved into 2 components. One is in the direction of the free stream and another is perpendicular to the direction of the free stream and let us say that this is the resultant force. So this force which is along the direction of the free stream is known as the drag force and which is perpendicular to the direction of the free stream is known as the lift force. This is where we are talking about a 2 dimensional flow but if it is a 3 dimensional flow there also may be a side wise force in the third direction. If there is also a component perpendicular to the plane where we are drawing the figure but otherwise these 2 components must be there because the flow at least must be a planar flow and these are very important because this drag force is something which will come in the form of frictional resistance and the lift force is something which is may give an upward motion to the body and this is very important for wings of aircraft. So if you have a aerofoil section like which represents the wings of aircraft then because of the lift force generated it may go from a lower elevation to a higher elevation. So both the lift force and the drag force are very important and it is very important to characterize those. So when we characterize the lift and drag force we have seen that the drag force we may characterize by a coefficient of drag Cd. So the coefficient of drag is the drag force by half rho u infinity square into some reference area. We will discuss that what should be the reference area. Similarly you have a coefficient of lift. This is the lift force divided by some half rho u infinity square. So the coefficient of the lift and the coefficient of the drag are just non-dimensional ways of representing the lift and the drag force. So when you have this drag force, this drag force has 2 contributors because see the resultant force along the direction of the flow is a resultant force due to shear having a component along the direction of flow plus resultant force due to pressure having a component along the direction of flow. So when we have the drag force, its physical origin is divided into 2 parts. What are these parts? One is known as skin friction drag which originates because of the shear and another is known as pressure drag or form drag. Then from the name pressure drag or form drag it is clear. First of all why then from the name pressure drag it is clear that it is because of the pressure distribution on the body. So just like the skin friction drag is because of the shear force distribution on the body, the pressure drag is due to the pressure distribution on the body. Why it is also called as form drag? Because it is a strong function of the geometric form of the body because the geometry of the body is what induces the pressure gradient. So that is why it is called as a form drag. In engineering one of the important objectives may be to minimize the drag force between a fluid and a solid. And if one wants to do that then one has to see that which one is the stronger contributor the skin friction drag or the form drag and it all depends on whether the flow is laminar or turbulent. So we will now try to look into the issue that first of all if the flow is if we consider the skin friction drag is it greater for a laminar flow or turbulent flow? If we consider a form drag or pressure drag is it greater for turbulent flow or laminar flow? So let us look into that. So if we consider say a skin friction drag, clean friction drag depends on what? It depends on the wall shear stress distribution. Wall shear stress depends on what? One is the viscosity of the fluid that does not change if the flow becomes turbulent from laminar. What changes is the velocity gradient at the wall. So now you tell that if you consider the skin friction drag for a flow which is laminar and for a flow which is turbulent then which should offer more skin friction drag. Obviously that will have more skin friction drag for which du dy is more. If you consider mu du dy the wall shear stress. So which should have more du dy? Think of a situation. Consider that you have flow in a channel. If you have a laminar flow what is the velocity typical if you have fully developed laminar flow velocity profile like parabolic distribution. This is what we have derived when we were solving this by using Navier-Stokes equation. But if it is a turbulent flow of course when it is a turbulent flow we are drawing only the average component of the velocity. How it will look? See for the turbulent flow the important thing is that there is a great level of mixing in the turbulent flow because of the interaction between eddies of different scales. So because of very efficient mixing between the in the turbulent flow the velocity so mixing what it tries to do? It tries to homogenize it. So it will try to have a uniform velocity profile almost throughout but at the wall it should satisfy the no slip boundary condition. So it should abruptly come down to 0 velocity at the wall. So the turbulent flow average velocity profile will be something like this. So if you now consider that where du dy is more at the wall for the turbulent flow because here there is a high change in u within a very short y distance close to the wall. So this is the turbulent and this is the laminar. So we can see that since du dy at the wall for turbulent is greater than du dy for the wall for the laminar flow considering all other conditions unaltered and when we say turbulent du dy you have to keep in mind this is the mean velocity that we are talking about. So that means you have the wall shear stress for the turbulent is greater than that for the laminar. That means you have the skin friction drag is greater for the turbulent flow. Now let us come to the form drag or pressure drag. When we come to the form drag, the form drag we are bothered about the geometry of the body. So the form drag all depends on the pressure distribution around the body. So form drag occurs because of what? Because of a boundary layer separation. Boundary layer separation will occur when the fluid in the boundary layer has insufficient momentum so that adverse pressure gradient strongly overcomes that and creates a reverse flow. So now in which case within the boundary layer you have more momentum for a turbulent boundary layer or a laminar boundary layer. You expect a greater momentum in the boundary layer in the turbulent boundary layer and since you have more momentum within the boundary layer for the turbulent boundary layer you have a greater chance of resisting the adverse pressure gradient. Therefore flow separation may be delayed by virtue of having a turbulent boundary layer. So if the flow separation is delayed what will happen? The separation point will shift to further downstream and the pressure distribution which is there around the body that asymmetry will be less and less. Therefore the drag force because of the difference in pressure between the points which are located upstream and downstream of the separation. Since the separation point shift towards the end towards the downstream then what happens? Then obviously you have a much smaller wake. Wake is the low pressure region beyond the separation point. So beyond the separation point the region if it is very small then that is in a way better because it will give rise to less form drag or less pressure drag. So if you have a turbulent boundary layer it has greater momentum it will delay the separation and in the process it will have a less form drag. So the turbulent boundary layer has higher momentum so it delays the separation and that means it has less form drag or pressure drag. See the engineering design has therefore a sort of conflicting things. So if you have a laminar boundary layer you have less skin friction drag but a greater pressure drag or form drag whereas if you have a turbulent boundary layer it is the other way. Your question is not to minimize this individually but the total drag force you have to minimize. So when you need to minimize the total drag force you have to see which one is dominating and when you see that which one is dominating it depends on what is the shape of the body. If the shape of the body is such that it induces a separation much earlier then the form drag is what dominates. If the shape of the body is such that it does not induce the separation so early then the skin friction drag is what dominates. Let us look into some movies where we will try to figure out that what are the important characteristics of flow behind different bodies. So if you look into this flow this is flow past a cylinder okay. So if you have if you consider this that circular thing as a cylinder where the length is perpendicular to the plane of the figure. If you play it once more you see that after the separation so the separation has occurred somewhere like maybe at somewhat in the middle section beyond that you have the region in the back where you have these rotating