good morning to all of you and welcome to this session of course now last class we are discussing that what will happen if the fluid flows through a convex corner or convex smooth surface let us see that what happens now if we consider similarly a type of oblique shock and you just draw the diagram that v1 is there now it will be deflected as per the geometry this surface is a convex surface this will be the v2 this line is parallel to this and these are the normal and the tangential velocities normal and the tangential velocity now according to our earlier considerations along the shock the property does not change no net force acting along this direction so vs1 is vs2 now for the same vs1 and vs2 the geometry shows clearly vn2 is more than vn1 see that mathematically also you can see that if you consider this angle as beta which was the oblique which was the oblique shock wave angle then the delta is this one so this angle is beta plus delta so this is the angle here beta plus delta because this line is the parallel to the shock so this angle is beta plus delta so vn1 is then what will be that vs1 tan beta where vn2 is vs2 tan beta plus delta and vs2 and vs1 are same so therefore from geometry and from trigonometric relations we see that vn2 that means vn2 is greater than vn1 so this cannot be in a shock so shock is not possible so therefore shock is not possible shock is not possible and therefore this case there will be an expansion wave or expansion flow with expansion waves this we will discuss so before coming to the discussion on expansion waves what we will do first we will make some mathematical analysis let us first do a mathematical analysis like this it is that it like this a plate type of thing let us make a slight change in the orientation theta d theta what happens to the flow condition let us consider first oblique this shock may be oblique shock or a mac wave oblique shock wave just we are now making a generalized thing that there will be a wave which may be mac wave which may be shock wave for that now what we are doing we are making a infinite small turning of the flow that means flow is turned by an infinite so that means the flow is v1 which has the component vs1 and vn1 is turned through an infinite small amount d theta and this value is v1 plus let us consider dvsmall change okay and this is the normal component which is vn1 plus dvn1 and this is the vs1 plus dvsmall change now let us first find out with this small change in this direction what will be the changes in the flow properties now for that we make a representations with infinite small changes in the quantity that velocity quantity similarly the pressure p1 let the pressure p just to represent by p p plus dp so temperature let us consider t here so this will be t plus dt and the density is rho which will be rho plus d rho that means all infinite small change now let us find out whether this changes are positive or negative and here this change on theta in this direction we will consider as a positive change in theta which I will explain earlier how it is known as positive and all this thing at first we consider this type of infinite small change in this initially it was flat so this make a change in the shape that means this is a corner type of thing so where there is a wave and this wave changes the flow turns the flow according to this by an angle d theta that means if you just this is make this is the original direction this is this angle is d theta this angle with the original direction of the velocity now if this be the thing let us find out first the continuity equation so continuity equation we can write that rho vn1 is equal to rho plus d rho into vn1 now we will not write any one we will make vn because here we are already making with the infinite small change so therefore we will consider all as vn vn plus dvn so one I will not use though I have written it in the diagram please change it vn dvn and neglecting the higher order term the product of the higher order term for example d rho dvn we get this equation rho dvn is it plus n that is v dvn that is vn d rho is 0 this we can get by simply telling rho vn is constant making a logarithmic differentiation or simply differentiation rho dvn plus v n d rho is 0 so this is one equation from the differential form from the continuity very simple then if you write the momentum equation with respect to an infinite small control volume here then the momentum equation we said p momentum equation means the momentum theorem in the direction this along this normal direction that means the net rate of momentum a flux normal momentum a flux is equal to the net force in the normal direction that means here area cancels out for both the term both the sides here also it will do like that p minus sorry p plus dp this side is p plus dp this side is p net force is equal to rho vn well into vn plus dvn plus dvn plus dvn plus dvn plus dvn plus dvn minus vn well so therefore this cancels so therefore we get dp is equal to rho vn dvn dp what we get here from here minus dp is equal to rho vn rho vn dvn sorry vn dvn rho vn dvn clear rho vn dvn now if I here what we do if I substitute the dvn from here that means this dvn if I write in terms of minus dp the dvn is minus dp rho by vn then what we get if we substitute dvn here dvn is minus dp by rho vn minus dp by rho vn so vn vn square so you will get a very good relationship that vn square is dp by d rho dp by d rho or vn is equal to dp by d rho clear just dvn is substituted here minus dp by rho vn now since this change is infinite small we can calculate the process to be free from dissipation and adiabatic so that this can be considered as an isentropic condition that means this can be written as and it can be shown that this way the process is isentropic also del p del rho at constant so therefore this expression is the expression for sound velocity at this state so therefore in this case the normal velocity is sound which means that a infinite small turning due to this infinite small disturbance type of thing infinite small turning infinite small angle of turning d theta makes a wave which is nothing but the mac wave vn is equal to a that means this can be shown this way now that this is simply a mac wave that means if this be the v1 then this is the v1 then the normal component of velocity this is the sorry this is the I am sorry this be the v1 this will look nice this normal component of velocity vn1 simply you write v0 and vn is equal to a and therefore this angle is the mac angle this angle this angle that means this angle means which angle that means this angle well this angle if this is alpha so alpha is what tan alpha is tan alpha is tan is this divided by this so sin alpha not tan alpha I am sorry sin alpha is I am sorry sin alpha is this divided by this that means a by v that is is equal to 1 by mac number mac m so therefore this is the this angle alpha is 1 by m sin inverse that means alpha is sin inverse 1 by m that means this small divergence we will call we will find we will ultimately make a mac wave we will create a mac wave and this will be inclined with this wave by an angle which is the mac angle now next is we do it well after that we write the equality of this equality of this let me do it here otherwise you will be in little trouble that this vs1 is equal to vs2 and vs1 is what now let us consider v and this is v plus dv so therefore if we write this we can write vs1 is vs2 so that means v cos alpha now I define this as alpha cos alpha v cos alpha is equal to v cos alpha this is alpha cos alpha v cos alpha is equal to v cos alpha is equal to v plus dv that means v plus dv and this angle then changes cos alpha plus cos of not plus minus alpha sorry cos alpha minus d theta this angle changes because this is alpha that means this is this is the alpha and this has been changed by d theta so therefore this angle is alpha minus d theta earlier we did it so therefore we can write that equality of this v plus dv cos alpha minus d theta is equal to v cos of alpha well again I draw that figure for you because I understand that you are in trouble sorry this is small angle theta I am just d theta I am just exaggerated it let us consider this that this is the sorry this is the v1 v1 and this is the okay this is the v1 and this is the alpha 1 so therefore this is the alpha 1 okay so sorry I have done some mistake sorry rather I have done some mistake that is why there is a problem I am sorry let we have this thing okay this is d theta so let us make because this is a positive change so therefore we make a thing like this okay as I did earlier so this is this so now this is very clear so this angle is okay this angle is alpha this angle I made a alpha this is the wave and this angle is this angle alpha so therefore this will be this v1 this is vn1 so this this is vn1 and simply v so this will be v cos alpha then what will happen here this will change here so this will be going to this direction this is v plus dv well so this has also a this is vn2 this is vn1 this is vn2 this is again I am writing so this is what is that this is v plus dv now this angle this angle this angle is this is alpha minus d theta clear this angle because this is alpha and this is d theta so therefore this angle is alpha minus d theta which is equal to this angle the same thing now I have to be little fast that now if I write v plus dv equality of the tangential component or parallel component cos of alpha minus d theta is v cos alpha now we have to be little bit fast now let us do it v plus dv now cos alpha sorry cos alpha minus d theta is cos alpha cos d theta minus sin alpha sin d theta is equal to v cos alpha now make the left hand side now v cos alpha cos d theta now for small d theta cos d theta one so v cos alpha now if I multiply with this v sin alpha sin d theta is d theta is d theta v sin alpha d theta plus dv cos alpha because cos d theta is one minus dv sin alpha d theta so dv d theta product of two small term sin d theta is very small sin d theta means d theta dv this is neglected so neglecting the higher order term the product of these two we get what v sin alpha minus v sin alpha d theta plus dv cos alpha is equal to 0 this is a very interesting result we get from which we can write dv by v is equal to minus tan alpha into d theta minus tan alpha into d theta dv by v now tan alpha can be written as minus d theta root over m square minus 1 why because we know that alpha is sin inverse 1 by m for such small turning the small angle d theta so that sin alpha is simple trigonometry tan alpha is 1 minus root over m square minus 1 dv by v sin alpha by cos alpha that is tan alpha dv by v tan alpha d theta which one that will be this is minus this is minus this is plus this minus dv by this oh then that will be plus cos a cos b to plus oh sorry I am sorry you are very correct cos a cos b will vary this is the final result that I know yes cos a