In this lecture, I will take up solution of the integral momentum equations or the integral equation of the velocity boundary layer. My task would be to introduce you to the general solution procedure and then using this procedure study the effects of the pressure gradient and suction and blowing. I recall again that integral solutions can be obtained for arbitrary variations of the free stream velocity u infinity at the edge of the boundary layer and the wall velocity at the at the surface of at the solid surface we call suction or blowing. To refresh our memory the integral momentum equation reads as d delta 2 by dx plus 1 over u infinity d u infinity by dx plus 2 delta 2 by delta 1 equal to c f x by 2 plus v w by 2. How do we solve this equation? Just recall it is the procedure here is quite the reverse of what we adopted for similarity method. In the similarity method a third order similarity equation was solved with appropriate boundary conditions to obtain the velocity profile. The velocity profile came out of the solution of the ordinary differential equation and from which the integral parameters such as delta 1, delta 2 and c f x were recovered by integrating and differentiating the profiles. In contrast in integral method the velocity profile is assumed usually a polynomial in y by delta such that it satisfies the boundary conditions. Having assumed this profile we evaluate the integral parameters delta 1, delta 2 and c f x and substitute them in the integral momentum equation. The IME is then solved to obtain delta 2 as a function of x and hence all other parameters as functions of x. So, the procedure is quite the reverse of the similarity method and to the extent that we have assumed a velocity profile that which satisfies boundary conditions but nonetheless is an approximation to what could be the real velocity profile at a given x. So, we say let u over u infinity which is the dimensionless velocity and it would be a function of x and y be a polynomial in eta variable where eta is y by delta a plus b eta plus c eta square plus d eta cube and e eta 4. So, there are five constants to be determined a, b, c, d and e and this we do by invoking five boundary conditions and the boundary conditions are as follows. At the wall y equal to 0 of course, u is equal to 0 which will render u equal to 0 but the second condition is that if you look at the momentum equation. Now, if I write this equation at y equal to 0 then clearly that term will be 0 because u itself is 0. v however will be v w into d u by d y at y equal to 0.  So, I use this as a boundary condition to say that nu d 2 u by d y square at y equal to 0 is equal to v w d u by d y at y equal to 0 minus u infinity d u infinity by d x and that is what I have written here as the boundary condition 4 I mean the equation 4 which is the second boundary condition at the wall. At the edge of the boundary layer y equal to delta u will equal u infinity and therefore the left hand side will be equal to 1 and so will each of these eta's will be 1. So, you will have a condition a plus b plus c plus d plus e equal to 1 also d u by d y is equal to 0 at the edge of the boundary layer d u d y is 0 and to the extent that the velocity approaches u infinity asymptotically the continuity of this first derivative survives d u by d y equal to 0 survives as we increase y and therefore the last boundary condition is that d 2 u by d y square will also be equal to 0. So, I have 1 2 3 4 and 5 5 boundary conditions which will enable me to determine a b c d and e. Let us see what those coefficients look like each of these coefficients can be represented in terms of the coefficient e a equal to 0 of course because of u is equal to 0 at y equal to 0 b will be equal to 3 minus e c will be equal to 3 into e minus 1 d 1 minus 3 e and e will equal 3 times v w star minus lambda plus 6 divided by 6 plus v w star.  It is a suction and blowing parameter and lambda is delta square by nu d u infinity by dx is a pressure gradient parameter associated with variation of free stream velocity u infinity with respect to x. Of course, I did say that we have to choose the values of v w star and lambda very carefully because in as much as we can allow for any variations of v w and u infinity, we must ensure that the assumed velocity profile is such that u over u infinity is always less than 1 inside the boundary layer for eta less than 1. So, values of v w star and lambda minimum or maximum must be such that this condition holds. Remember v w star can be both positive or negative depends on suction or blowing and lambda depending on whether it is an adverse pressure gradient or a favorable pressure gradient can also be positive or negative and we have to choose these parameters of within a certain restricted range only so that the boundary layer approximations are well held. I have plotted the three graphs. The middle graph is for no suction or blowing that is v w star equal to 0. When lambda is equal to 0, you will have the flat plate because d u infinity by dx is equal to 0. As you can see here, this will be the profile. Lambda equal to positive values means accelerating boundary layer because d u infinity by dx then is positive. Lambda negative would be d u infinity by dx because d u infinity by dx is negative and therefore a decelerating boundary layer. So, if I choose arbitrarily values of lambda, you will see up to lambda equal to 12, the u over u infinity values are well within 1 and up to minus 12 they are very much within 0 to 1. But if I take lambda equal to 30 which is a very highly accelerating flow then of course, u over u infinity exceeds 1. In fact, that is what would happen for all values of lambda greater than 12 and therefore such values of lambda are not admissible. Likewise, values less than lambda equal to minus 12 are not admissible because velocity itself will turn negative. This is the importance of this common which I made here.  