structures and all those are low pressure regions. So but if you consider a different shape body you may also see a very similar thing. This is flow past a building. So if you so it is basically a building simulated and if you see that there is a flow separation there is a low pressure region in the back. So whatever is the region which is towards the right after the boundary layer separation has occurred that is a low pressure region and it strongly depends on the shape. So let us look into the case if you change the shape what happens. Let us have a shape like this. So if you see now this is such a shape where the boundary layer separation is not there it is almost avoided it of course depends on that what is the direction of the relative velocity between the solid and the fluid and that we will see but just you can see that because of the section the section is such that it is not blunt that you can see the previous bodies were sort of blunt and these those are technically called as bluff bodies. This type of a shape is called as a streamline body. So a streamline body will have a much less tendency of boundary layer separation and that let us try to see an example where we have a combination of streamline and bluff body. So let us so the sort of board that is moving it is like a streamline shape and it is sailing fine in the water but it you see now closely the flow around the stirrer you see that this is this is quite bluff and the flow around that is something which is having the effect of flow past a bluff body. So I mean you may have combinations of bluff and streamline body together in the same effect and if you want to see that what is the consequence in engineering design we will of course we will try to understand this later that what is the consequence in engineering design but just to see that if you do not consider any boundary layer separation effect boundary layer separation effect comes if you consider boundary layer effect. Now if you do not consider boundary layer effect it is like an inviscid flow which is a potential flow you see that case at the bottom it does not show the boundary layer separation at the top you see that you can get a boundary layer separation and you have a low pressure region but if you design the car the backside like a streamline shape then you may delay that separation and that will reduce the drag. So you will see that many of the racing cars are designed in that way so to avoid or to minimize the drag force we will come into these examples one after the other when we will look into more details of flow past different shape bodies but our important conclusion is that if you have bodies of different shapes depending on that different drag forces may dominate. So what are the important measures that you may take to delay the boundary layer separation because boundary layer separation is an important issue that gives rise to a form drag or a pressure drag. So what could be the measures? There are several measures which are possible one of the measures is known as boundary layer suction. So let us just note this down that what are the measures possible measures to delay boundary layer separation. Number one is boundary layer suction. Boundary layer suction is what? Let us say that you have a solid boundary and there is a boundary layer that is formed of course not for such a straight surface the form drag will be important. Let us say that you have a curved boundary.  In the process what you do you are basically increasing the momentum of the fluid within the boundary layer.  So in the process what you are doing you are enhancing the momentum of the fluid within the boundary layer. We have seen that one of the reasons of boundary layer separation is that the fluid in the boundary layer does not have sufficient momentum to overcome the adverse pressure gradient. So in this way so we have looked into one example earlier in the previous class say where you have some fluid which you put through the holes from the top and you suck that from the bottom. So this is one of the ways in which you can create greater momentum in the boundary layer. You could also do it in the other way. You might inject fluid into the boundary layer. So increasing the momentum is not so much dependent on this whether it is upwards or downwards. So you might have boundary layer injection. Then of course changing the shape of the body that is streamlining the body. So if you have a bluff body you may redesign it to make it of a streamline shape okay. Then may be by artificially roughening the surface. If you roughen the surface what happens? You may create sufficient perturbations to trigger the onset of turbulence. So roughening the surface artificially. These are some of the very practical things and later on in one of our lectures we will see that sometimes the cricket ball is roughened in one side and what effect does it have on creating the swing in the cricket ball in a particular direction. And I mean these are some of the basic scientific tools that go behind. So we will just work out a problem quickly on the calculation of the resultant drag force on a body. So let us say that a circular cylinder with p infinity u infinity as the free stream conditions measure an angle theta from this direction and it is given that boundary layer separation occurs. We will see that when boundary layer separation occurs in such a case in detail later on. But say for this problem it is given that boundary layer separation occurs at theta is equal to 108.8 degree. This is from experiments. The wall shear stress is given by tau wall is equal to 1.5 rho u infinity square into Reynolds number to the power – 1.5 into a function of theta where the function of theta is equal to 0 for a range of theta between 108.8 degree to 180 degree and integral 0 to 108.8 degree f theta sin theta is equal to 5.93. This is also from experiments. Also it is given the pressure distribution in a normalized way is given by p – p infinity by half rho u infinity square is equal to g theta such that integral 0 to 180 degree g theta cos theta d theta is equal to 1.17. This is also from experiment. So experimental pressure distribution and shear distribution is given as a function of theta. From that you find out what is the total, what is the net coefficient of drag. So you can clearly see that after the boundary layer has got separated say 108.8 degree beyond that you do not have a wall shear stress effect because as if the effect of the wall has got detached from the boundary. So now how do you find out the resultant force?  So the length of this one is what? Length of this one is r d theta. If you have a total force on this you have one as the shear tau wall and another as the pressure. So what is the force due to the wall shear stress df due to the shear? So that is tau wall into r d theta into the length of the cylinder that is number 1 but what you want is the drag force coefficient of drag. So you want the force component of this in the direction of the flow. So what will be that? So basically this into sin theta. So you will have df drag due to shear is equal to tau wall into r d theta into l into sin theta. So you have the total drag force due to shear is equal to tau wall into r d theta l sin theta integrate 2 into 0 to 180 degree. Tau wall you know as a function of theta and so you substitute that. So tau wall is equal to this into f theta. f theta sin theta d theta integral is already given to you. So you can substitute that here. It becomes a very simple calculation. Similarly what will be f drag due to pressure? In place of tau wall the effect will be because of p and sin theta will become cos theta. So 2 integral p r d theta l cos theta from 0 to 180 degree. So the total drag is the sum of these 2 that is the total drag and what is the CD? CD is the total drag force divided by half rho u infinity square into reference area. For this kind of a case so the circular cylinder is like this and flow is taking place cross it. So the reference area is taken as the projected area perpendicular to the flow. So what is the projected area perpendicular to the flow? L into 2r. So this a reference that is called as a frontal area or projected area. Projected or frontal area that is equal to 2r into l. So if you do that let me give you the final answer which you may check. The final answer is 1.17 plus 5.93 divided by square root of Reynolds number. So what we can see here is that the drag coefficient at very high Reynolds number may be virtually independent of Reynolds number. And what are the important things that we see? This 1.17 is from where? This is from the form drag. This is from the skin friction drag. So very high Reynolds number flow may have the form drag is the sole determining factor for very high Reynolds number flow. So you can clearly see the effect of the form drag and the skin friction drag. So let us stop here today. We will continue again in the next class. Thank you.