minus b is cos a cos b sorry plus sin a sin b the minus will come if it is sin a minus b or cos a plus b correct very correct so there will be minus d theta by root over I am happy is very good dv by v is equal to minus d theta by m square now we go to the well energy equation now we go to the energy equation I am in little we know that energy equation we wrote that 2 gamma that is h 1 c p t 1 that is written as gamma by gamma minus 1 into p by rho plus v square why 2 because v square by 2 I am just I am writing this thing it is v square by 2 gamma by gamma minus 1 is what c p into r c p is r gamma gamma minus 1 that means it is c p by r and p is equal to rho r t so therefore it comes from what it comes from c p into t but 2 c p t this is c p into t gamma r by gamma minus 1 r t is p by rho and v square by 2 so I am multiplying 2 on both the sides that means this is the static enthalpy plus the kinetic energy we discussed is earlier that is why I am writing straight because here I do not want to repeat it again now for an infinite small change the quantities are shown like this then rho plus d rho yes plus p now if you do it now you again you see that 2 gamma by gamma minus 1 into p by rho plus v square is equal to this side 2 by gamma minus 1 now you take p by rho common that means you take p from the denominator and rho from the numerator if you take p from the denominator this will be p plus d p to the p 1 plus d p by p to the power 1 that is 1 plus d p by p that means 1 plus d p by p so therefore 1 plus d p by p I am writing in one shot and rho if you take 1 plus d rho by rho to the power minus 1 and if you make the binomial theorem and second order terms you neglect then it becomes is equal to 1 minus d rho by rho only here this will be multiplied so that finally we can write 1 plus d p by p which is there already p common d p so denominator contribution is that 1 plus d rho by rho to the power minus 1 will be multiplied for which only one term will come 1 plus d p by p minus d rho by rho all right sorry this is in the first bracket I get plus v square plus 2 v d v I just again neglect the higher order term so v square v square will be cancelled so this thing will be cancelled 2 gamma by gamma minus 1 p by rho 1 will not be there so therefore 2 gamma by gamma minus 1 p by rho d p by p minus d rho by rho will become equals to 0 so ultimately will become equals to 2 v d v so ultimately we can make this one like this 2 gamma by I can write it p by rho into d p by p minus d rho by rho into d p by p minus d rho by rho d rho by rho is minus 2 v d v if there is any mistake you tell me this is ok now what we can do we use a formula that d p by d rho we know that d p by d rho is equal to for an isentropic process because already we have taken the for the process the entropy is constant and that becomes equal to a square so we will use that if you use this that and what you do this gamma p by rho already you use as s square gamma p by rho so therefore you can write 2 gamma gamma p by rho s square so just see that what I am doing this I am using and d p by p I am taking common then what is there so d p by p that is p by rho d rho by d p and if we use this equation this will be ultimately 1 by 1 minus gamma is equal to minus 2 v d v what I am doing gamma p by rho is s square d p by p I am taking common that means this will be d rho by d p into p by rho and d rho by d p into p by rho is 1 by 1 minus gamma so if you equate this 2 then you will find this then gamma minus 1 in gamma minus 1 will cancel so therefore from here we get straight away d m d p by p we get straight away that d p by p d p by p is what d p by p now gamma minus 1 and gamma minus 1 will change so therefore gamma only gamma that means 2 2 calcins minus v d v by gamma that gamma will not be there so gamma minus 1 so that gamma so only gamma v d v by no gamma will be there 1 minus 1 by gamma 2 a square rho there gamma will not come gamma p by rho is a square so this gamma will not come so therefore gamma v d v divided by a square that means d p by p is equal to minus gamma v square if I multiplied gamma by a square v gamma m square sorry this 1 d v by v gamma minus sorry this is gamma m square because I multiplied with v v square by a square is m square now we know the value of d v by v so d v by v we have already found out just I see d v by v is equal to minus d theta by root over m square minus 1 so therefore we get d p by p is equal to d v by v m square d v by v is again I see minus d theta root over m square so minus minus can sense so it will be gamma m square root over m square minus 1 into d theta so now I just I will just multiply gamma make it like this d v by v d v by v well so this is d v by v is this one and I get d p by p is this one from the energy equation now after that I will do for another same thing I will do for another same thing is the mach number now mach number you can define in terms of its square mach number square is v square by a square because a unnecessarily contains under root of that that is why we are now if we consider a is gamma a square is gamma p by rho then this will be gamma p because a square I am writing gamma p by rho that we know already we wrote so therefore if we make a differentiation logarithmic differentiation then 2 m d m by m is equal to 2 v 2 m no 2 d m by m this will be 2 v 2 d v by v 2 d v by v I am taking the logarithmic 2 d m by m ok 2 m that means 2 l n m d m by m is equal to 2 d v by v plus d rho by rho minus d p by v this will be 2 v 2 d v by v I am taking this is ok 2 d m by m is equal to 2 d v by v d v now you just substitute these values but before that you have to know d rho by rho d rho by rho is another one which you have to find out now before that we find out what is d rho by rho how you will calculate d rho by rho it is very simple we have considered a isentropic flow p rho to the power gamma square so take a logarithmic differentiation so d p by p is the plus or there we can take that side minus gamma d rho by rho minus d p by p plus gamma d rho by rho is 0 minus so d rho by rho is minus 1 by gamma d p by p and that it is alright d p by p is plus gamma d rho by rho is 0 ok p rho to the power gamma is constant for the isentropic flow for the isentropic flow p rho to the power gamma is equal to constant we are considering the flow where the entropy does not change that is the isentropic flow so therefore d p by p plus gamma d rho by rho is 0 minus gamma d rho by rho so minus 1 by gamma no no p p into rho to the power gamma is constant is the p rho to the power minus gamma exactly you are correct p rho to the power minus gamma p by rho to the power gamma is constant I am sorry so therefore it will be then plus plus p rho to the power minus gamma I am sorry p by rho to the power gamma sorry sorry p by rho to the power gamma is constant p by rho to the power gamma is constant. So, d p by p is equal to gamma d rho by rho. So, d p by d rho by rho is 1 by gamma d p by p. What is d p by p? d p by p 1 by gamma m square that means that gamma will not be there. So, therefore very good d rho by rho will be m square by root over m square minus 1 very good I am sorry p v to the power gamma is constant, but it is p by rho to the power gamma is constant I am extremely sorry this will be p into rho to the power minus gamma constant very correct p by rho to the power gamma constant. So, therefore there will be a minus sign m square root over m square.   So, if you clear this thing you will get this is a very standard expression 1 plus gamma minus 1 by 2 m square this is a very standard expression minus d theta by this is minus d theta I am writing minus here m square minus 1.    So, this is plus d theta this is plus d theta. So, minus d theta I write here which I write earlier root over m square minus 1 now you see the beauty is that we made a change like this this is the concept now where the way was like this which changes change the thing like this this is d theta now this d theta is positive in the this is considered to be positive in this direction this changes is positive this is because this makes a change in a way that it makes this velocity that there is a reduction in the tangential in the normal component of velocity or we find out that p 2 is more than p 1 that here we will see that if we consider this d theta as a positive one then we see that the positive d theta. That means in this direction a change will make the velocity d v less than 0 if here if d theta is greater than 0 then what happens d v less than 0 d theta greater than 0 d v d p d p greater than 0 d theta greater than 0 d p d theta greater than 0 d rho greater than 0 and d theta greater than 0 d m less than 0 this is typically the shock wave that means where we can positive change in the angle here the velocity decreases pressure increases rho increases and magnetic but the other way if d theta is less than 0 then d v will be greater than 0 and d p will be less than 0 d rho will be less than 0 and d m will be greater than 0 that means the flow will accelerate with a change in a reduction in pressure and density and with a flow will accelerate that means with a increase in velocity with the increase in Mach number also with a reduction in pressure and the reduction in density and this is known as expansion waves or expansion flow that I will explain now I will show you is there anything is okay now what happens I will just tell you now if you consider a change like this now any finite change a now you think a change that is a finite change in the angle that means a concave corner or a concave wedge type of thing concave a surface like this that is a concave change then this can be considered as sum of many infinite small changes and what happens a number of waves will be generated where the Mach will be changes and these waves will be ultimately converging and we will give you a finally converging wave that is the converging wave that is the shock wave that is the oblique shock oblique shock wave this nature will be like this but if we have a thing like this then what will happen this will start somewhere here that may be for example here not it may not be very sharp then what will happen this type of thing will give a diverging type of wave and this wave is known as these are known as these are the this is just for drawing I am showing this is the diverging wave this is known as expansion wave expansion wave this is expansion wave this will never convert this will never convert expansion wave and within this the flow takes place like this ultimately goes on diver like this and throughout this expansion wave region the flow is remains isentropic the entropy change will be very less and this flow is known as Prandtl Meyer flow Prandtl Meyer flow this flow is known as E me Prandtl Meyer flow E me why Prandtl Meyer flow this flow is known as Prandtl Meyer flow this is an now for example if this is also like this but if