Likewise, if u over u infinity is negative then delta 2 can be negative and that is not admissible. This is similar profiles for v w star equal to minus 2 which means the suction case and again I have plotted several values. Before I do look at that, let me go back again to v w star equal to 0 value. Obviously, when lambda equal to 0, I said this is a flat plate solution, but lambda equal to minus 12 gives a 0 gradient at the wall which means separation must occur. It is a peculiar value lambda equal to 7.052 and the importance of that you will recognize a short while from now. Let me go back again to the suction profile. Here, you will see for lambda equal to 12 plus 12 u over u infinity exceeds 1 and of course, for 28 exceeds very much more. Likewise, here for lambda equal to minus 12, there is a velocity which goes less than 0. On the blowing side however, up to lambda equal to 20 or little more, there is a u over u infinity well within 1. So, blowing permits much higher pressure gradients favorable pressure gradients. On the adverse pressure gradient side, again lambda equal to minus 12 is the limit. Integral method, we evaluate three thicknesses. The first one is very well known to you delta 1 which can be where the integration limit from 0 to infinity is replaced by 0 to delta. Simply because from delta to infinity, u will remain equal to infinity and therefore, both these integrals will be 0 between delta and infinity. Therefore, the limit infinity can be replaced by delta in both of them. In addition, we define a shear thickness mu u infinity divided by shear stress. You will notice that it has a length dimension we call delta 4 and it is called the shear thickness mu u infinity by tau all x. The reason for this you will understand very shortly. So, we have three thicknesses delta 1, delta 2 and delta 4. We could have recovered value of delta 4 even in the similarity method because we know how the tau all x varies with x. So, if I substitute our velocity profile u over u infinity equal to all this as a function of delta, as a function of eta into our definitions, then you will see that delta 1 by delta would become 1 over 4, 1 plus e by 5. If I represent e as 3 v w star minus lambda plus 6 over 6 plus v w star, then it will simply read like that. Delta 2 by delta, this integration is somewhat involved because it involves product of u over u infinity square and that would result into 3 by 28 plus e by 70 minus e square by 252 or what I have given here by simply replacing e. Most importantly, delta 4 by delta would simply result in 1 minus 3 e 6 plus v w star divided by lambda plus 12. This is quite easy to see. If we see our equation, then remember delta 4 is mu over u infinity divided by tau all x and this is equal to mu times u infinity divided by mu times du by dy at y equal to 0. If we look at our velocity equation, then you will see du by dy at y equal to 0 will become equal to u infinity into 6 over 6 plus v w star into 2 by delta plus v w star into 0 plus lambda by 6 into 1 over delta. You will see then if I take delta common, I will get this as u infinity by delta into 6 over 6 plus v w star into 2 plus lambda by 6. Therefore, delta 4 will become equal to mu mu gets cancelled here and u infinity divided by u infinity by delta 6 over 6 plus v w star into 2 plus lambda by 6. Therefore, this and this gets cancelled and delta 4 by delta will read as what I have shown there 6 plus v w star over lambda plus 12. This shows very clearly that if lambda is equal to minus 12, delta 4 will become infinity or if delta 4 becomes infinity, then tau all x must be 0. Therefore, lambda equal to minus 12 represents separation. Values of u over infinity were not applicable in our profiles for lambda less than minus 12. We reorganize the integral momentum equation now by multiplying each term by u delta 2 by mu.  Then you will see this term simply becomes u infinity by mu into d delta 2 square by dx divided by 2.   Therefore, multiplying throughout by 2, I get u infinity by mu d delta 2 square by dx equal to 2 times v w delta 2 by mu plus delta 2 by delta 4 minus delta 2 square by mu sorry this should be multiplied by 2 plus delta 1 by delta 2 I forgot d u infinity by dx into 2 plus delta 1 by delta 2. Again, the equation maintains its dimensionless form. Now, all I have done is in our derivation delta 2 by delta 4 is replaced by s and we call it shear factor. Delta 1 by delta 2 is replaced by h, which we call shape factor. Delta 2 square divided by mu d u infinity by dx and that would simply be equal to lambda times delta 2 by delta whole square as a pressure gradient parameter. Remember what was lambda? Lambda was delta square by mu d u infinity by dx.  Each term is dimensionless. You can see this is velocity, a length dimension because this is squared and this has a length dimension and this is nu. So, it is a kind of Reynolds number which represents rate of growth of momentum thickness delta 2. Kappa is a pressure gradient parameter. This is really a universal relationship. What we mean therefore, that the relationship applies no matter what is the variation of u infinity or the wall velocity. It is a universal relationship between integral parameters delta 2, delta 4 and delta 1. Let me go to the next slide. By universal, we mean that it is applicable applicable to all types of variation of u infinity including the ones we used in similarity method u infinity equal to c x raise to m. Kappa which is proportional to du infinity by dx implies when it is 0 implies a flat plate solution because u infinity equals constant. On the other hand, the right hand side f k or u infinity over nu d delta 2 square by dx equal to 0 implies that delta 2 is constant with x. As you will recall from our similarity method, it represents stagnation point solution because for m equal to 1, all thicknesses delta 1, delta 2, enthalpy thickness, heat transfer coefficient all are constants with x. That is the characteristic of a stagnation point solution. Shear parameter equal to 0, delta 2 over delta 4 equal to 0 implies that delta 4 is infinite which in turn implies that tau wall x is equal to 0 and it represents separation. All values of V w plus n lambda for which delta 1, delta 2, delta 4 are less than 0 must be discarded because for these values u over u infinity is either greater than 1 or u over u it is less than 0 which means those are inadmissible values of V w plus n delta lambda. Now, for u infinity equal to c x m, it is easy to derive that kappa will be equal to delta 2 star square divided by 2. I will show you how this is the case. If u infinity is equal to c x raise to m and kappa is equal to delta 2 star by nu du infinity by dx, then you will see that this becomes delta 2 square by nu c m x raise to m minus 1 or I can write this as c x raise to m into delta 2 square by x into m. I can write like that and this is nothing but c x raise to m is nothing but u infinity into delta 2 square by x into m which I can write as u infinity sorry there should be a nu here. So, divided by nu I can write this as u infinity x by nu into delta 2 by x whole square into m or that is equal to delta 2 by x square into re x into m. Now, if you recall in our similarity method we had defined delta 2 star as delta 2 by x re x to the half. So, this essentially becomes delta 2 star square into m and that is what I shown here. Similarly, you can show that f kappa which is equal to u infinity by nu d delta 2 square by dx can be shown to be equal to 1 minus m delta 2 square star square for that value of m. Similarly, here delta 2 square is corresponding to the value of m you are concerned with. You can also show S for example, what is S? S is equal to delta 2 by delta 4 and that is equal to delta 2 divided by mu u infinity by tau all x or that is equal to delta 2 tau all x divided by mu u infinity. This term can be shown to be equal to f double prime 0 into delta 2 star. It is simply a question of manipulation here and you will see the level at tau all x. For example, this will be delta 2 into mu times du by dy at 0 divided by u infinity into mu.  