Stories and content and weird darkness can be disturbing for some listeners and is intended for mature audiences only. Parental discretion is strongly advised. Gone from my sight, or parable of immortality, a poem by Luther F. Beecher. I am standing upon the seashore. A ship at my side spreads her white sails to the morning breeze and starts for the blue ocean. She is an object of beauty and strength, and I stand and watch her until she hangs like a speck of white cloud, just where the sea and sky come down to meet and mingle with each other. Then someone at my side says, there she's gone. Gone where? Gone from my sight. That is all. She is just as large in mass and hull and spar as she was when she left my side and just is able to bear her load of living freight to the place of her destination. Her diminished size is in me and not in her. And just at that moment when someone at my side says, there she's gone, there are other eyes that are watching for her coming and other voices ready to take up the glad shout, there she comes. And that is dying, often attributed to Henry Van Dyke. Welcome, Weirdos. I'm Darren Marlar and this is Weird Darkness. Here you'll find stories of the paranormal, supernatural, legends, lore, the strange and bizarre, crime, conspiracy, mysterious, macabre, unsolved and unexplained. The Last Voyage of Demeter is an extract from the most terrifying vampire fiction in literary history, Bram Stoker's Dracula from 1897. The thrilling novel is a gothic horror classic written in epistolar reform through a series of journal entries, newspaper articles and correspondence. This is the book's suspenseful chapter 7, delving into the final sea voyage of Demeter, the Russian ship unknowingly carrying Transylvania's undead Count Dracula. When a ghost ship arrives in Whitby Harbor, the locals search for clues about how the doomed vessels crew vanished. Soon the captain's log is discovered, but the translated correspondence does nothing more than strike terror in the hearts of all who read it. Weeks before its final destination, strange and supernatural events began haunting the ship. The captain started keeping a log to record the death, darkness and fear that had taken a hold of his crew. Of course, The Last Voyage of the Demeter was also recently made into a film, but we're working from the original writings of Bram Stoker here, not a movie script. If you're new here, welcome to the show. While you're listening, be sure to check out WeirdDarkness.com for merchandise, to visit sponsors you hear about during the show, sign up for my newsletter, and our contests. Connect with me on social media. Plus, you can visit the Hope in the Darkness page if you're struggling with depression or dark thoughts. You can find all of that and more at WeirdDarkness.com.  One of the greatest and suddenest storms on record has just been experienced here, with results both strange and unique. The weather had been somewhat sultry, but not to any degree uncommon in the month of August. Saturday evening was as fine as was ever known, and the great body of holidaymakers laid out yesterday for visits to Mowgrave Woods, Robin Hood's Bay, Rick Mill, Runswick, States, and the various trips in the neighborhood of Whitby. The steamers, Emma and Scarborough, made trips up and down the coast, and there was an unusual amount of tripping both to and from Whitby. The day was unusually fine until the afternoon when some of the gossips who frequent the East Cliff Churchyard and from that commanding eminence watched the wide sweep of sea visible to the north and east, called attention to a sudden show of mares' tails high in the sky to the northwest. The wind was then blowing from the southwest in the mild degree which in barometrical language is ranked number two light breeze. The Coast Guard on duty at once made report, and one old fisherman who for more than half a century has kept watch on weather signs from the East Cliff foretold in an emphatic manner the coming of a sudden storm. The approach of sunset was so very beautiful, so grand in its masses of splendidly colored clouds that there was quite an assemblage on the walk along the cliff in the old churchyard to enjoy the beauty. Before the sun dipped below the black mass of kettle-ness, standing boldly a thwart the western sky, its downward way was marked by myriad clouds of every sunset color, flame, purple, pink, green, violet, and all the tints of gold, with here and there masses not large but of seemingly absolute blackness in all sorts of shapes, as well as outlined as colossal silhouettes. The experience was not lost on the painters, and doubtless some of the sketches of the prelude to the great storm will grace the RA and RI walls in May next. More than one captain made up his mind then and there that his cobble or his mule as they termed the different classes of boats would remain in the harbor till the storm had passed. The wind fell away entirely during the evening, and at midnight there was a dead calm, a sultry heat, and that prevailing intensity, which on the approach of thunder, affects persons of a sensitive nature. There were but few lights in sight at the sea, or even the coasting steamers which usually hug the shore so closely kept well to seaward, and but few fishing boats were in sight. The only sail noticeable was a foreign schooner with all sails set, which was seemingly going westwards. The foolhardiness or ignorance of her officers was a prolific theme for comment whilst she remained in sight, and efforts were made to signal her to reduce sail in face of her danger. Before the night shut down, she was seen with sails idly flapping as she gently rolled on the undulating swell of the sea, as idle as they painted ship upon a painted ocean. Shortly before ten o'clock, the stillness of the air grew quite oppressive, and the silence was so marked that the bleeding of a sheep inland or the barking of a dog in the town was distinctly heard, and the band on the pier with its lively French air was like a discord in the great harmony of nature's silence. A little after midnight came a strange sound from over the sea and high overhead the air began to carry a strange, faint hollow booming. Then, without warning, the tempest broke. With a rapidity which at the time seemed incredible and even afterwards is impossible to realize, the whole aspect of nature at once became convulsed. The waves rose in growing fury, each overtopping its fellow till in a very few minutes the lately glassy sea was like a roaring and devouring monster. White crested waves beat madly on the level sands and rushed up the shelving cliffs. Others broke over the piers, and with their spume swept the land thorns of the lighthouses which rise from the end of either pier of Whitby Harbor. The wind roared like thunder and blew with such force that it was with difficulty that even strong men kept their feet or clung with grim clasp to the iron stanchions. It was found necessary to clear the entire piers from the massive onlookers or else the fatalities of the night would have been increased manifold. To add to the difficulties and dangers of the time, masses of sea fog came drifting inland, white, wet clouds which swept by in ghostly fashion so dank and damp and cold that it needed but little effort of imagination to think that the spirits of those lost it see or touching their living brethren with the clammy hands of death and many a wand shuddered as the wreaths of sea mist swept by. At times the mist cleared and the sea for some distance could be seen in the glare of the lightning which now came thick and fast, followed by such sudden peals of thunder that the whole sky overhead seemed trembling under the shock of the footsteps of the storm. Some of the scenes thus revealed were of immeasurable grandeur and of absorbing interest, the sea running mountains high through skywards with each wave mighty masses of white foam which the tempest seemed to snatch at and whirl away into space, here and there a fishing boat with a rag of sail running madly for shelter before the blast, now and again the white wings of a storm-tossed seabird. On the summit of the East Cliff the new search light was ready for experiment but had not yet been tried. The officers in charge of it got it in working order and in the pauses of the inrushing mist swept with it the surface of the sea. Once or twice its service was most effective as when a fishing boat with gun whale under water rushed into the harbor able by the guidance of the sheltering light to avoid the danger of dashing against the piers. As each boat achieved the safety of the port there was a shout of joy from the mass of people on shore, a shout which for a moment seemed to cleave the gale and was then swept away in its rush. Before long the search light discovered some distance away, a schooner with all sails set, apparently the same vessel which had been noticed earlier in the evening. The wind had by this time backed to the East and there was a shutter amongst the watchers on the cliff as they realized the terrible danger in which she now was. Between her and the port lay the great flat reef on which so many good ships have from time to time suffered and with the wind blowing from its present quarter it would be quite impossible that she should fetch the entrance of the harbor. It was now nearly the hour of high tide but the waves were so great that in their troughs the shallows of the shore were almost visible and the schooner with all sails set was rushing with such speed that, in the words of one old salt, she must fetch up somewhere if it was only in hell. Then came another rush of seafog, greater than any hitherto, a mass of dank mist which seemed to close on all things like a gray paw and left available to men only the organ of hearing for the roar of the tempest and the crash of the thunder and the booming of the mighty billows came through the damp oblivion even louder than before. The rays of the searchlight were kept fixed on the harbor mouth across the east pier where the shock was expected and men waited breathless. The wind suddenly shifted to the northeast and the remnant of the seafog melted in the blast and then Mirabil Diktu between the piers leaping from wave to wave as it rushed at headlong speed swept the strange schooner before the blast with all sails set and gained the safety of the harbor. The searchlight followed her and a shudder ran through all who saw her for last to the helm was a corpse with drooping head which swung horribly to and fro at each motion of the ship. No other form could be seen on deck at all. A great awe came on all as they realized that the ship as if by a miracle it found the harbor unsteered saved by the hand of a dead man. However, all took place more quickly than it takes to write these words. The scooter paused not but rushing across the harbor pitched yourself on that accumulation of sand and gravel washed by many tides and many storms into the southeast corner of the pier jutting under the east cliff known locally as Tate Hill Pier.  