this is a sharp one and this is a sharp one this I have shown also then it will give a converged oblique shock but this will give a this type of fan type of thing so that is why this is known as this is known as expansion fan expansion fan so this is the thing that means if this is a sharp corner like this is a convex all these oblique shock waves march one another and gives rise to a single oblique shock wave across which there will be an increase in pressure increase in density and a decrease in velocity and Mach number and just the opposite will be there in the case of a concave surface like this when the flow takes place there will be a series of expansion waves and which will be diverging in nature and create a fan like thing and if we think of a sharp corner then they will make a fan like that this will be attached here and throughout and the same thing will happen I will explain afterwards in case of a flow fluid at some pressure P higher than P atmospheric pressure if this valve is opened or the diaphragm is raptured then the flow will commence then the flow will commence and the expansion will go like that and you will see that there will be a zone of expansion wave that will be created here so that I will explain afterwards so this is the picture by which an expansion wave is created now what we will do we will now calculate this d theta Mach number relationships what is that now what is most important is that d m by m d theta let me write that d m by m is 1 plus gamma minus 1 by 2 m square into minus d theta divided by root over m square minus 1 now for an expansion wave I now do not give this minus d theta sign rather rather first of all let me give this minus d theta sign then I will tell you now if we integrate this with respect to m that means that is m square root over m square minus 1 by m root over m square minus 1 by m into 1 plus gamma minus 1 by 2 m square d m if we integrate this this is a 1 plus gamma minus 1 m square whole to the power minus 1 yes whole to the power minus 1 d m whole to the power minus 1 d m rather I must write in a different fashion root integration root over m square minus 1 divided by your correct gamma minus 1 by 2 m square into d m by m I think this is ok now if I calculate from 1 theta 1 to theta 2 and we can calculate from m 1 we can integrate from m 1 to m 2 so we can get a relationship that what should for a given change in the angle what should be the change in the mach number so we can make an integration now better giving any limits because we do not know the limits we better integrate it simply by considering that it indefinite integral we do not take first of all this minus sign because it is the case where we only consider the concave surface so we take theta is equal to integration of this root over simple integration of this root over 1 plus gamma minus 1 by 2 m square d m by m now if you make this different indefinite integral you have to impose some constant some constant because the integration constant will be there you have to impose some condition or the constant instead of impose some condition to eliminate the constant of integration then we consider at m is equal to 1 theta is equal to 0 arbitrary that means we consider that when the flow is sonic that m is equal to 1 then theta is equal to 0 but this thing I will explain after what that when m is equal to 1 what could have been the value of theta that I will tell after what that means now we put a condition that at m is equal to 1 when the m is equal to 1 then theta is equal to 0 if we put a condition and integrate this then you will get a relationship that I will now write to you that integration I am not doing that can be done by making integration by parts and just I am giving you the result now theta is root over gamma plus 1 by gamma minus 1 tan inverse root over gamma minus 1 by gamma plus 1 m square minus 1 minus tan inverse root over m square minus 1 now this is the expression where theta is 0 arbitrarily when m is equal to 1 this I will be discussing after what when specially I will solve the problem this arbitrary nays will be understood that how it is taken care of let us first for the sake of mathematics consider some arbitrary condition that theta that is the turning is 0 when m is equal to 1 just mathematically I get now here another very interesting observation is that when m tends to infinity then what is the value of this turning this will not infinity because tan inverse infinity is pi by 2 tan inverse theta limit as theta tends to pi by 2 is infinity okay no not sorry sorry sorry sorry limit tan theta limit tan theta tan inverse infinity is equal to pi by 2 I am sorry tan pi by 2 is infinity so therefore tan inverse infinity is pi by 2 that means limiting value that is the limiting value I wanted to write that when theta tends to pi by 2 I wrote correctly limit tan inverse theta theta limit tan inverse theta theta tends to pi by 2 it is alright so this is tan inverse infinity is pi by 2 so therefore theta is this is the trigonometric relationship because tan pi by 2 is what that sin pi by 2 cos pi by 2 cos pi by 2 is sin pi by 2 1 cos pi by 2 it is okay means tan pi by 2 is infinity okay because sin pi by 2 1 cos pi by 2 is 0 so therefore it is infinity so therefore this will be root over gamma plus 1 divided by gamma minus 1 into pi by 2 minus pi by 2 that means is equal to pi by 2 into root over gamma plus 1 by gamma minus 1 and this value for gamma is equal to 1.4 for air this theta max or the limiting value you can take max because m tends to infinity is 130.5 degree okay now what happens is that 130.5 degree that means if the turning angle is more than that what happens I just show you if the turning angle is more than that let us consider a turning like this that this is the turning which is equal to theta max let this is theta max so a flow which is taking place this way is turned like this and they may go to this the pressure may fall to zero and if there is a turning which is like this then there may be a pressure zone which here is in this zone the pressure is vacuum pressure vacuum pressure so this zone is actually the vacuum pressure zone or the zero pressure zone that means if the turning angle is more than this maximum angle but we are not interested in this type of situation now so only this turning angle this concept is there now I will tell you we will solve some problem then only these things will be made more clear otherwise it will be difficult just let me do these things where is the problems yes let us make let us solve some problems now example one air flows at m1 is equal to 1.8 with a pressure of 90 kilopascals and a temperature of 15 degrees Celsius down a white channel the upper wall of this channel turns through an angle 5 degree away from the flow leading to the generation of an expansion wave leading to the generation of an expansion wave find the pressure Mach number and temperature behind this expansion wave find the pressure Mach number and temperature behind this expansion wave now what is this let us see the problem problem is like this air flows at Mach number 0.8 with a pressure of 90 kilopascals and this down a white channel the upper heel of the channel that means this the upper wall of this channel turns through an angle of 5 degree so therefore what happens there is a this type of flow takes place that means the flow is taking place flow changes like this the flow changes its direction like this okay now here the Mach number is 1.8 well this pin is not working well Mach number is 8 T1 is 15 degrees Celsius I think this pin what better P1 is 90 kilopascals okay then what happens that this one now this one M2 P2 and T2 now you see this one will make you clear about that arbitrary constant that from the flow leading to the generation of an expansion wave so first of all what you have to do we have to find out from the isentropic table first of all this flow is an isentropic flow with this Mach number 1.8 what is the value of P0 by P1 from isentropic table the value of P0 by P1 from the isentropic table is 5 point that is already done 5.746 and the value of T0 let this section is 1 this section is 2 so P01 T01 by T1 and that is 1.648 try to understand that now in isentropic table if you remember earlier I told you that isentropic table shows P0 by P1 T0 by T1 rho 0 by rho 1 A star by A all these things I told and there one theta value was there at the end for all isentropic table there is one theta value that theta value is the theta value for the Prandtl Meyer expansion or expansion wave which is also isentropic they follow these isentropic table values so therefore corresponding to this Mach number 1.8 I the P0 by P1 this one I the T0 by T1 I read a value of theta and that theta value is equals to the value 20 theta becomes equal to 20.73 degree now you understand what does it mean that means this Mach number is generated by turning an angle 20.73 degree Celsius where the Mach number was 1 you understand that means from a one Mach number this turning will be then the final turning angle theta this was the theta so theta for this thing theta 2 that the final theta is 20.73 degree plus 5 degree is 25.73 degree against this theta we will find out the P02 by P2 we will find out T0 2 by T2 from the isentropic table and what we will find out we will find out the value of M2 the Mach number everything we will find out if we know this thing so therefore we will find out the Mach number P02 now P02 by P2 now this value will be 25.73 so P02 by P2 in this case is 7.585 T02 by T2 is 1.784 and M2 is 1.98 well that means try to understand what is the thing that we are finding out from this Mach number that to get this Mach number through an expansion because this theta is kept against a Mach number from now your concept will be clear from this expression what is that expression I just wrote after integrating this thing immediately I wrote an expression where is that well where is that expression just now theta yes I wrote this expression this expression is valid provided theta is equal to 0 if this condition is satisfied that means when I compute this isentropic table at a given Mach number this theta means from Mach number 1 this Mach number is obtained with this angle of turn so therefore for this Mach number if we have a angle of turn 20.73 through an expansion wave we can generate this Mach number from Mach number 1 so therefore the if we have to find out the property here by turning with respect to an expansion way we have to add 5 degree with this value as if from Mach number 1 this turning is been made so then we relate this to the Mach number 1 condition through the calculation of theta for this Mach number 1 point that is the beauty of this type of problem so we find out this against this turning angle we get p02 by p2 t02 by t12 now p01 and p02 is same because this is the isentropic flow so therefore p02 by p2 is this p2 is p02 