These deductions are very important as we shall see shortly. Let me plot the results of remember I have calculated S v w plus kappa I have assumed values of kappa and calculated H also from the velocity profile that we assume that is delta 1 by delta delta 2 by delta 1 delta 4 by delta. For a boundary layer without suction or blowing the acceleration and deceleration parameters. So, acceleration parameter I have gone up to 12 and deceleration I have gone up to minus 12 because I cannot go less than minus 12. Then the kappa values take these values this is 0.095 and this goes on to minus 0.157. Delta 1 by delta 2 as you can see compared to 0 where it was about 0.3 with acceleration the displacement thickness reduces and with deceleration it increases. Same thing holds for a momentum thickness divided by delta it reduces and increases. Inverse is true for shear thickness the shear thickness goes on increasing whereas, on the negative side it when there is suction it goes on reducing. So, much so that at minus 12 it reduces exactly to 0. The shape factor H delta 1 by delta 2 is remarkably constant for highly accelerating on an acceleration side, but on decelerating side it goes on increasing quite significantly. This is the right hand side with some values negative and then positive.  Therefore, it represents stagnation point solution. If you look at here the stagnation point solution will be somewhere here and its value will be lambda equal to 7.052 and kappa equal to minus 7.824. The similarity solution for delta 2 star m equal to 0 was 0.63 and delta 2 star m equal to 1 was 0.292. Therefore, kappa for m equal to 1 will be 0.0841 and f for k m equal to kappa m equal to 0 would be 0.44. We will make use of these numbers very shortly, but remember this is the flat plate solution. 7.052 lambda is a stagnation point solution and minus 12 is a separation solution. This is what I have plotted here. On the x axis you have kappa, the pressure gradient parameter and f kappa, which is the rate of growth of momentum thickness parameter on the y axis. When kappa is positive, we have accelerating flow or favorable pressure gradient. When kappa is negative, we have the decelerating flow or adverse pressure gradient. The results are plotted when there is no suction and blowing and therefore, V w star is equal to 0. You will notice that when kappa is equal to 0, the value of f k must represent the flat plate solution. And when f k is equal to 0, as we just said, it must represent the stagnation point solution. So the intercept on the y axis represents the flat plate solution, whereas the intercept on the x axis represents the stagnation point solution. And f k values turn negative when you have very highly accelerated flow, whereas when the flow is decelerating, f k values are positive. Now, using the relationship between kappa and f k with integral parameters, I have also plotted the parameters here, the similarity solutions here. You will notice that this is the m equal to 1 solution, this is m equal to 0.33 solution minus 4, m equal to minus 4, minus 0.04, minus 0.065, minus 0.085 and minus 0.09 is the separation. The separation is seen at about kappa equal to minus, let us say about minus 0.07 in similarity solutions, whereas in integral solution, the separation occurs at minus 0.1567. So on the integral solution deviates from similarity solution for kappa less than 0, because we are allowed for arbitrary variation of u infinity, but for specific variation u infinity equal to c x m, the results go along there. Now, in order to develop close form solution, we can see that at least for very moderate decelerating flows and accelerating flows, a near straight line approximation can be made. This was done by a scientist called Thwaites. It is simply f kappa equal to a minus b kappa and the a will be the value of kappa equal to 0 and therefore, represents flat plate solution a delta 2 star square m equal to 0, whereas b will be simply when f k is equal to 0 or the stagnation point solution and therefore, b will equal a divided by delta 2 star square of m equal to 1. If you look at our previous slide, I have said delta 2 star m equal to 0 is 0.663. So delta 2 star square would be square of 0.663 which is 0.44 and therefore, delta 2 star m equal to 1 is 0.292. So 0.44 divided by 0.292 will give me this value of 5.17. So a will become equal to 0.44, whereas b will equal minus 0.4. So f k being equal to u infinity, so rate of growth of momentum thickness is equal to a constant minus another constant times delta 2 square by nu du infinity by dx. This is a Thwaites curve fit, a universal curve fit for the case in which suction and blowing are absent. We will make use of this relationship as you will see on the next slide. So just see, this was the relationship. I can manipulate this two terms, this term and this term as d by dx of du delta 2 square u infinity 5.7 equal to 0.44 nu to convince you. Let me open up again the equation. Then you will see d delta 2 square u infinity equal to 5.17 by dx will equal delta 2 square into 5.17 into u infinity raise to 4.17 du infinity by dx plus u infinity raise to 5.17 into d delta 2 square by dx. This is what it would mean. Therefore, if I divide this 1 over nu u infinity by raise to 4.17, I will get 5.17 into delta 2 square by nu du infinity by dx plus u infinity square by nu d delta 2 square by dx. That is equal to 0.44. Therefore, you will see that I can write this equation in this form. If I were to integrate this equation from 0 to x, then delta 2 square u infinity raise to 5.17 at x will equal delta 2 square u infinity raise to 5 by x equal to 0 equal to 0.44 nu 0 to x u infinity raise to 4.17 dx. The solution is applicable to any arbitrary variation of u infinity and restriction imposed by similarity method is now removed. We use this relationship to calculate delta 2 at any x because u infinity at that x will be known. Of course, you must know delta 2 square at x equal to 0. If you start from x equal to 0 itself where delta 2 is 0, then of course, that term will be 0. Evaluate kappa