Every sparr rope and stay was strained and some of the top hammer came crashing down. But strangest of all the very instant the shore was touched an immense dog sprang up on deck from below as if shot up by the concussion and running forward jumped from the bow on the sand making straight for the steep cliff where the churchyard hangs over the laneway to the east pier so steeply that some of the flat tombstones, rough steams or through stones as they call them in the Whitby vernacular actually project over where the sustaining cliff has fallen away. It disappeared in the darkness which seemed intensified just beyond the focus of searchlight. It so happened that there was no one at the moment on Tate Hill Pier as all those whose houses are in close proximity were either in bed or were out on the heights above. Thus the Coast Guard on duty on the eastern side of the harbor who at once ran down to the little pier was the first to climb on board. The men working the search light after scouring the entrance of the harbor without seeing anything then turned the light on the derelict and kept it there. The Coast Guard ran aft and when he came beside the wheel bent over to examine it and recoiled at once as though under some sudden emotion. This seemed to peak general curiosity and quite a number of people began to run. It is a good way round from the west cliff by the drawbridge to Tate Hill Pier but your correspondent is a fairly good runner and came well ahead of the crowd. When I arrived however I found already assembled on the pier a crowd whom the Coast Guard and police refused to allow to come on board. By the courtesy of the Chief Boatman I was as your correspondent permitted to climb on deck and was one of a small group who saw the dead seaman whilst actually lashed to the wheel. It was no wonder that the Coast Guard was surprised or even odd for not often can such a sight have been seen. The man was simply fastened by his hands tied one over the other to a spoke of the wheel. Between the inner hand and the wood was a crucifix the set of beads on which it was fastened being around both wrists and wheel it all kept fast by the binding cords. The poor fellow may have been seated at one time but the flapping and buffeting of the sails had worked through the rudder of the wheel and dragged him to and fro so that the cords with which he was tied had cut the flesh to the bone. Accurate note was made of the state of things and a doctor, surgeon J. M. Kaffen of 33 East Elliot Place who came immediately after me declared after making examination that the man must have been dead for quite two days. In his pocket was a bottle carefully corked empty save for a little roll of paper which proved to be the addendum to the log. The Coast Guard said the man must have tied up his own hands fastening the knots with his teeth. The fact that a Coast Guard was the first on board may save some complications later on in the Admiralty Court where Coast Guards cannot claim the salvage which is the right of the first civilian entering on a derelict. Already however the legal tongues are wagging and one young law student is loudly asserting that the rights of the owner are already completely sacrificed his property being held in contravention of the statutes of Mortmain since the tiller as emblemship if not proof of delegated possession is held in a dead hand. It is needless to say that the dead steersman has been reverently removed from the place where he held his honorable watch and ward till death. The steadfastness says noble is that of the young Casablanca and placed in the mortuary to await inquest. Already sudden storm is passing and its fierceness is abating. Crowds are scattering homeward and the sky is beginning to redden over the Yorkshire Wolves. I shall send in time for your next issue further details of the derelict ship which found her way so miraculously into Harbor and the storm. Whitby 9 August The sequel to the strange arrival of the derelict in the storm last night is almost more startling than the thing itself. It turns out that the schooner is a Russian from Varna and is called the Demeter. She is almost entirely in ballast of silver sand with only a small amount of cargo, a number of great wooden boxes filled with mold. This cargo is consigned to a Whitby solicitor, Mr. SF Billington of Seven, the Crescent, who this morning went aboard and formally took possession of the goods consigned to him. The Russian Consul, too, acting for the charter party, took formal possession of the ship and paid all harbour dues, etc. Nothing is talked about here today except a strange coincidence. The officials of the Board of Trade have been most exacting in seeing that every compliance has been made with existing regulations. As the matter is to be a nine-days wonder, they are evidently determined that there shall be no cause of after complaint. A good deal of interest was abroad concerning the dog, which landed when the ship struck, and more than a few of the members of the SPCA, which is very strong in Whitby, have tried to befriend the animal. To the general disappointment, however, it was not to be found. It seems to have disappeared entirely from the town. It may be that it was frightened and made its way onto the moors where it is still hiding in terror. There are some who look with dread on such a possibility. Lest later on, it should itself become a danger, for it is evidently a fierce brute. Early this morning a large dog, a half-bred mastiff belonging to a coal merchant close to Tate Hill Pier, was found dead in the roadway opposite to its master's yard. It had been fighting and manifestly had had a savage opponent, for its throat was torn away and its belly was slit open as if with a savage claw. Later, by the kindness of the Board of Trade Inspector, I have been permitted to look over the logbook of the Demeter, which was in order up to within three days, but contained nothing of special interest except as two facts of missing men. The greatest interest, however, is with regard to the paper found in the bottle, which was today produced at the inquest, and a more strange narrative than the two between them unfold. It has not been my lot to come across. As there is no motive for concealment, I am permitted to use them and accordingly send you a rescript, simply omitting technical details of seamanship and supercargo. It almost seems as though the captain had been seized with some kind of mania before he had got well into blue water and that this had developed persistently throughout the voyage. Of course, my statement must be taken come grano, since I am writing from the dictation of a clerk of the Russian Consul, who kindly translated for me, time being short. You've heard me talking a lot recently about built bars. They're my new go-to solution for dessert or even for my breakfast so I don't have to stop and eat and I'll admit it's also been at a late night snack for me recently. These are the best protein bars I've ever tasted, plus they're low sugar, low carb, and low calorie. Today in the mail I received one of their newest flavors, the Cappuccino Puff Bar. With my love for coffee I just had to try this. So that was my breakfast this morning and when I first bit into it all I tasted was the chocolate outer coating. But then the coffee flavor started coming through stronger than I expected and it is amazing. It gives you a Cappuccino aftertaste as well, which is awesome. So now I can have my coffee in the morning and a Cappuccino Built Bar, but only for a short time because it is a limited release. So if you want to grab your Cappuccino Puff Built Bar while you can, visit WeirdDarkness.com slash Built and look in their Limited Release section. It's WeirdDarkness.com slash Built and use the promo code WeirdDarkness to get 10% off your entire purchase. They also have limited releases of a S'mores Chunk, which I've not tried yet, and a Cookies and Cream, which I have had in the past, which is also great. I'm glad they brought that one back. Again, it's WeirdDarkness.com slash Built and then use the promo code WeirdDarkness all one word to save 10% on your entire purchase. Log of the Demeter. Barna DeWittby. Rich in 18 July. Things so strange happening that I shall keep accurate note henceforth till we land. On 6 July, we finished taking in cargo, silver sand and boxes of earth. At noon set sail. East wind, fresh. Brew, five hands, two mates, cook, and myself, Captain. On 11 July, at dawn entered Bosphorus. Boarded by Turkish Customs Officers. Backsheesh, all correct. Underway at 4pm. On 12 July, through Dardanelles, more Customs Officers and flag boat of Guarding Squadron. Backsheesh again. Work of Officers thorough but quick. Won us off soon. At dark, passed into Archipelago. On 13 July, passed Cape Matipon. Brew dissatisfied about something. Seemed scared but would not speak out. On 14 July was somewhat anxious about the crew. Man all steady fellows who sailed with me before. Mate could not make out what was wrong. They only told him there was something and crossed themselves. Mate lost temper with one of them that day and struck him. Expected fierce quarrel but all was quiet. On 16 July, mate reported in the morning that one of crew, Petrovsky, is missing, could