by this one and p02 is p01 which is p1 into this one so therefore we can calculate that p02 is p02 divided by 7 point 585 and p02 is p01 and that is is equal to 5.746 into p1 is 90 kilo Pascal divided by 7.585 and that becomes equals to what that becomes equals to well p2 I am giving the value 68.2 kilo Pascal and similar way if you calculate t2 that is we can calculate t2 in the similar way because we know t02 by t2 so t2 is t02 divided by 1.784 and that becomes equal to t02 is t01 and t01 we have calculated 1.648 into t1 that means 1.648 into t1 t1 is 288 divided by 1.784 and that gives you a value which is already calculated and that value is what t2 value is minus 7 degree Celsius so this way you can calculate okay we can solve another problem but I do not think time is left so we cannot solve any problem anymore time is over well another problem just I give you for your exercise a simple wing just you write this problem may be modeled as a 0.25 meter I will give you in wide flat plate set at an angle of 3 degree to an air flow at Mach number 0.25 okay and the pressure in the the pressure in this flow being 60 kilo Pascal assuming that the flow over the wing is two dimensional estimate the lift and drag force per meter span due to the wave formation on the wing so this is a very interesting problem so this problem actually you can solve the problem is like this there is a flat plate it is modeled by a flat plate which is 3 degree like this now when the flow takes place like this what happens there is a this is a shock and oblique shock and they are takes place this expansion wave so float goes by expansion wave in the upper part and the shock wave this is the shock wave shock wave by lower part so there will be an increase in pressure this is one this is two this is three you can find out the pressure here in this upper part from the expansion wave theory you can find out the pressure p2 this is p1 is given t1 is given m1 is given t1 is not given p1 is given however so you can find out the p2 and p3 when you can find out the p2 and p3 then you can make the vertical component as the lift force and the horizontal component as lift force this width is given per meter span in this direction I can tell you the well this result that the lift force will be lift force will be 6.23 kilo Newton per meter of span length and drag force will be very small 0.33 this is only because of the pressure that means you calculate the oblique shock concept as I did with this mach number finding out the shock wave angle find the turning angle is 3 degree and find out this p3 similarly sorry find out the p2 here sorry find out the p2 and find out the p3 by using the expansion wave theory we for this mach number mach number is what mach number is 2.5 you find out what is the value of theta with that add 3 degree and for that turning angle you find out the ratio of pressure make the stagnation to static stagnation pressure same as that so you can find out the static pressure here you can find out this pressure from the oblique shock angle for this m1 and this delta here the deviation is delta then you find out the shock wave angle beta and then modify the mach m1 sin beta find out the shock table normal shock table what has the pressure ratio you find out p2 the problem is simple but very interesting that you can find out the aerofoil wing it happens that one part there is an expansion wave another part there is a shock wave takes place so because of the shock wave this part the pressure is more this pressure will be more p2 will be more and here the p3 will be less so finally if this is the 3 degree so it will be p3 lift will be p3 minus p2 into that is a vertical direction lift and horizontal direction drag is cos of 3 degree and drag will be p3 minus p2 sin of 3 degree so that I give you the hint that this way you can solve this problem okay today after this so therefore with this I close the lecture on this introduction to compressible flow and I will close this course here so I think you just go through all the courses all these materials that have been taught and I wish you all the best to learn the subject okay thank you


Imagine that you are in the city of Medina in the 11th year after Hidra. Our Prophet, Salallahu alayhi wa alayhi, he has just passed away and the event of Saqifah has just occurred. Now the Shia of Imam Ali alayhi salam are being forced to give bait to the new ruler. I want to know what would you do in this situation? Would you, for example, give bait under Taqiyyah and help the Ahlul Bayt, alayhim salam, in secret? Would you speak out, risking your life and the lives of maybe even your friends and family? Or would you do something else? I would go to my Imam, Imam Ali alayhi salam, and I would ask him what he wants from me and what I should do as a person that follows him. And I would seek Fatimah al-Zahra to see how I should act upon this tragedy. Yeah, of course the Imams, the Ahlul Bayt, alayhim salam, they are there to guide us. So naturally we would want to go to them and ask them what should we do? I want you now to picture that you are standing outside the house of Fatimah al-Zahra, alayhim salam. This house that saw Jibra'il alayhim salam come down from the heavens and give the revelation where our Prophet sallallahu alayhi wa alayhi used to come to that house and greet Amir al-Muhmi, kiss Fatimah al-Zahra, and cuddle Imam Hassan al-Rusayn alayhim salam.  And Fatimah al-Zahra alayhim salam, she refuses to let them inside.  How would you feel seeing such an awful sight and how do you think you would react to that? I would try to protect Fatimah al-Zahra. I would want to stand in front of her. It's such a horrific thing to witness this 18 year old girl the beloved of our Prophet oppressed in such a manner.  What do you think you would do to make that situation easier or more bearable? I would say that they are the household of the Prophet. They are the enemy, they are the purest of the purest. I would try to make Hassan al-Hussain quieter and make them feel better. I would try to make Fatimah al-Zahra feel better.   Now none of us know where our lady is buried.   If you could say anything to her what would you say? I wouldn't need to say anything because you would know what is my heart. I would just stand there, smell the fragrance of Jannah and I would just try to take a bit of her dust and put it on my face for Tabarak and I will ask her for Shafa'ah and forgiveness. Our Prophet sallallahu alayhi wa alayhi would say whenever he missed the scent of Jannah he would smell his daughter Fatimah alayhi salam and I pray that we all lived to see that day where we may smell that scent of her grave.


But what the hell but Everyone and welcome to another spud about horror game. I don't know what it is Everyone and their grandma's making a spud about horror game. It just seems to be like a little trend right now I guess but today we find ourselves here on this spudge Bob whore That's literally the title of the game and as we can see spud Bob is a little busted Like why does he have long legs to begin with? Let's go ahead and play this Oh, okay. Looks like we have begun Okay, would I be like in some sort of abandoned building or something? Okay, I'm go.  Yo, what? Oh my god. Why does it why does it walk like that? Oh, okay, we lost him. What is this? Can we grab like some sort of gas canteen or something? Dude, oh my god, he's right there. He's totally like this way spud Bob What has happened to you my friend? Why are you just standing there? Oh great.   Come on Dude, what is going on in this place? Okay, where is this lot? Oh great. Come I can't run away from this dude. I need a green key. Okay. We didn't find a green key Oh, there's a generator. I need to oh, okay. So this is gaps. Okay.  What oh my gosh All right, there's a green key That's the key that we need in. Oh, there's another gas can. Okay. Nice Okay, so we grab the green key. We need to put the gas cans But they belong at the generator Okay, what is it for key? Oh, okay, this might open up that one door looks like an elevator or something Okay, we lost him though. We did it Dude, he's so quick Okay, um, how do we turn this on? Okay, it's started already. Oh my god, please don't Okay, we opened that door Okay, we need to go in there. Uh, I'm gonna go in here. Oh great.  Oh, he's right outside the elevator. Never mind What yo what what is going what the squidward?  What is goofy man Not even scary at all. Okay, we got a we got a jigsaw or screwdriver. I don't know what the heck that was, but it's so dark in here Oh great. SpongeBob is here. Why is SpongeBob here? You're kidding me, right? It's like they just want us to die. Oh, there was something there. I take down the screwdriver. Okay. I'll come back around I gave him a little snoop snoop. Okay, where'd this squidward go? I'm kind of terrified of the squidward because He got the longest arms in ohio and he runs super quick I think I saw a screwdriver right here. Yo, what? Oh my Oh That is terrifying. Why am I scared? I am actually kind of terrified for my life right now No, no, no, no SpongeBob We almost got trapped again. We need a screwdriver Where's the screwdriver? Oh my Bro What is this place? I think this is like an asylum in ohio or something Oh squidward is chasing me No, the screwdriver is right there. Why are the screwdrivers? They're at in between the couch I think they got mad and they just stepped the couch or something They got so angry that just you know, like screw it. I'm stepping the couch with the screwdriver There's SpongeBob. Leave me alone Oh, why is it getting quicker? Oh my I don't know why squidward terrified me. Okay. I got the screwdriver now. What? Jake solid. Yes pliers. Yes screwdriver. Yes What does this even mean? Like what am I supposed to do? Instead of still getting chased What am I supposed to do now? Maybe I need a key Okay, I'm so I need to lose this guy like Right now Oh, what if I go back to the elevator two minutes? I didn't survive for two minutes. You're kidding me Okay, this is easy. It's gonna be easy man. Oh great. Wait, what? Am I tripping or is there two SpongeBob now? Is that the same one? Is it just teleporting now? I don't freaking know. There's a lot of screaming going on. Oh, there is two SpongeBob Oh my Bro, what? They just keep multiplying Okay, so we're supposed to survive for two freaking minutes without getting caught It's these crazy maniac chasing me. Yeah, this is easy. I got it man Oh my god, there's an oh, why does he walk pretty zesty?  I'm just gonna keep going in circles, bro. You know what trained me for this kind of duty zombies Thank you kind of duty zombies because of this I can do because of that. I can do this now Why do they run like that? All right, we need seven more seconds. Come on. The elevator's down the hallway.  