from du infinity by dx. Now that you know delta 2 square, you can now evaluate our kappa which is… Once you have evaluated delta 2, you can now evaluate delta 2 square nu du infinity by dx because you already know what u infinity x is. For this value of kappa, you can evaluate s value. If you are knowing the kappa value, you can interpolate to get s value. You get a shear stress value from which you can evaluate s and delta 4. From delta 4, you can evaluate the skin friction coefficient to nu over delta 4 u infinity which is what we wish to evaluate anyway. That is the purpose. In other words, knowing u infinity as a function of x, we get delta 2 as a function of x from which we get kappa from which we get s as a function of x. In fact, we get all other parameters delta 1 as a function of x and so on and so forth because we know the shape factor variation with x and we can get C f x also as a function of x. In the previous table, I had held v w equal to the no suction and blowing. Now I am going to set lambda equal to 0 which is the case of a flat plate, but allow for suction and blowing and that is what I have done here. I allow for blowing parameter to go up to 5. On the suction side, I go up to minus 4.2. Delta 1 by delta with blowing compared to v w star equal to 0, the delta 1 by delta increases as we expect. Delta 1 by delta decrease as we increase suction. This also increases. It is not seen here because I have plotted results only up to second decimal place and on this side it reduces, but notice that at minus 4.4 delta 2 has already turned negative and that is not permitted. So, I cannot go below lambda less than minus 4.2. So, feasible solutions are possible only for lambda greater than minus 4.2 as you can see here. The shear stress also has almost vanished here which means this is where separation is about to take place. The shape factor is increased enormously to 47.25 from its average values around 2.7 on the positive side, on the blowing side and on this moderate suction rates, it is about 2.4, but it increases very rapidly to 47.5. This is almost the separation polar profile and these are the values of f k. Likewise, I have now included effects of both lambda and for a certain v w star which is minus 0.2. That means it is a suction case with v w star equal to minus 0.2 and here I have gone up to 15, but notice that beyond 14.8 or so, s has become negative. Therefore, this is not acceptable solution. So, lambda equal to 15 is not acceptable. On the adverse pressure gradient side you will see I have gone up to minus 13, but at minus 12 it is 0 already. So, this is the separation occurs and minus 13 is minus 0.03. So, this is not advisable. So, effect of pressure gradient on at a certain suction state is valid between minus 12 and 14.5 only. The remarkable feature of this solution is that for very mild acceleration to all the adverse pressure gradients, the value of v w plus is almost constant. In this v w plus is almost constant on the suction side. For lambda equal to 0, f k is about 21. You can see that 0.21 and that was equal to delta 2 star square and v w plus equal to minus 0.21. This amounts to v f equal to minus 0.21 divided by root 0.21, 0.458. This is the blowing side and again you will see for adverse pressure gradients less than minus 12 you have negatives. So, you cannot go below that. Again on v w plus is remarkably constant and this will correspond to v f equal to about 0.2619. For simultaneous variations of v w star and lambda, close form solutions can again be developed. In the regions in which v w plus is constant, you can curve it f k equal to a minus b k or a relationship of this type can be established where a and b are functions of v w plus. So, v w star equal to minus 0.2, you get a equal to 0.21, b equal to 4.2, v w star equal to plus 2, you will get 0.84 and 7.4. Manipulation would give again d delta 2 d by dx of this equal to that and therefore, you will get a solution. The procedure remains exactly the same as before. Only the values of a and b change with value of v w star. So, I am taking now a case of flow over a cylinder. It is an impervious cylinder. So, there is no suction or blowing. There is an approach velocity v a. Potential theory will show that the free stream velocity u infinity would vary as u infinity by v a equal to 2 times sin 2 x star where x star is x divided by diameter.  Then for this variation of free stream velocity, I can show that delta 2 by d red will be simply from equation here using this relationship. I can determine delta 2. Remember delta 2 at x equal to 0 at the stagnation point will be 0 and from there I integrate. So, I can show that delta 2 by d red will be that and kappa will be this. Our objective is to determine the location of the separation point corresponding to kappa equal to minus 1567. Red is equal to v a d by nu which is the Reynolds number defined for flow over a cylinder. Here are the results. u infinity by v a is a sin function which goes and beyond 90 deceleration sets in whereas, on the below 90 degrees there is a flow acceleration and this is the variation of kappa and you can see it has reached minus 0.1567 at about 108.3 degrees and therefore, it is associated with separation. So, we have located the separation point from stagnation point from the known velocity distribution arbitrary velocity distribution. Similarly, now consider a cylinder in which there is a blowing taking place from the cylinder surface. Then I can curve it as I said f kappa in this manner for different values of v w star and theta separation what v w star equal to 0 was 108 and that goes on reducing. You will expect that a flow over a cylinder with blowing would the separation would occur at an earlier location and that is what you see up to v w star at point 2. The separation point has advanced. Average skin friction up to the separation point defined in this manner of course, is highest at v w star equal to 0, but with blowing skin friction was on reducing. So, as expected separation angle is advanced with increase in blowing rate with reduction in average skin friction due to thickening of the boundary layer. This shows you the power of the integral method. Of course, what it cannot do is to go beyond the point of separation and complete the analysis of flow over a cylinder, but nonetheless it is a very useful tool to determine flow through conversion or diversion nozzles. For example, where the boundary layer where the free stream velocity would either accelerate or decelerate with x and you want to determine the thickness of the boundary layers developing on the wall, because it is this thickness which determines the discharge coefficients of such nozzles.