not account for it. Took larboard watch eight bells last night. Was relieved by Abramoff but did not go to bunk. Men more downcast than ever. All said they expected something of the kind but would not say more than there was something aboard. Mate getting very impatient with them. Feared some trouble ahead. On 17 July, yesterday one of the men, Ogeron, came to my cabin and in an awestruck way, confided to me that he thought there was a strange man aboard the ship. He said that in his watch he had been sheltering behind the deck house as there was a rainstorm but he saw a tall, thin man who was not like any of the crew come up the companion way and go along the deck forward and disappear. He followed cautiously but when he got to Bowes found no one and the hatchways were all closed. He was at a panic of superstitious fear and I am afraid the panic may spread. To ally it I shall today search an entire ship carefully from stem to stern. Later in the day I got together the whole crew and told them as they evidently thought there was someone in the ship we would search from stem to stern. First mate, angry, said it was folly and to yield to such foolish ideas would demoralize the men. Said he would engage to keep them out of trouble with a hand spike. I let him take the helm while the rest began thorough search all keeping abreast with lanterns we left no corner unsearched as there were only the big wooden boxes there were no odd corners where a man could hide. Men much relieved when search over and went back to work cheerfully. First mate scowled but said nothing. 22nd July. Rough weather last three days and all hands busy with sails no time to be frightened. Men seem to have forgotten their dread. Mates cheerful again and all on good terms. Praised men for work in bad weather. Past Gibraltar and out through straits. All well. 24 July. There seems some doom over this ship. Already a hand short and entering on the bay of Biscay with wild weather ahead and yet last night another man lost disappeared. Like the first he came off his watch and was not seen again. Men all in a panic of fear. Sent around Robin asking to have double watch as they fear to be alone. Mate angry. Fear there'll be some trouble as either he or the men will do some violence. 28 July.  Knocking about in sort of maelstrom in the wind of a tempest. No sleep for anyone. Men all worn out. Hardly know how to set a watch since no one fit to go on. 2nd May to volunteer to steer and watch and let men snatch a few hours sleep. Wind debating. Sees still terrific but feel them less as ship is steadier. 29 July. Another tragedy. Had single watch tonight as crew too tired to double. When morning watch came on deck you'd find no one except Steersman. Raised outcry it all came on deck. Thorough search but no one found. Are now without 2nd mate and crew in a panic. Mate and I agreed to go armed henceforth and wait for any sign of cause. 30 July. Last night rejoiced we're nearing England. Weather fine all sails set. Retired worn out. Slept soundly. Awakened by mate telling me that both man of watch and Steersman missing. Only self and mate in two hands left to work ship. 1 August. 2 days of fog and not the sail sighted. Had hoped when in the English Channel to be able to signal for help or get in somewhere. Not having power to work sails have to run before wind. Dare not lower as could not raise them again. We seem to be drifting to some terrible doom. Mate now more demoralized than either of men. His stronger nature seems to have worked inwardly against himself. Men are beyond fear. Working stoddedly and patiently with minds made up to worst. They are Russian. He Romanian. 2 August. Midnight. Woke up from few minutes sleep by hearing a cry seemingly outside my port. Could see nothing in fog. Rushed on deck and ran against mate. Tells me heard cry and ran but no sign of man on watch. One more gone. Lord help us. Mate says we must be past Straits of Dover as in a moment of fog lifting he saw North Forland just as he heard the man cry out. So we are now off in the North Sea and only God can guide us in the fog. Which seems to move with us and God seems to have deserted us. 3 August. At midnight I went to relieve the man at the wheel. When I got to it I found no one there. The wind was steady and as we ran before it there was no yawing. I dared not leave it so shouted for the mate. After a few seconds he rushed up on deck in his flannels. He looked wild eyed and haggard and I greatly fear his reason has given way. He came close to me and whispered hoarsely with his mouth to my ear as though fearing the very air might hear. It is here I know it now. On the watch last night I saw it. Like a man tall and thin and ghastly pale. It was in the bows and looking out. I crept behind it and gave it my knife but the knife went through it empty as the air. As he spoke he took his knife and drove it savagely into space. Then he went on. But it is here and I'll find it. It is in the hold perhaps in one of those boxes. I'll unscrew them one by one and see you work the helm. And with a warning look and his finger on his lip he went below. There was springing up choppy wind and I could not leave the helm.  He is mad. Stark, raving mad. It's no use my trying to help him. He can't hurt those big boxes. They're invoiced as clay and to pull them about is as harmless a thing as he can do. So here I stay and mind the helm and write these notes. I can only trust in God and wait till the fog clears. Then if I can't steer to any harbor with the wind that is I shall cut down sails and lie by and signal for help. It's nearly all over now. Just as I was beginning to hope that the mate would come out calmer for I had heard him knocking away at something in the hold and work is good for him.  His horror turned to despair and in a steady voice he said you had better come to captain before it is too late he is there I know the secret now the sea will save me from him and it is all that is left before I could say a word or move forward to seize him he sprang on the bulwark and deliberately threw himself into the sea. I suppose I know the secret too now it was this madman who got rid of the men one by one and now he has followed them himself. God help me how am I to account for all these horrors when I get to port when I get to port will that ever be for August still fog which the sunrise cannot pierce I know there is sunrise because I am a sailor why else I know not I dared not go below I dared not leave the helm so here all night I stayed and in the dimness of the night I saw it him God forgive me but the mate was right to jump overboard it was better to die like a man to die like a sailor in blue water no man can object but I am captain and I must not leave my ship but I shall baffle this fiend or monster or I shall tie my hands to the wheel when my strength begins to fail and along with them I shall tie that which he it dare not touch and then come good wind or foul I shall save my soul and my honor as captain I'm growing weaker and the night is coming on if he can look me in the face again I may not have time to act we are wrecked may have this bottle be found and those who find it may understand if not well then all men shall know that I have been true to my trust God and the blessed virgin and the saints help a poor ignorant soul trying to do his duty of course the verdict was an open one there's no evidence to induce and whether or not the man himself committed the murders there is now none to say the folk here hold almost universally that the captain is simply a hero and he is to be given a public funeral already it is arranged that his body is to be taken with a train of boats up the esk for a piece and then brought back to Tate Hill Pier and up the Abbey steps where he's to be buried in the churchyard on the cliff the owners of more than a hundred boats have already given in their names as wishing to follow him to the grave no trace has ever been found of the great dog at which there is much mourning for with public opinion in its present state he would I believe be adopted by the town tomorrow we'll see the funeral and so we'll end this one more mystery of the sea are you a member of the darkness syndicate the darkness syndicate is a private membership where you receive commercial free episodes of the Weird Darkness podcast and radio show behind the scenes video updates about future projects and events I'm working on you can share your own opinions on ideas to help me decide upon Weird Darkness contests events and merchandise you can download word search puzzles based on episodes of the podcast you can hear audio books I'm narrating before even the publishers or authors get to hear them you can also hear auditions I've submitted for other voiceover projects and get updates on the progress of those I've been cast in such as my voice acting roles as Wolverine and J. Jonah Jameson in a couple of Marvel fan series or as Green Lantern Hal Jordan in a DC fan project you get all of these benefits and more starting at only five dollars per month join the darkness syndicate at WeirdDarkness.com slash syndicate that's WeirdDarkness.com slash syndicate Lucy was very restless all night and I too could not sleep the storm was fearful and as it boomed loudly among the chimney pots made me shudder when a sharp puff came it seemed to be like a distant gun strangely enough Lucy did not wake but she got up twice and dressed herself fortunately each time I awoke in time and managed to undress her without waking her and got her back to bed it is a very strange thing this sleepwalking for as soon as her will is thwarted in any physical way her intention if there be any disappears and she yields herself almost exactly to the routine of her life early in the morning we both got up and went down to the harbor to see if anything had happened in the night there were very few people about and though the sun was bright and the air clear and fresh the big grim looking waves that seemed dark themselves because the foam that topped them was like snow forced themselves in through the narrow mouth of the harbor like a bullying man going through a crowd