I'm not sure if I'm okay elevator repair getting the elevator go go go go go go Press the button. What? Oh my god, there's so many of them It's not over You're kidding right It's not over. Why is it not over? What what what am I supposed to do now? Dude, I can't believe there's still more.  You're kidding me, right? I'm still getting chased after all I've been through Okay, uh, they have to be next. I need a blue key. Oh, right Now we need to find the blue key Just when you thought it was over Bam, there's more Oh, great. I thought I was dead Okay, what are these? Why am I getting pushed around so much? Where do I leave me alone? Okay, you don't find the blue key. I don't know where I'm gonna find this blue key somewhere out here. It's so dark Can't see a thing I got where they were launching me like I'm a rag doll. Oh, no, no, no Oh, no Okay, I got the blue key. I got the blue key. I forgot what we needed this for it was one of these doors Okay, it's this one. There you go. Nice. What is this? White key picked up. Where do we use the white key? Is it here?    He saw me. No This is not good This is not good. I'm trapped Come on, come on, come on, come on, bring his ankles snap Okay, we're good here. We need to find this white key. Oh, it was Squidward Okay, where do we use this door? Oh, maybe here We made it That's the end don't like cutscene or something I feel like it got ripped off man after all that trouble. I went to menu dude All right. Well, there we have it. SpongeBob heart um The game is good. I like it But it's just a little too insane for me But I think you know your boys still managed to go through we beat it fair and square Yeah, the pretty cool fun game But like I said, I don't know what's going on with so many SpongeBob horror games I feel like it's like a little trend going on or something But hey, keep them coming man. I love playing nostalgic characters for my childhood And with the horror factor makes it even more fun. Well, yeah, I'll do the link For the game and the description for you guys so you guys can check it out for yourselves They don't definitely give you a hard time I'm pretty sure you won't be able to pass it if you do well Hey, thumbs up for you guys. All right, you guys well Thank you all for watching thank you all for the main support and I will see you guys on the next one man.  We're on the sinister Squidward apparently Squidward goes crazy and he goes on the rampage and kills everybody in Bikini Bottom. So yeah, that's pretty much it and uh as SpongeBob says I'm ready This should be interesting. I wake up every day go to work and come back home That is pretty deep. Damn, bro. Nothing ever changes.  I can't stand working here.    Get it. Get it. Get it. Oh my god. What's up with his eye, right? Um, oh, can we throw this? Hey catch We just killed the man with the Coffee mug, right? Can we throw the crass register though? Okay, we can't hey lady.  Whoa chillers Squidward. All right. Hey, hey cowboy catch this Oh that hit him right in his parts. I'm sorry, man Didn't mean to do that. Okay, um What oh what we got an AK? Okay Like gta right here my boy, right? Hey put your hands in there.  Oh Popo popo rolled up man. I'm sorry kids Okay, we're surrounded Wait now he wants to objective uh fire mr.   Krabs. Hey, uh, mr. Krabs. It's locked. Where is the key? Okay, dang. We got to find a key Okay, what is that crabby patty? Okay, uh, where is the key? Where can we find a key in here, man? It's a kitchen for god's sake. Um Maybe in the fridge Oh Wait, is that the key? Why is there a key in the fridge? Well, that looks kind of good.  Are those hot cheeto puffs. Oh, man. All right, um Let's open this Mr. Krabs, I know you're in here man Where's he at? Uh, I know dude. I could see him in there I can see that dude hiding inside of the chest. Let's open it What is happening here? It's not a gun.   Am I supposed to am I supposed to pull the trigger? I'm sorry mr.  I'm out of here Dude, this is insane Oh, man, that's one way to start a game, right? Bikini reporter, squidward crested crab killer Squidward kills eight dead murderers rampage Oh, he's on the run The crabby crabby patty mobile Oh the po po Oh, just ran someone over Center star squidward Wait, is this like an intro to the game? Because if it is this is nuts breaking news a mass shooting happened today at presty crabs The perpetrator squidward tentacles has somehow managed to escape law enforcement And has kidnapped his neighbors spongebob and patrick The bikini bottom police have reported that he is currently holding the two of them hostage And has threatened to kill them if they try to intervene In other news chumb bucket has reported an increase in sales since the incident The chumb bucket squidward did something this bad I should go find spongebob and patrick and help them. Oh squidward. Oh cool. Okay, so we're playing as sandy cheeks That's pretty sick because as we all know sandy gets down with the karate And yeah, she's pretty cool. All right, so uh, explore the house press you to hide in closets Wait, I think I just heard squidward walking Press F to use your flashlight Okay. Oh, we are playing as sandy Okay, so I just heard like okay. We need to cure something. I heard squidward. I heard like his his little There it is again. Oh that does not look it. Let's hide hide hide Okay, you can hear squidward getting closer We're never safe Okay, maybe it's not safe. Oh god. Okay. We need to run. Okay. We lost him Okay, living room. Oh, dude, this is sick. Dude.  Oh, squidward's getting closer I know he's around that corner.  What's here? Why is it locked? Okay, that is weird. Oh crowbar. Nice. We found the weapon Can we fight off squidward with this? Maybe. I don't know. Oh, rubber ducky. Okay. You can't click the rubber ducky. Why?  Okay. Where do we do this crowbar at? Maybe over here. There's a door No, you can hear patrick getting tortured in there. What? What is going on in this place? Oh wait crowbar Okay, we did something. Oh patrick Yo, how do you stop this? Stop, I'm sorry patrick. I can't turn the machine off.  Where's squidward? Dude, where'd the squidward go? He was sprinting right at us F you Okay, he's gone All right, there you go. Let me close this back up Close Okay, does not want to close um Patrick hold on and everybody how's this guy still alive to like all right, um What am I supposed to look for bro? Honestly, I'm lost right now. Okay. There's no inventory tab or anything Okay, squidward's over there Okay, there has to be something in this room Okay, I think he's actually coming back around maybe I don't know We will find out if we get caught in here. Oh wait, there's a note. Okay. No control Okay, how do you go upstairs? How do you open this? We need to find like a panel Or something that opens that door Okay, maybe out here I just hope squidward doesn't catch me slipping out here, man. Okay, we need to Bruh, I knew that Of course. Yes, bada bing bada bang. Oh Finally, I'm free. I got circumcised again. Yo, what? Did I just hear that? Oh man Wild and you're wilded patrick Okay, do we go talk to him patrick my boy Sandy thank you for saving me. You're welcome. Let's get you out of here Okay, let's go and one more thing patrick. Did you see spongebob? I think I did squidward took him to the living room to the living room I was just have to leave Leave patrick to the exit.  Okay, you need to be quick in that patrick you're moving pretty slow, man patrick I need you to get to the exit right now. I think I lost him Dude hurry up I can't stress enough how bad how slowly you're walking, dude Okay, please squidward did not come out I really he's almost here Hurry up patrick. I feel like squidward is gonna catch us Okay, come on exit go Okay, cool. So we managed to get patrick out of here safe in town and where's the police? Why is the popo not here at squidward's house? Investigate the living room Um, where did squidward go? He's not in here. Oh, of course Oh Just go the other way Dude, of course. So when I have to go in the living room, he decides to be in there, right? Like it only makes sense Did he just the spear? Okay, he turned Can you investigate the living room? What exactly do you want me to investigate? Okay, I can't move what? Okay, this is weird. I can't seem to get around. There you go. Um This is the living room, right? There's nothing here. Maybe this Painting now the drawers the anchor The wardrobe the plants the couch the bookshelf. Maybe it's a secret bookshelf The alarm Okay, I have no idea what am I supposed to do here the tv No barnacles right. There's got to be something around here, man. What can it be wait? Okay, so I was right. It has to be the bookshelf. What am I supposed to always see this? Bro, how did I not notice that at the beginning? Okay, where does this lead me? Okay, where does this take me man? It's getting fishy out here It's like a whole different secret area. Okay, nice Wait, what is that? Oh a chainsaw? Bro, how is there a chainsaw? We can't seem to grab it That would have been so awesome grab the chainsaw and then just fight off squidward. Okay, um What exactly am I looking for up here? Okay, see uh, oh rubber ducky again Rubber ducky is everywhere Gary Oh my gosh, bro Dude, you can see like his insides.  I don't even want to know dude Sorry, Gary. All right, Pete. Gary. We will miss you. I love you little creature Okay, that's I just came from there Okay, we're sick. Oh sponge bob. Oh my that is like some saw mechanism type of thing He's gonna get his arms split Hey sandy, did you come to help me? Yes sponge bob. What is this machine?  I'm coming to clap those cheeks. Yo, what's coming sandy? You have to hide in the closet I'm gonna clap my cheek sponge bob.  No, please I will do anything if you let me go. Um Squids don't have dicks.  Okay, what am I find ways to stop the machine? Doesn't do anything. Are you kidding me? One drop. I think you're dead buddy. I'm sorry How do you find ways to stop the machine? No, don't hide in the closet. Help the man. Help the sponge dude. Oh, I think you can die Maybe oh, I did see a wrench. I had I had seen a wrench. I had seen a wrench over here. Maybe if we grab this wrench Okay, nice. Maybe we stick it inside the congue wheel Oh Okay, he's so blind. Maybe we stick it inside the congue wheel. It'll stop it Nothing's happening Okay, there's something nice side grid now we gotta stop the other side Okay, now they're asking for too much man Okay, Squidward is right there. Is there anything that I can grab an object? I need an object. Maybe Gary's dead body. No It was worth a try but I guess not um Squidward. Oh, he's going that way. That's that's not good man. Okay. Is there another tool? Somewhere over here Why is he chasing me? What? Oh my god. He was running towards me full speed No lie. Okay. Um, great. There's nothing here Oh, sorry. Oh great.  There's something here. Oh, wait. Why is the bucket glowing? Oh, okay So I guess we get the bucket We fill it with water and then we throw it on the electric panel so that's just destroy the other side Okay, Squidward's going down there. We should be good. I'm here. I'm sorry. Oh my gosh, man There you go. You saved me. You're welcome. Look sandy.  This will be the last time. It's time for me to die.  What didn't this might have been one of the best spongebob games I played I don't know what it is something about these spongebob horror games I just love playing them. I guess it's just like the nostalgia and then like the The scary like the horror factor added to it that just makes it more amazing for me All right, you guys. Well, there we have it. Um, this was Squidward's sinister by rin bash Think I said that correct. I don't know. Um, if you guys want to play it I'll leave the game linked down below in the description so you guys can check it out for your sounds And yeah, it was pretty cool 10 out of 10 This was it was just a crazy though like the dialogue and all that but that it was a awesome game All right, you guys well, thank you all for watching and I will see you guys in the next one. Peace