YouTube all right out at the airport actually remember when I used to come out here for uber not anymore Today I came out to drop to love off. She is headed to New York City to see her sister. So safe travels on and The reason I filmed that blue horse. I don't know if you this I don't know if you remember if you even seen this video But basically the second most popular video now on the vlog is all about that blue horse And the reason is is not necessarily because of the content But because of the title I knew the vlog was gonna be go check it out. Go check it out upper right hand corner I knew it was gonna be a successful video because of the title and So anyway that blue horse has a crazy history crazy story About it. I'm a sad actually but I go check out that vlog. All right. Head back home to work What a day. Oh, it's kind of bright gonna keep these on all right. Love is in New York The boys are with grandpa. I'm home alone Working from the house, but taking a little midday break pick some weeds You know get outside in the beautiful sunshine. The rain is gone. Remember the rain And the tree blew over now and the crazy clouds now I digress It's beautiful out now. So I'm gonna take advantage for maybe 15 20 minutes pick some weeds out here And that is that folks nothing too exciting just pounding ground on a Thursday So I'm excited for the weekend. I must say that much. Oh, I hope you guys having a great day. Let's go 615 p.m. And No one's at the house except for me What do I do? What do I do? What do I do? Is that the question today? What are you doing your family's out of town? I don't even know it's like I don't even know what to do. There's too much time on my hand. Just kidding. I'm gonna do a lot I'm gonna work on the yard Work on the dishes Work on the toys, you know, there's always something to do. There's always but first dinner cop salad try need healthy try need healthy everybody going for the salad over the you know the pasta or the What else we got up here hash browns for the salad I forgot to snap at the beginning I forgot to snap at the big I did not want to pick this out of the ground and put it in the shed where it's supposed to be No, because guess what? I'm gonna use it tomorrow but that's a small thing a small little action where you kind of deny yourself of The slothfulness of just letting your stuff lay out. It could rain tonight. It's not gonna but it could in theory It could rain, you know and this tool, you know, it shouldn't get too wet or else it'll rust and it'll wear and tear All I'm saying is is like I'm trying and you're probably trying to and this is definitely the question of the day. How do you? How do you? Accomplish like the little tasks that seem so meaningless, but at the end of the day have so much impact When you add them all up all the little decisions make every single day and then they add up to big decisions So how do you make those decisions? What goes through your mind? What goes through your heart? I don't know. I know this is a little philosophical for a weed picker, but Work with me here. Work with me here. All right Let's put it away ladies and gentlemen Seek beauty like we're doing right now I'm losing my mind. I'm losing my mind. I don't even know if I talked about this in yesterday's blog I can't I can't remember, but I'm gonna repeat it. Why not? There's still good in this world. There is still good in this world still great people Good good people in this world. How do I know that? Remember in that vlog up there The tree blew over our neighbor's tree blew over. Well a couple days ago. I Walk out to my front yard and I look over at the tree and The tree is not there. Why is the tree not there because it's been cut up into little perfect pieces with a chainsaw By our other eight neighbor by our other neighbor So it's like our neighbors are looking out for each other and guess what that's what I think we should do as neighbors Look out for each other even if what? All right. What if I did not upload tomorrow? Or the next day I I would hope I'd hope that Somebody would be like wait a minute stuff didn't upload wait a minute and guess what for all you other youtubers I know when you're not uploading. I know Bobby oh All right, I know when you're not uploading and I'm like thinking about you guys me like what are you guys doing? Where you at? What's up? So I digress all I'm saying is there's still good in this world. Keep fighting I'm not just borrowing that line from Frodo. Come on. It's real. It's real and Our neighbor cutting up our other neighbor's tree without even asking just going over and doing it for the person is amazing work hard


What you snackin' on, babe? Some pistachios. What are those good for? They're good in potassium. It's good for pregnant ladies and hungry fishermen, outdoorsmen. This stool, it's good for pregnant people. This is my kitchen stool, it's my makeshift. Let's just back out for a second. Let's keep backing up. This is how we're starting this vlog. Yes, my feet are burning up, sweetheart. I'm going to stand over here in the shade. Welcome to today's vlog, y'all. First of all, I just want to say thank you for everyone that tuned in on the last one. Moving out of the parent's house. A massive monumental day in our lives. How long was that? Five months? Yeah. We lived with our parents, with my parents for five months. The reason is because we had to at first find a home and then had all the stuff going on with Willis and then pregnancy. It was a crazy time. We wanted to move before Willis and be settled into a house and then start the pregnancy process, you know what I'm saying? But life comes at you fast and here we are now. Stephanie is due September 14th. You are correct. Boom. So we're a ways out. Yes, and now it is time to nest. So we are so blessed to have this house. We are absolutely in love with it. We're going to show you around. It is a bit discombobulated right now. Actually, it's a lot discombobulated. We are still moving in. I would have showed you it last time, but it was just crazy. There was nothing in there. It was just boxes. So now it's time to show you guys around a little bit. Now that we've gotten the boxes settled in, gotten the room settled up a little bit, welcome to the treehouse. All right, let's get into the tour here. The reason that we wanted to get this particular house, it really mixes the two things that we love the most. We wanted to have a place that we can raise our baby and something that just mixes both of our worlds that we love. And