somehow I felt glad that Jonathan was not on the sea last night but on land but oh is he on land or sea where is he and how I'm getting fearfully anxious about him if I only knew what to do and could do anything 10 August the funeral of the poor sea captain today was most touching every boat in the harbor seemed to be there and the coffin was carried by captains all the way from Tate Hill Pier up to the churchyard Lucy came with me and we went early to our old seat whilst the cordage of boats went up the river to the viaduct and came down again we had a lovely view and saw the procession nearly all the way the poor fellow was laid to rest quite near our seat so that we stood on it when the time came and saw everything poor Lucy seemed much upset she was restless and uneasy all the time and I cannot but think that her dreaming at night is telling on her she's quite odd in one thing she will not admit to me that there is any cause for restlessness or if there be she does not understand it herself there is an additional cause and that poor old Mr. Swales was found dead this morning on our seat his neck broken he had evidently as the doctor said fallen back in his seat in some sort of fright for there was a look of fear and horror on his face that the men said made them shudder poor dear old man perhaps he had seen death with his dying eyes Lucy is so sweet and sensitive that she feels influences more acutely than other people do just now she was quite upset by a little thing which I did not much heed though I am myself very fond of animals one of the men who came up here often to look for the boats was followed by his dog the dog is always with him they're both quiet persons and I never saw the man angry nor heard the dog bark during the service the dog would not come to its master who was on the seat with us but kept a few yards off barking and howling its master spoke to it gently and then harshly and then angrily but it would neither come nor cease to make a noise it was in a sort of fury with its eyes savage and all its hairs bristling out like a cat's tail when puss is on the warpath finally the man too got angry and jumped down and kipped the dog and then took it by the scruff of the neck and half dragged and half threw it on the tombstone on which the seat is fixed the moment it touched the stone the poor thing became quiet and fell all into a tremble it did not try to get away but crouched down quivering and cowering and was in such a pitiable state of terror that I tried though without effect to comfort it Lucy was full of pity too but she did not attempt to touch the dog but looked at it in an agonized sort of way I greatly fear that she is too super sensitive in nature to go through the world without trouble she will be dreaming of this tonight I'm sure the whole agglomeration of things the ship steered into port by a dead man his attitude tied to the wheel with a crucifix and beads the touching funeral the dog now furious and now in terror will all afford material for her dreams I think it will be best for her to go to bed tired out physically so I shall take her for a long walk by the cliffs to Robin Hood's Bay and back she ought not to have much inclination for sleepwalking then thanks for listening if you like the show please share it with someone you know who loves the paranormal or strange stories true crime monsters or unsolved mysteries like you do you can email me anytime with your questions or comments at Darren at WeirdDarkness.com Darren is D-A-R-R-E-N WeirdDarkness.com is also where you can find information on any of the sponsors you heard about during the show find all of my social media listen to audiobooks I've narrated sign up for the email newsletter find other podcasts that I host including Church of the Undead visit the store for Weird Darkness merchandise and more WeirdDarkness.com is also where you can find the hope in the darkness page if you or someone you know is struggling with depression or dark thoughts also on the website if you have a true paranormal or creepy tale to tell you can click on tell your story you can find all of that and more at WeirdDarkness.com last voyage of Demeter was written by Bram Stoker I have links to both this and the full Dracula novel in the show notes Weird Darkness is a registered trademark copyright Weird Darkness and now that we're coming out of the dark I'll leave you with a little light Leviticus 17 verses 10 through 12 if any one of the house of Israel or of the strangers who sojourn among them eats any blood I will set my face against that person who eats blood and will cut him off from among his people for the life of the flesh is in the blood and I have given it for you on the altar to make atonement for your souls for it is the blood that makes atonement by the life therefore I have said to the people of Israel no person among you shall eat blood neither shall any stranger who sojourns among you eat blood and a final thought everyone knows the phenomenon of trying to hold your breath underwater how at first it's all right and you can handle it then as it gets closer and closer to the time when you must breathe how urgent the need becomes the lust and the hunger to breathe and then the panic sets in when you begin to think that you won't be able to breathe and finally when you take in air and the anxiety subsides that's what it's like to be a vampire and need blood Francis Ford Coppola and a final final thought I have never met a vampire personally but I don't know what might happen tomorrow Bella Legosi I'm Darren Marlar thanks for joining me in the weird darkness Hey weirdos I'm really excited to let you know that I am stepping into the marvel universe as the voice of J Jonah Jameson in a new animated film coming in 2024 called Spider-Man Turning Point that's right I get to play Peter Parker's jerk of a boss and not only am I a voice actor for this film I'm also an executive producer because I believe in it we even have a celebrity voice actor in the cast Mike Vaughn was the voice of Ghostface in the screen tv show well he's voicing Harry Osborn if you'd like to see some of the slick animation the storyboards character concepts the first teaser trailer for the film and more visit weirddarkness.com slash spider-man we even have an original musical score in fact you're hearing Green Goblin's theme behind me right now that's weirddarkness.com slash Spider-Man when you visit there you'll also have an opportunity to get involved if you'd like getting your name in the credits getting a social media shout out from the Spider-Man Turning Point production get an animated thank you from Spider-Man himself just for you and more I cannot wait to bring my J Jonah Jameson to you in 2024 learn more about our upcoming animated film Spider-Man Turning Point at weirddarkness.com slash Spider-Man that's weirddarkness.com slash Spider-Man not yet have you ever noticed that in just about every post-apocalyptic tv show or movie the electrical grid is gone no power at all anywhere no places to plug in a radio to get news and you can forget about charging your mobile devices or relaxing in an air conditioned house or apartment we rely on electrical power did you know that the power grid we are currently surviving off of was designed in the 1800s it's so fragile that in 2003 a tree branch hit a power line in Ohio and it shut down 21 power plants and close to 100 people died because of it and it's not just natural disasters in january a power station in north carolina was damaged by gunfire marking the third time it happened the terrifying truth is that our national security experts are warning us that our aging power grid is now more vulnerable than ever and these attacks just raise a new level of threat those post-apocalyptic tv and film scenarios could easily turn from fiction to fact imagine a blackout lasting not days but weeks or even months your life would be frozen in time at the moment the power fails lights all over the country would go out throwing people into total darkness that's why having your own personal source of solar power is more important than ever with the patriot power generator you get a solar generator that doesn't install into your house because it's portable you can take it with you wherever you go even use it indoors and it's powerful enough for your phones medical devices even your refrigerator right now you can go to four patriots dot com that's the number four patriots dot com and use the code weird to get 10% of your first purchase on anything on the website including the lifesaving patriot power generator you'll also get their famous guarantee for an entire year after your order plus free shipping on orders over 97 dollars and the reason i approached four patriots to be a sponsor a portion of every sale is donated to charities who support our veterans and their families prepare for the future go to four patriots dot com today and use the code weird to get 10% off that's the number four patriots dot com promo code weird and ensure you will survive the future hey weirdos be sure to click the like button and subscribe to this channel and click the notification bell so you don't miss future videos i post videos seven days a week and while you're at it spread the darkness by sharing this video with someone you know who loves all things strange and macabre if you want to listen to the podcast you can find it at weird darkness dot com slash listen


And then there's this term called the first pass effect, which means that when a medication is administered by the oral route and it passes through the liver, it is biotransformed or metabolized to such a high degree that there's not enough drug concentration left in the bloodstream after it goes through the liver to have the desired effect that we're trying to achieve with the medication. And so that only happens for oral medications. And so if we know that medications have a high first pass effect, then usually we have to think about other routes of administration besides an enteral route or a GI route that will allow to kind of bypass this first pass effect where the liver takes away some of that medication effectiveness.