Hi everyone, Shawn with jaspyscasebreaks.com here doing 2019-2020 upper deck the Cup hockey six box case break pick your team number four Where all Carter ship? It's the cup. It's great stuff. This is my first in-person look at it, but Awesome stuff, so I'm glad we get to do this obviously with some delays because of weather Dallas and stuff, but here is our list of customers and their corresponding teams From Mike Tower and the ducks my ducks down to Chris Cataloni and the Jets So here is our case the cup simply put Where'd you see him? Nicholas de Lella with the last spot mojo blue jackets Because I don't know what is in the baseball mixer, but we can look at that later on so let's pop this open And get started Did he did he record as Shrek Rex? Is that what you're saying? I just watched Beverly Hills Ninja because I think somebody the other night was saying that Beverly Hills Ninja was on Netflix So of course First day I had available. I wouldn't watch it There we go six boxes of fine fine Greatness Okay, so let's flip these around so I can get the seal. I'm glad that Chris Farley wasn't the cable guy such a good Jim Carrey cable guy Are the tin sealed too? I don't think so Cool good luck guys. I'm excited. I hope you are too I Cable guy He's stupid so okay, and I think the card's right on top right no cover All gas no no breaks Straight no chaser I'm guessing Let's go clip show I Dylan Larkin 207 out of 249 for the Detroit Red Wings getting a started Mike Tower I I First auto is Adam Fox two-color patch and auto 125 out of 249 for the New York Rangers and Edward how these are beautiful cards Wow, I mean, I don't know what else I expected Carter Vahegh 84 out of 99 signature materials three-color patch and auto Can put a little bit more effort into the auto Carter acetate auto Olaf Colzig 43 out of 99 enshrinement auto that should be Washington Capitals Michael Wheeler Dmitry Timischoff 207 out of 249 for the Maple Leafs Danny Giannsopolis and Casey middle stack that's not how it goes 16 out of 37 Rookie patch auto one two three four colors very nice That is buffalo Right, yeah buffalo savers Pete Olyseal that's an update. That's 1819 the cup So this is an update RPA of Casey middle stat from 1819 the cup I'll see you there. I Was like Casey Mill set was not a rookie last year small chance. I may pop in On Sunday or Monday, but if I don't see you I'll see you on Tuesday. Okay, cool. There you go It's a nice one That's not true Rex We sing it to honor Canada and their great prosperous lands Their sweet and native land I believe and the sweet sweet maple that they produce I don't think he wants I don't think it's a secret that Joe wants to be a famous singer Every year takes off to go to go try out for American Idol Wow Anthony Edwards Box to Alex the brink at 175 out of 249 For the Blackhawks Jason wainer nice three-color patch and auto Brady Keeper 120 out of 249 for the Florida Panthers Solomon Cookeleman another nice patch here Dominic Kubelik 61 out of 99 I don't know what somebody called that stitching, but it's my favorite type of stitching four-color patch there For the Blackhawks Jason wainer Monon reum.  That's signature. That is awesome Joe, what do you know about the first female goalie in? Hockey history. I used to have this girl's of she I used to have this girl's poster the cat in Mighty Ducks No, I used to have this girl's poster or like magazine and that's cool. It's a blue ink auto It literally looks like it's like my work is really nice Tampa Bay Ica Polo Nice, that is awesome.  I Know Rick very big card one-of-one Honestly that man in Riumi got me though I didn't even notice the signature on there just because I get matched up with the pads and stuff on the background of the picture I mean Quinn Hughes is great Clip troll baby. Yeah, it's not just the plate the plate itself. It's actually like encased in a card. It's pretty nice And still First up hurricane Andres Fetchnikov 198 out of 249 Caroline Hurdicam's Josh proofs Yeah, refer aren't they like three of the same printing plate just all three different color ones. I think those are awesome Lean Bergman One two three four color patch auto 103 out of 249 rookie For the sharks Frank Lupo What was this stitch called chain stitched? It's obviously the uh the yellow feather Dominic Kubelik another nice one for the black Hawks 35 out of 36 That one's Jason wainer again You had another nice Jason Kubelik earlier too I love being able to like see a patch and be able to tell where it comes from the uh the actual You know patch on the jersey Or sweater in hockey Acetate auto Glen Hall 47 out of 99 Also for the black Hawks jason wainer for my ducks Quad patch john gibson 22 out of 49 for mike tower and the ducks. Yeah pretty much rex They're as good as they get man and John clingberg four color patch auto 13 out of 99 Dallas stars Chad Osowski Also 1819 update on this one. There you go You are correct William I'm doing a Half Box for thomas shabbat 14 out of 249 for the senators and jarell taylor cody glass 53 out of 99 rookie patch auto three colors on that one four vegas very nice one there for rick robinson To oh to vote to revinen two out of 50 for the canes three color patch and auto Hurricanes josh pruce There you go rick congrats man. Man. This is so nice day with the cup tom wilson Washington capitals michael wheeler the photography on these ones are super cool Looks like it was stacked on top of other ones that he signed so you can see a little bit of blue on the back But that's awesome There you go michael You got two more in this box another quad relic john gibson again 24 out of 49 You have the 22 out of 49 and now the 24 out of 49 mike tower and the ducks again There you go michael congrats man And final hit for box number four eric bronstrom 244 out of 249 four ottawa again and jerel taylor box five So Henrik sedine's 179 at 249 for vancouver schaumatic Nathan bastion rookie patch auto three colors 222 out of 249 for the devils Sean mattax rex is calling the connor I'd be okay with that I'm sure edward would too How about another dominant kubalic 60 out of 99 on this one? blackhawks jason wainer again R temmie panarin Hard to see the auto there that blue ink really does hide itself, but that is pretty cool New york rangers edward who? whoa silver sticks splendor six or eight out of ten matt sundine What is that supposed to be that piece of silver? That's for the maple leaves and danie john so uh geon saapolis miniature manufactured metal hockey stick Okay, well there you go eight out of ten on that That's pretty cool looking That's honoring 1,346 games played And final hit box five ilia macaef Also for toronto and danie john saapolis For this mountain collapses That's some nice stuff to take photos of already. Let's see if we can add to the photo stack Magic within 10 Tobias Bjornfoot For the kings rob clements 38 out of 249 on there for you rob. Yeah, I mean it's as good as it gets. That's for sure Jonathan david said in three color patch in auto 116 out of 249 for ottawa and jurrell taylor Austin matthew somebody said a huge hit was coming It did two color patch in auto one out of eight toronto maple leaves danie john saapolis mike madonna signature renditions dallas stars chad ojowski These cases are crazy triple relic claud giro shon koutier and kevin haze nine out of 33 Going to philadelphia And nicholas dillello our final hit patrick wah 187 out of 249 all-time alum for the avalanche and shon maddock There you go guys No randomizers. No nothing else. That was 2019 2020 upper deck the cup hockey six box case break pick your team number four From jaspyscasebreaks.com. I'm shon jaspyscasebreaks.com. Thanks for hanging out. See you next time


So I'm really pleased to be here tonight at the CCTV Channel 17 holiday party and Matt Kelly is joining me and Matt is a new Channel director for Channel 17 and also the executive producer of CCTV Productions welcome. Thank you. I'm really really excited to be here excited for the holiday spirit here and 2013 is gonna bring so you've been on the job for two weeks. What it's been what has it been like? overwhelming But what's really great is everybody's been so welcoming and Very helpful very willing to assist me trying to learn the the lay of the land so to speak so the first week was a little bit Challenging, but the second week already feels Comfortable like it is home in a sense. So that's been just really heartwarming And are we starting a plan for the legislative session? Yes, we've already started contemplating our Signature series under the dome Jill Kruinsky is here We're gonna be speaking a little bit tonight and further in a week ahead about upcoming topics that we're gonna want to cover So that it dovetails with what the legislature is talking about so that we can bring in senators and representatives to speak on Those topics to you the viewer. That's great. Yeah, and then we're gonna go right into town meeting. Yeah, it's very very quick So no downtime. It's learning on the job as they say and luckily you Didn't have to work the general election, which we've all been doing. So it's a very it's a it's a jam-packed four or five months Well, I was down in Montpelio or that so that was exciting as well as I was telling you throughout this whole process I'm a I grew up here in Burlington But I left in 1990 so 22 years ago And so coming back to Burlington a lot of the issues are still the same They've not been solved. It's just the people that have changed and what have you been doing for the past 22 years? Oh gosh, it's been a whirlwind tour of the country at least Bay Area New York City Los Angeles and Hawaii and now back here so a big circle to come back where it all started Well, I'm so glad that you're on the team. It's very exciting So Margaret Harrington is right there. Maybe you could bring her over and we can interview her So we're