that's that's the outdoors for me. Stephanie loves the outdoors as well. Cooking, dietitian, she wanted a decent kitchen. So like it took so, so long to find a combination of that because I will basically live straight up in the woods. I need a little bit of internet, but other than that, I'm just, I'm happy with a cabin out in the woods. So this is a combination of both. So let's step on into the treehouse now and y'all let me tell you, it definitely is a treehouse. When you look around the entire home, it's just nothing but trees when you look outside. OSG, I just want to come home every day and just smell the sweet smells of whatever's going on in here. Of the home cooking. We'll start out with the kitchen, your domain. My domain. Well, welcome to my... Much more room now. Yeah, much more room, got plenty of play. I wouldn't know I was unboxing. I don't even know how I fit everything in our own kitchen. I don't know how you do either. Now, she's got lots of cabin trees and pantry and all that stuff. You guys are going to be seeing some pretty, pretty amazing recipes and food stuff out of OSG. This is my favorite, favorite thing. Look, it's a spice rack. She got her spice rack. Spice rack. Getting fast. So while I'm cooking over here, I can just reach over here and grab some spices. It's a little dark in here. It is a little dark. I already got my baking section set up. This is what I was talking about. Making cinnamon rolls. Yes, we talked about it in the last video. Pretty much every special occasion we've had in life, we like to do cinnamon rolls when it's a special time. We only do them a few times a year. And now is that time. So cinnamon rolls are being made. We're going to fill this house with a sweet smell of cinnamon rolls. The dough is actually rising over there. Look, let's take a look at that. Let's take a little gander. What does that look like? That just looks like a pile of putty right now. It'll turn into something good. Just saying that's probably the main reason we got this house because it's a combination of your kitchen needs and my need for the woods. When you step out of the kitchen, you're basically right in the living room, which it's kind of a small space, but we're not huge TV watchers. So it's not going to be a big deal. This is our old couch from the old house. It doesn't really fit this space. Obviously stuff is not, this is not how it's supposed to be. You don't have tripods and all boxes and everything. That is kind of, yeah, you're used to seeing that, huh? No comment. Okay. Got a couple more projects I'm going to be working on. On this deal. And if you remember Stephanie's office, it's kind of, it kind of looks the same as far as like the way she had it, but a little bit more space for her in here. She is a dietitian certified now by the state of Texas. So she's been doing her practice. You're still open for business, right? I'm still open for business. So she's been doing her deal working. And this right here is going to be baby's room. Baby's room who you do not know the name of yet. But we already got some, some pampers rolling in. And I'm going to go ahead and say the baby has a great room. Baby has probably the best room in the house when you look out. It's just trees. Look at all that tree-ness out there for baby. He or she is going to be looking at lots of birds, lots of wildlife and that's the reason I love it. Because I get to just stare at nature every day. By the way y'all, we are planning gender reveal video as we speak right now. We're going to do it on this channel. So you can check that out very soon. I'm not going to show you the boarding bathroom stuff. You know, this is just to get the general gist of the house and why we like it and why we're here and everything. This isn't like MTV Cribs or anything. But this room up here on the upstairs is really I think everyone's favorite room. My parents live really close to here. One of the reasons we wanted to move right here is because it's so close to my mom and dad. And for raising our family really helps to have family close. So this is actually my mom's favorite room. This is going to be my favorite room when we get done. It just looks out over the trees. This is kind of how it is around the whole house.  But there's basically nothing in here right now. I've been doing my editing over there. We're going to put deer heads up on the walls. Yes, we are. This is going to be like the little...  Hold baby. Look at the deer heads. Look at the ducks. Maybe some fish up here on the walls. And read some books about like survival or how to call in deer in the woods, something like that. And then we got our bedroom. It's a bedroom, whatever. Then we also have a little deck out here. This is why we call it the tree house, y'all. Keep saying that, but it's for real. This is on the third deck right here. See how far down that is. And you can actually see the lake. The trees are really growing in right now, but the lake is right over there. We'll be able to get down to the water pretty quickly. We're going to be doing a bunch of videos down there. Probably don't want to mess around up here too much. It's a pretty steep fall, but it is a really awesome look at the trees, all the nature. Got the birds and squirrels coming up here. I really like this space because I could just come out of the bedroom, get me a cup of free-range coffee, get in tune with nature, get ready to start day, you know, get that nature zen going on. That's what it's all about, man. Enjoying the great outdoors and now it's right out our back door. So it's awesome. So now that I've kind of showed you the boring stuff, I want to show you guys where you're going to be seeing a lot of videos. On this channel is for the fishing cave. You know, I've been talking about the fishing cave. You guys send in so much cool stuff. And I've had, I had a garage at the other house. I could not fit all of your stuff. So now if we go downstairs, it's really dark down here because it's a basement. But this is going to be, don't pay too much attention to what it looks like now because it's going to be transformed into the bass cave. The fishing cave. This is going to be it. It's got a little spare bedroom and stuff like that. There's a bed right here for right now. One of the fishing fruits is going to be coming down. So we got, we got some extra beds and stuff to stay with us. And we already have a little company. If you guys remember my old office, I had my desk in there and I kind of had some mounts and stuff going on with some, you know, I had all my camera gear and all that. That's still going to be the same. We're going to do that over on this side and then this side right here is going to be just totally transformed. This is going to be a huge wood wall. I'm going to do some projects in here. I'm going to take you guys along to show you all that stuff. But fish mounts, we're going to do a bunch of different, just outdoor fishing, hunting, everything outdoors in here.  