Hey everyone, it's Gabrielle over here today at Oxford Toyota. I have Steven coffee here with me. Now Steven's actually going to tell you guys about a service special we've going on for the rest of July and for the month of August. So what is that? Actually if you come in see us we got a smooth driving package. Maybe you can squeeze one last trip in for school starts. It's a synthetic oil change up to five quarts. We're gonna throw in a rotating balance for a brake inspection and do a four-wheel alignment. You're looking at $149.95. We've got some definite savings there. So give us a call getting a point to schedule it. We'll get you taken care of. Alright sounds good. I'll have all our contact information below. Thanks guys. We'll see y'all soon. Bye.


I have no questions for you. No, I do actually. Darren base posted something. Are you guys signing him or is that a practice squad? Yeah, we're out into the practice squad. As far as the injuries, do you have any decision there? Getting close. We don't have to make it right now. Things are turning in the right direction for Josh, but again, a lot of things are fluid. We got to weigh everything as everybody gets back in here and we practice and then obviously going through tomorrow. See what the health of the team looks like going into the game week. You said on Monday that you felt like maybe you'd have more decisions on Gage and Davidson by midweek last week. Is there a lot more clarity there now? Yeah, I think we feel good about how they're progressing, but let's see how they look at practice, but they'll be out there practicing today. What did you learn the self scout was this week? I think you just got to see how we're trending offensively. You look at everything. It's a good time to reflect after five games, see how we've evolved, how teams are playing us, look at our personnel usage really in all three phases, where we have guys, especially in special teams, our coverage units, and then defensively, how teams are attacking us, what we're calling, how we're using our personnel. So it's a really good time to be objective, have the pressure of getting ready for a game a week and game planning so you can really take a hard look at yourself. We thought it was very productive. For you as a self scout different as a head coach versus when you were really just off the square? We're just watching defense. Is there any other things that have changed for you? Absolutely, that's a good question. You've got to look at it in your mind first, because you're so involved with the offense, but you've got to be the head coach of the whole team. So for things you look at as a play caller offensively, but then it's the whole team, and our staff does a good job. I talk all the time with Dean and Marquise, and we look at things, but you do, you have to take it a whole objective of the entire team. A lot of it is just making sure we're looking at everything the right way. Personnel uses what we're playing, when you're making calls, you're responsible for everything. So that's what I signed up for, and thankful I got this job. I want to go back to something you said on, I guess it was Monday, about with the bi-week and now the rest of the guys' heads, these rookies are about to play a whole college season, and I was just curious what you really broke down with them during the bi-week in terms of, hey, this is more than what you're used to, so how did you just prepare them immensely for what's ahead? A lot of it is. It's continuing education, making sure that they take care of themselves, mentally and physically. It's a long year, I always felt for these rookies, it's the longest year they'll have in their personal career, because as soon as their season ends, you jump right in, and a lot of these guys jump into the All-Star game, so they may practice for the All-Star game, and then they all have places they go where their agents have deals where they work out certain locations, and they prep for, they didn't have a combat this year, but they prep for your pro-days, and then you're just constantly nitpicked as you go through the draft evaluation, and it's just different for them. And you get all the way up until the draft, and then you go to a new environment, and then it's kind of like drinking from a fire hydrant, and then you have a couple weeks before you start camp, and it's just a really long year for those guys, and you try to prepare them mentally, but a lot of things, you have to experiment first time, so we try to do a good job educating them, making sure they understand where there are season, how long the season is, to pick the brains of the veterans, and then everybody, we try to support them, but yeah, we got 12 games. It is a full season left ahead. With some of these guys, I mean, they did play well against two weeks ago against the Jets. I mean, how much do you kind of constantly think about, okay, we saw these guys do well, it's maybe time to ramp up some reps with them? Yeah, it just depends. It also, who's up? A lot of these guys, we feel, have earned reps, but there's some good players that maybe have been out because of injuries or other issues, and they come back. It's a good problem to have when you've got to make tough decisions on game day, or who's going to get the majority of the snaps, or as you're playing on the game plan. So there's good problems we feel good about. Again, a lot of these guys got a lot of snaps in the preseason, and we think that's paying off for us, and hopefully these guys continue to produce on game day. That's ultimately what matters. I've covered Bates before. He's a really good special teams player. Was that part of the reason why you... Yeah, I've known Darren and known Darren a long time. Another Memphis guy. So we've been with him in Tennessee. He went to high school with my brother. Excited Darren's here to see if he can help us.  Yeah, gotten better week to week, and that's the whole challenge in his business. Can you improve week to week with obviously as a team, and we feel like it's in the right direction, but it's a long season. You just don't want to have these peaks and valleys. You want to constantly be building tough matchups every week. My aim is going to present a number of challenges that are a little bit different than what we've seen, and we've got to be ready to roll because I know they'll be ready. You guys have both seen each other early in the year. Do you think that has any pluses, minuses given that you've already played them? I like a division opponent.  You get a feel for them. You have a little better feel for their personnel, but the teams, like I said, we're a completely different team than we were when we went down there, and so are they. That's how I kind of compare it to like, hey, you played somebody early in the year, and you're a division opponent, you play them a little bit later. This is maybe very protecting many practice squad players this year. I was just wondering the philosophy of choosing not to do that versus doing it. Well, I mean, there's a lot of different things, and I won't go full-fledged into our strategy, but, you know, it's a good mechanism if you want to use it. It's not that you see a lot of people poaching off practice squads. So, like I said, if you need it, you got it. But again, every team has the opportunity to use how they see fit. We've used it the way we've seen fit so far, and we feel pretty good about it. I know that you asked you this two or three weeks ago about, like, practice squad strategies and using kind of as long-term trials. Do you think that all the new practice squad rules have kind of made it, like, that whole mechanism way more strategic than it was even five years ago, for how you used different things in different ways? Absolutely, and I like it. I think it allows you some creativity. It allows you to invest a little more in player development, and then ultimately, like you said, if you want to protect guys, and again, it's protecting them during the week, but if you choose to go poach guys off other teams, you know, you get them on your active roster for a few weeks after that. So, there's a lot of different mechanisms to claiming. I like the strategy of that. I think it allows you to be more creative so it's not so cookie cutter. Do you do anything good with your bi-week? I try to be productive. I try to be a good husband and dad. It was a beautiful weekend here in Atlanta, so it was good. I feel good, got some work done, and also got my most important job. I was able to be a dad and a husband for a couple of days. Not too bad. It was more, you know, pitching in with the kids and doing my part there. What'd you do? I slept a lot, man. I slept a lot. I liked a bit, you know. That's good. That's a great weekend. I'll take it. I'll take 50 more of those. Yeah. Good. Good to see y'all.