here at the CCTV Channel 17 party and we love this party It is a great opportunity for us to visit with folks that come in and make TV and attend our events and there really are diehard champions of free speech and community engagement and Coming up. We have Margaret Harrington who is been working on Anti-nuclear activism for many years and we're so glad you're with us To twice in one day you get to be on TV. Yes, how wonderful and happy holidays and everything like that It's such a pleasure to work with Channel 17 and I've been doing it for about four years now with the nuclear free future program and You've always been a wonderful person here for me and everything and I've loved working with Rob Riber and Tuyolendl so much And welcoming the new director, which is seems like a nice guy He is he's very outgoing. It's wonderful. Now. Tell us. What was the topic of your program today? It was Nuclear waste the gift that keeps on giving and it was about that huge problem nuclear waste both at American nuclear power plants and all over the world and Especially It's an ongoing problem and there are wonderful experts right here in Burlington the Gundersen's Arnie and Maggie Gundersen who've been on the program several times over the last few years They're a wonderful resource in the community and they can be seen What kind of impact do you think your programs have I think that it gives information to people who are not Really apprised of the situation because in many ways we are blocked off from what's really happening for example Seven women can be arrested down at Vermont Yankee for trespass of the Vermont Yankee power plant and yet their story isn't publicized at all for They went down there for 22 times to make it a Direct action against nuclear power and especially Vermont Yankee down there because it's unsafe and so dangerous And yet they are ignored by the by the press but here on they've been here on the nuclear free future program and That's very important. I think that people know that there are activists out there and concerned people and in the case of My guest today who is arnie gundersen a chief engineer with fair winds energy education somebody who knows exactly what is going on So that's that's why it's important and why channel 17 is Important because it gives more the the in-depth information on the issues that Really should not be swept under the rug or in a corner. Well, Margaret. Thank you for your work to do that We exist here for you. So thanks for making use of it. Thanks for for making it possible Good to see you So we're gonna be speaking here with Bob appell longtime public servant. Welcome. Nice to see you. Thank you So nice to be here. You've been toiling in the fields of civil rights for many many years between that criminal defense 35 years Yes, and now you are moving on to a new position. What is it? I'm joining a law firm to be known as Cone Wrath Danon and appell in Heinzburg, Vermont It's a firm the Eileen blackwood recently departed to become city attorney here in Burlington. So and Eileen's practice is similar or was similar to my interest in employment Discrimination and employment cases and school cases. So and I hope to do some criminal defense again. I sort of miss it It's once you do it it gets into your blood. So I am looking forward to the change And what have been the highlights of your career so far? Wow a Question I know a question the opportunity to serve the people of Vermont in a variety of roles and I think do some important work particularly around Making us who are white in the dominant culture understand that people who don't look like us may have different experiences I think generally although Vermonters lack malice on race they also lack experience with different cultures I live in Hardwick I'm over here a lot and it's like two different worlds. So You know, I I think getting past the sense that we don't have racism here Has been a struggle and will continue to be a struggle But I think we're making progress in that regard the other issue I mean I've been asked that question a bunch in the past week and I have to say that the issue of criminalizing people with psychiatric disabilities is a very important one to me Started when I was a public defender investigator seeing people come through with very serious mental health issues and they go into jail and don't You know, they don't get treatment. They get managed I am all for holding people accountable But we also want to take the opportunity while we're paying to house them to try to improve Their lot in life and therefore make the community more safe. So that's been a long-standing issue to me And then the other pieces around physical access removal of physical architectural barriers and housing in places of public accommodation Vermont is full of old housing stock old commercial stock And it's a challenge again. It's a lack of understanding by people who are I like the term temporarily able to body as I get older I mean, I think we're all gonna have infirmities and the notion of providing universal access which makes it easier for people with present physical Mobility issues makes it easier for all of us. So I think that's an important issue going forward and racial profiling by police those have sort of been my focus Do you think that the mental health courts has has helped in the area? I do. Unfortunately, they only exist in three counties that being Washington Rutland and Chittenden and when you're outside of Rutland Washington and Chittenden there's virtually no public transportation and When you're in the throes of the criminal justice system, you're often ordered not to drive You may be under suspension You know it becomes very challenging and I've been pushing that that opportunity become universal and not an accident of geography So and also drug courts. I mean the other driver of criminal You know something like 85 90% of inmates have substance abuse problems either drug addiction and or alcoholism You know and the other Statistically it always sticks with me is People in jail under the age of 22 90% or high school dropouts and half of those were on Individual education plans meaning they were eligible for special ed. They have some form of disability So again, it goes back to the notion of we're criminalizing people with disabilities instead of trying to build their capacity to lead productive safe Healthy lives and contribute to our community. So I'm sure that we will continue and my success Or in the staff there can will continue on these issues and I'm hopeful that the community joins in with that and I really want to thank you and your staff here you've been very open to Engaging the community on these issues over the years I've had the opportunity to sit here with a variety of hosts and it's just it's just wonderful that you provide this sounding board for issues that all too frequently are not covered by Commercial media. I have to say I think the commercial media is coming along Without a doubt, but I think you You have shown great leadership and I commend you for that and hope you can do it for many many more years Thank you, Bob. It's a real mutual admiration society. So good luck with your new position Yeah, and we'll see you soon. We want you we'll get you on. Thanks. All right. Very good. Thank you so much So happy holidays. We have Mike McNamara who's the chairman of the CCTV board How are you? Same to you. So glad that you're here. Glad to be here. So, um, you've been Continuing with your long-standing series on housing and community development the Vermont housing and communities show Next show will be the first wednesday in february And what was the most recent program that you did? We just did a show on the fiscal cliff With airheart manka of the affordable housing Coalition just talking about what the ramifications of housing In the upcoming federal budget discussions and also what we might expect in the legislature coming up in the state And do you think we're going to go over the fiscal cliff or? My I think we have there's a good possibility. We could go over the cliff Yeah, I read an article where someone wrote, um, we created this cliff. It doesn't mean we need to all go over it That's right. That's right that we did create it and You know, they created it because they couldn't come to the grand bargain and Now they're trying to come to the grand bargain only at a very compressed Period of time. So I know, uh, congressman welch thinks we're going Going over and the hope is that if we do go over It will set the stage to to fix it in a short period of time But sometimes things take longer in washington than they Than they should so So how have you, um, enjoyed working in vermont in the political scene? I mean for many years you have been in public service and when you compare it to washington Well, I came from massachusetts and of course Politics can be very corrupt in massachusetts there very clean in vermont comparatively speaking Um, as we say in vermont, we play in a small sandbox So people have to be nice to each other because you're going to see them You know on the street or at the dump or wherever you bump into people And uh, we've really appreciated having you in a leadership position at cctv. It's been great. I've been on the board now for three years four maybe And um, it's great to see to learn about the other side of how everything Goes it's one thing to sit here and talk to people that's easy But what you and the staff do are just amazing to put all the programs together like channel 17 like common good vermont It's really pretty amazing. It's certainly fun to work with you Well, and it's certainly fun to work with you and all the new blood you've brought in Recently, we hated to see jess wilson go but um, you know, she's she's moving on and seems to be doing well And we're bringing new blood in like matt and uh, I think it's all going to be good Thanks so much michael so much too. Happy new year All right, so um, again, here we are at cctv channel 17 holiday party and we've got arnie gundersen It's always a pleasure to have arnie. How are you getting some air time today? How are you? Are we live? Oh my god? Oh, this is scary. I know well, don't be scared. It's fine. I'm here with you Okay, so um, I know you've been quite busy in the past. Well forever But what have you been working on in particular in the last couple months? Well, I got back from tokyo The beginning of september. I was there for 10 days um I was invited by a bunch of citizens groups and I spoke to The diet which was fascinating. That was the that's their house of representatives kind of the japanese law association and Um, uh, at the university of tokyo, there was a symposium and then a couple other citizen group meetings as well um, yeah on my least favorite topic fukushima um, but apparently, you know, maggie and I have been Really honest Unlike their own government. So apparently we're