And I want to get a really cool wooden table and put it right in here and have, you know, my fishing memorabilia there and have you guys' stuff in here, the things that you've sent in and just have an outdoor creation room. So I'll be able to make a lot more videos with a really cool background. It'll be really sweet. So that's going to be a huge project and I'll take you guys along for that. But I'm so excited to have that, you know, in our older house. I just, I didn't have the space to be able to do it. I'll be doing a lot of live streams and extra fun stuff down here. It's going to be full of fish, man. It's going to be a cool fish cave. So right when we step out the door here, this is underneath the deck and then look right here. You guys know what that is. That's a silver bullet. Silver bullet is just right out here on the back doorstep. It just makes it super efficient to be able to make outdoor videos come in there and then everything's just an extension of what I'm doing outside. So just my mind's blown really how perfect this place is. Now I know what you guys are thinking. Where are you going to put all your tackle, dude? Where's that going to go? Well, I think I might have a spot out here. So this is the garage area. We've got a lot of work to do in here. The house actually had some foundational issues and things shifted around. And so there's some walls missing. This is a house that has a lot of character, but it's also had a lot of love put into it. It's unique and it comes with its own little problems, but it's really cool at the same time. So there's just an AC handler just hanging out right here in the garage. Maybe put some sponsor stickers on that. Cover that thing up. You know what I mean? But I think I'm going to make this area over here kind of like regular garage stuff and stuff like that. And then this over here is going to be all the fishing stuff. So I've brought all the racks from home. And I think I'm going to do pegboard up. I still got to finish all these walls. So a lot of projects left to do, but this will be like that tackle cave that you guys were used to seeing in the other garage except bigger. I got so much tackling. So much of it is at my dad's right now. I was like, Dad, let us stay here. I'll give you unlimited tackle, whatever you want. Rods, reels, lures, he gets access to whatever, but he's still got a ton of it. So that's basically it. This is an old lake lodge community. There's a lot of cabins and stuff around here. And we absolutely love it. I think it's so perfect for me and Stephanie and our baby to be able to raise our kid up in the outdoors in the woods. I got so many great memories of just playing in the creeks and climbing trees and all that fun stuff. So it's going to be great. There is a play set already over there. It's going to be a while until said baby is able to play on that. So I'm not sure if we're going to keep that in or not, but it is a pretty nice play set. It's just, it's really colorful. I think it's like crayons or something. Doesn't take very long at all when you start walking through the yard to get deep into the woods. Like I can already tell you we're going to be doing battle with creatures out here, with ants, with bugs, with all kinds of squirrels, possums, raccoons. There's hogs and stuff that live back there. So we will be dealing with that. Should make for some good content though. The rolling has begun. They already smell amazing. I know. They're so delicate. Don't they smell good already? It's incredible. There's nothing better to go into a new house than OSG in the kitchen, making them singiman rolls. Lots of you covered up that baby bump right there. That apron style. Oh yeah. Don't want to get the belly full of power. We're going to be chowing. This is definitely how we're going to be finishing this video. I don't know how long this takes, but in the meantime, I've got a story to tell the fishing breaks. Oh yeah, I haven't told them yet. It's been hell to get to this point, but I know we're supposed to be in this house. My dad actually found it. He was driving around different neighborhoods. You know, he knew we were looking for houses, and this wasn't very far away. He spotted it, and it hadn't gone to the main market yet. And then Stephanie just sees it, and she's like, oh my gosh, I like this, and just walks right on in. And she's like, you guys doing a home tour? And they're like, well, we kind of not really. And she just starts walking in and touring the place. And we're like, man, this has got just the combination of everything we like. It's an older home. And so it was built, I think, the year I was born. So it's pretty old. The couple that had it, they really put a lot of effort into it to make it what it is today. But anyway, we were able to talk to the couple that own the house. And we just automatically had a connection with them. I didn't know how deep that really went until we started talking a little bit more. And then we go to move into the house. I come to find out that they had started watching our videos. They found out about Willis. And the wife, she had a brain tumor as well. And she almost died in a car accident. She had a seizure, like the doctors were saying. I would have if I didn't have my tumor removed. And that's how she found out about it. Right away, we had that connection. And I was like, oh my gosh, you know, this is crazy. Because even before that, they felt like we were the couple that were supposed to move in to this house. So I just know, I feel that we are supposed to be here. I feel like God places here. This is where we're supposed to be. Raise our family and grow this channel. It is amazing to wake up every day and feel that. Right? Absolutely. Why are you standing over there? I don't know. I don't know where you want me to stand. She's acting like this is a solo. You just go in here and do that on the camera. No, I shouldn't be saying that with you right here. This is where we're supposed to raise our family. So we've both had that 100% conviction. And if you also haven't figured out why it's called the tree house, then... We can't help you there. I can't help you. We just time lapsed forward. There was no time lapse. We'll be lapsed forward. We did. Well... Oh my gosh, it smells amazing. Is that icing? That is the icing. Don't burn yourself now. Oh.  