Yes, but I apologize for calling this time as president yesterday Dean and I mentioned a paragraph on non-proliferation to you I'm not sure you had a chance to See it today. I thought if you did you could tell us we know what you want Well, I thought he was going to write me. He told me it's preparing me a memo and I never could see it Explaining it going into each other Discussing it. That's what Rusk said. Well, I Have an animal you misunderstood because I don't think I'll try to get I thought that that's what he said Now if he doesn't intend to send anything else, I'll go back on this I have it right in front of each nuclear weapons state party to this tree undertakes not to transfer nuclear weapons Our other nuclear explosives directly and directly to the non nuclear weapons state or group of states either individually or Or by virtue of its membership in the military alliance Our group of states now that's the key, Mr. President What that says to you is that that this proposes we restrict transfer of ownership of the warhead itself and This would still allow us to say to the Germans That if you want to buy in to some form a collective ownership of the launch vehicle a missile or an airplane You can do that, but you can't buy into collective ownership of the warhead itself Which of course they never could have anyhow because we don't have authority under the law to to transfer ownership of the warhead But no, but we're heading didn't an LF contemplate that we would get amendment back No, sir, it did not not not not with respect to ownership not to relinquish its control over nuclear weapons or other nuclear explosives Well, that's what that's a low now Not in any way to assist encourage or induce any non nuclear weapons state To manufacture otherwise acquire nuclear weapons other than the most they keep the key President that one you read at first which says that you can't transfer directly or indirectly to a single nation or collective group of nations Ownership in the warhead Germans will will grumble about it and I think there's some in state who opposed this that particular language was drafted by Dean himself Bob Bowie For example, I think opposes it Dean favors it. I favor it What will Russians do it? We're not sure they'll accept it. It is not the language that Gromyko proposed but it We think there's a reasonable chance they'll either accept this or suggest some relatively minor modification of it


Brewers make the postseason just the fifth time in their history. They're one of seven teams to have never won a World Series, and they've only been to one. And that was back in 1982. Does this team have the magic? They certainly are playing like they do. They have the depth, especially offensively. And you've seen Kristen Yeliz emerge as the MVP and the star, another great Marlin traded, by the way.  You saw Jesus Aguilar emerge as a true power threat. You know, it boosted bronze play to want to be a part of it. And you saw them develop one of the best bullpins in all of baseball. So it's fun to watch. And you're awaiting as a fan for them to fail because they've had epic failures to second half as a team. But right now, they're a top dog, and they're playing, and they're confident at the right time. I'm really, really happy for this organization. Really proud. I know a bunch of guys over there. Enjoy all that middle of it. For sure, man. Enjoy that champagne. Bob Uker. There he is. Bob. Look at like he came from fishing. He came from fishing, Bob. But how amazing is that, man? I'm going to piggyback on you, Don Trill. And I'm just going to jump on the bullpen bandwagon right now. Listen, in August, when the team was 13 and 13, the bullpen was pitching to a 6ERA. In the month of September, they are now 15 and 7. The bullpen is pitching to now a 2ERA. That is a huge movement going forward. That was absolutely the backbone of their squad earlier in the season. And now, all of a sudden, they figured out late again. And if you want to win big games like these guys are playing right now, you've got to have shut down innings, and that's what they're getting. Well, when they acquired Lorenzo Cain and yell at you, thought, OK, they're improving things with the bullpen. They're still one of the top in the top five and hitting home runs in all of baseball. But this is a very different Milwaukee vibe than the ones who had leads at the All-Star Brake, sizable division, whatever, and faded.  You saw Sassine, he's got 14-15 wins. You did not see that coming. So they took a lot of pressure off that starting rotation, told them, hey, you don't have to be great. This be solid. Get us a lead, and we'll get to the bullpen and we'll shut it down. That's our formula. They also can hit the ball out of the ballpark with the best of them. You cannot sit and have lulls to their lineup. You have to execute pitches. They hit for power to all fields, and they have right-handed and left-handed power. This is a fun team to watch, and I tell you what, the Brew crew gives that stadium rock. You see the energy up there, so this is the first time in a long time for them to go in the postseason. I expect them to do some damage. At a chance now, just, well, tied for the division, officially, depending upon what the Cubs do, if the Cubs lose against the Pirates at home, then Milwaukee will catapult into first place.


Part two. The whole sea, these pipes here, they are actually to alter the oxygen that is calorific and that increases the temperature of the carbonizing temperatures, which results to affecting the quality of pH of the output, which is a big thing. So, once we have more of the biochips in this, we use it as a fertilizer base, and we have special formula, special nutrient formulas that we add to it, making a great fertilizer that we brand saffi saffi.


Hey, four things I want to share with you about boundaries that I've learned over the years, many more things, but here's four. First of all, boundaries are not about protection from, but they are about protecting you from within. Part of respecting others is respecting their boundaries, but part of respecting yourself is creating and building your own boundaries. Secondly, boundaries aren't based in defensive mode. They may be interpreted as that, but boundaries are to do with self-love rather than dislike or hatred or aggression towards someone else. Boundaries are an act of self-love. Thirdly, boundaries are about self-respect. They're not about someone else's respect for you. Boundaries are you respecting you. They are not an attempt to try and get someone else to respect you. And fourthly and finally, boundaries are about empowering you. They're not about controlling someone else. Again, others will interpret your boundary as an attempt to adjust and edit and control their behavior. But really, a boundary is about empowering you much more than it is about controlling anyone else because we all know you cannot control anyone else except you. So a boundary is a huge gift of self-love to yourself.


The deaths that have occurred on our roads this year of motorcyclists have been across the spectrum of experience, age, occupation. 21 people a year should be having dinner tonight with their family and friends and that's just not going to happen. The figures are stark. The figures are stark. 70% of the motorcycle fatalities are motorcyclists at fault. Travelling towards me at 178 kilometres an hour. Speed limit up here is only 50, you're doing 109. Riding a motorcyclist at night with a bike helmet on as in a push bike helmet on with a pillion passenger, 18 year old pillion passenger, that's a disaster waiting to happen. Someone's going to die there. Why on earth would you get on the back of a bike if you had that drunk? If I had a reading as high as his I'd be in hospital, I'd guarantee and so would you. I plead with you to enjoy yourselves but at the same time you must, you must ride within your abilities and comply with our road rules.