well respected over there So they I guess they appreciate it that at least somebody they could find on the internet was telling them the truth Yeah, and so I think um, it has really fallen out of the news that what's been going on in japan So so what is the current situation there in terms of the contamination and the quality of life? Uh, yeah contaminations all over the place and um I was in tokyo and I had my little plastic bags and my little spoon and I was collecting samples and I brought them back and Uh, the the ground in tokyo is as radioactive if it was in the united states We would be shipping it to texas as radioactive waste And and people are walking around in and that's that has become the new norm And you know the the theory as well. It's low and you won't get cancer But when you spread that out tokyo's 35 million people Um, you know clearly people are gonna get cancer that that the the neat thing is that um There's essentially a rebellion underway led by women And in that culture what it's it's really extraordinary to see women take step forward and um You know their husbands sort of still believe the party line But um women are saying, you know, I'm taking the kids and leaving Because we are not going to live within 100 miles of this plant and you can either come with me or not So there's an extraordinary change Um political change in in uh in the off of yeah, so it sounds like a real domestic change too In terms of the house household dynamics and culture. Oh, yeah. Yeah, it really is and and I think once you cross that line You don't go back. You know, I think it'll be very difficult for the women to Disappear and become subservient to the men again, which I don't think you'd want to happen Anyway Well, I want to thank you so much for your work and certainly keeping our our audience posted by participating in programs here at channel 17 You guys were there before cnn and before all those guys So I really feel like I owe it to to you know to channel 17 because you were listening before the world wanted to hear Well, yeah, thank you Arnie for all your work. Good to see you. Happy new year So we're here at channel 17 and cctv's holiday party. We've got a wonderful staff working In the background. We've got sylvan on camera They're gonna work in the control room and we have just a wonderful group of people Terry, how are you? Why didn't you come join me? Terry, um, jeralamin is one of our regular access folks You're a public access user. Why do you support community access television? Not because it's an opportunity for The general public to get their point of view across I I do produce a program called vermont today on vcam channel 15. I'm on it 9 30 every monday evening 11 o'clock on wednesday evenings and 6 30 Thursday mornings, and we have a very interesting program this time talking with two Two residents of wake robin who are relatively wealthy and they're advocating higher taxes for the wealthy To solve our budgetary problems. And that's the only fair thing to do When after the second world war the tax top tax rate was 90 percent and now it's way down About 30 percent. In fact, some of the richer people like warren buffett pay less than their secretaries to So it's really not fair and so we'll look forward to that program Yes, so I interview Keith Olson who's a former professor. He lives at wake robin don hornstein who is a managed a mutual fund on wall street and stan greenberg who is Blind and Has another point of view Well, I can't wait to see that and we're just so glad you're using vcam. That's great news It's always great to see you. Thanks a lot. Okay governor hoff. It's always a pleasure to see you Come on over here in the light with me We'll get right here by the camera. How are you my friend? Well, I'm okay Yeah, well, I'm glad you made it. This is awesome. Well, I've made it here for a number of years You know No, no doesn't feel she has to cook anything for dinner That's what we're counting on That's good. So, you know, we go back a long time from our very first series of programs that we did with you Yeah, I think we do and um, you know nats been working on the archives I think we have almost 19 000 pieces of media Do you really? I know what are you gonna do with it? Well, we're archiving it people can actually Watch a lot of it online or they can come here and watch them and you know, it goes back to 1984 Really? Wow, that's a while ago It's almost who's back as far as I do Well, you know this year was a big year because they just completed a book about the work that you did while you were governor, right? Who did wasn't that the didn't that book get published about the sixties? Three guys And it's a very nice book really. Yeah, very complimentary and very complete Nice book. So you're pleased with how it turned out. Oh very much so It must be feel good to have your legacy documented so people can understand what happened during that period Well, it's nice to have your legacy documented period So much happens in this world that nobody gets credit for so it's nice to get credit for something You deserve a lot. You've been a real leader and inspiration to us. So thank you so much and thanks for coming tonight Okay, so um phil hoff is um our former governor here in the state of romana He was governor in the sixties and uh, we are always really happy that he and jone come and visit with us Hello, lisa. How are you? We've got lisa condon the newlywed. How are you? I well happy holidays. Happy holiday Good to see you. Thanks for that to be here So tell us what you've been working on you're just a hive of industry and the nonprofit and the community in the business sector Wow, I've been working on quite a bit. Uh, the most recent thing and it actually we're just kind of shutting it down From a crowd campaign fund for uvm extension and doing the raps campaign Which is uh rebates for roll bars program But you know, I continue my quest for doing good in the community of burlington So how did that campaign go? Well, we wanted to raise $23,100. We raised about $10,000 of that And since it was the first time we were doing a crowdfunding campaign. I think that that's excellent Um, and what that equals out to is actually putting roll bars for 15 of the 35 farmer 15 roll bars On 15 families of the 35 families on the waiting list. So that's important and maybe just to remind people Why roll bars on tractors are so vital? Absolutely. So farmers in general Are 800 more likely to die than the average worker And what roll bars do they are 99 effective from saving a farmer's life when a tractor actually rolls over So that is really amazing because they're expensive and the families can't afford them. So this program subsidizes them. Absolutely It's a 75 subsidization for subsidization. I guess that's a word. I just made sure I like the word um, and so what that does is it allows these families to actually purchase them and tractors have a 40 plus year lifespan So it actually gets passed from generation to generation and families get to then not only keep the tractors But keep the farms and we as people of burlington or across the country get to have the bounty that they provide. It's wonderful Well, you deserve a lot of credit for all your community activism. So thank you so much And thanks for being on the cctv board. We miss you. I miss you. Okay. Bye. Bye So richard kemp is here with us richard is a um long time Supporter and uh, I don't know how many episodes of your program you've done but over a hundred Fantastic, but I also served on the board of directors. So is that right? Don't you remember? I do and you served on the channel 17 trustees as well. Yes. I'm Committed to public service Great commitment. I'm sitting, you know standing here with a person that has made an enormous impact in citizens life of the city of burlington And the person is not me. It's the person holding the mic Thank you so much. And it's both of us really when you get right down to it Yeah, you let me make television and I keep on doing it. You do it. Thank god Yes, richard show near and far great program and a great party. It's always nice. It is. It's really it's nice. It's a very Delightful group of people. So thank you so much so much for what you continue to do day in and day out I don't know if you work on sunday or not, but I try not to Although I was addressing envelopes on sunday Thank you, richard. So I want to um, thank everyone for joining us I think abdulla is going to join us abdulla is one of our volunteers He comes every um every week to run the cameras and direct the shows. How are you my friend? Hi lorry. I'm so glad. Thanks for joining me here See, I'm enjoying Yeah, exactly. We got the lemonade flowing right in this operation. So tell us why you volunteer here at channel 17 Yeah, first I started from being community producer Which is it was interesting to go get the occupied New york or burlington news story out and bring it in here And get their voices out So I started from there and And I realized I like to serve So why not just keep on serving so And I uh talked to rob and rob said, okay I think yeah, you need to get a one on on a one year Contract to serve. I say all right. Uh, I sign up for it and you see make sure you come every day I say, okay outcome and you don't have to worry I worry about that.  Yeah, and Except when I'm sick, that's the only time Well, everybody's allowed to be sick and then you've recently got a new job. Is that right? Yeah, yeah Yeah, two or four months ago now. Maybe uh, way block of motion Fantastic How's that going for you? It's great. And yeah, great people to work with and I as you Maybe can remember I told you when I had my accident how everybody came out to help me from there. I never had So uh found myself surrounding such a people that are so caring for someone else, you know, so I'm thankful For what happened to me Well, we're grateful for you and all your help Abdullah. It's just a pleasure to work with you. Thank you so much. Thanks a lot Thanks for joining us today Cheers, okay. Lee Turhun community activist Lee. How are you? Good. How are you? We've worked together a long time You know, we were talking about that earlier as we were sitting enjoying your wonderful dinner. What a spread It's really nice. Yeah, we were talking we were telling some youngsters about the old days when we first got this Beautiful community asset And it's just so awesome that you're still here.  Yeah, true Any good stories any success stories from making television that you want to report from making television?  That was a lot of fun. Yeah Yeah, it was fun.  Yeah, which was um out on apple tree point And that went away and now we have a wonderful project that's about to be break ground in the spring And so I get to leave on a high note Fabulous and we get to leave on a high note too here at the channel 17 cctv party. Thanks for joining us and thanks for watching