Put the icing on when they're nice and hot. So it just melts. Smells like home. It smells like home. This is it now. It does. It's official. My baby making the house feel right. Got to love it. Goodness gracious. Do you have this recipe available? I'm sure people are going to ask for it. Yeah, it's on my blog. It's on the blog. She's an old school kind of girl. She does blogs. So I can have all my recipes up there. But it's there forever. It's out on the internet. You too can make these kind of things, but you got to put some love in it. Man, I can't wait to shout out on that. This is it. You know how you have to break a champagne bottle on a boat, on a ship when it's official? Here at the Rackley household. At the tree house. We make cinnamon rolls to make the house official. So I think this is only going to happen once because I think we're going to be here a really, really long time. But anyway, that's how we did it. Like, hey anniversary cinnamon rolls. Hey, birthday cinnamon rolls. Hey, just caught a nine pounder cinnamon rolls. When was the first time that I made these? Yeah, the first time we were married. Yeah. Yeah, that's only for once. Yeah, it was our first Saturday and we were like, you know what, let's just make those cinnamon rolls. Let's just let's just chill in the new house. Let's soak it in. And it was great. And it really made the house feel like a home. And this, this is what this is. Let's make a house feel like a home. Gonna put a little milk on that right there. Oh my goodness. I'm going to have to go for a nice long walk after this. We're going to grab us a glorious cinnamon roll and LFD and mom, they're on their way over here. They found us a furniture cabinet for three dollars. A furniture cabinet? That's probably what it's called. It's an arm wire. An arm wire. Arm wire. Whatever. However you say that. It's time. It's time. Cinnamon roll dance, cinnamon roll dance. No, go for the center tomorrow. That's key. It's key when you're cinnamon roll eating. You go for the center on the next day. You eat the crusty ones while they're still hot and gooey. Because it continues to cook. Okay. Camera guy back there. Oh, yes. Science. I should bring that up. I know a lot of y'all are crafted well trained. I don't know about trained, but maybe you're just good at crafting things. We've got some amazing stuff. Winston is going to have his own little artwork in this house as well that you guys have sent in. We're looking to keep this place as natural as possible, but also bring out some of the park-like elements that are here. A lot of stuff with wood. I want to do some park signs and stuff like that. So I'll give you more details on that later, but I know some of you guys are awesome. I want to feature some of your work here at the house and give you credit for it. Because I know some of you guys are going to send that in. And we are going to reopen the P.O. box. P.O. box. Can we list it here right now? I don't have the number. But it is open. Will you have it tomorrow? I will have it tomorrow. There's a lot to take in right here. I know this is a big video, but P.O. box is being reopened. Okay. Let's just stick to the cinnamon rolls right now. Uniform throughout there. Ugh. Wow. That's better than the last one. Oh my gosh. I'm a lucky man. Look at the gooeyness. Look at the uniform. Cinnamon-ness throughout. It's perfectly amazing with a glass of milk. Thank you so much, honey. You're welcome. God, those cinnamon rolls were good. Filled me through the rest of the unpacking day. We still got a lot left to do. But it's going well, guys. Can't thank you enough for all the support, all the positivity through this whole entire last year to get to this point right now. Made it. Just feels so amazing. So if you guys want to see more of this, we're going to be doing more cooking, fixing up the house, basically just stuff out here and nature in the woods around the lake. Lake life, basically, yes. Family. Watch us grow the family right here. Subscribe to our other channel now. We just created it. It's the Lake Life family. So go over there and you'll be able to see all the off-the-water stuff, basically. The link will be in the description for the new channel, the PO Box. And actually right here as well. Go click on it. Right here. It's right there. Lake life. Family. Go do it. And we're so excited to just be in the outdoors. Can't wait to bring you more action from here. Raise our family here. We love you guys. Thank you for tuning in. We hope you subscribe to the other channel. And we'll see y'all on the next one. Look at our trios!


Hello everyone welcome back to another After Effects tutorial. This one I'm going to show you how to time remap or speed ramp in just about 30 seconds here. What is it? Well let me just show you here the original video. Here's footage and if I hit play we've just got this lady kind of swimming in the ocean doing her thing. She's going to dunk her head under. Great no big deal now if we look at what I've done here if we go to the new version you'll see here that what's a 21 second clip has now been sped up to about three seconds and then it just stops just like that. How did I do it? Let me show you from scratch. Okay take the video whatever you're going to use put it on your timeline. Excellent next step right click on it and you want to go to time enable time remapping. Here's the critical part you now want to go ahead and determine what part of the video you want to speed up. So if I want this whole video to be three seconds long even though it's a 20 second video I'd go to like the three second mark somewhere around here something like that I'd grab this key frame move it in click it on there and now watch when I hit space bar zip zip zip zip all of it's done in three seconds. Now if I wanted this to be different I would move this out and let's say I wanted parts of the video to go fast parts to go regular speed parts to go slow I would just go over here and click add key frame as I see fit maybe this frame is where I want her to have another change in speed and right when she goes in the water right about here I want to change some speed and then what you got to do is all you got to do is you just have to move these key frames as you see fit so if I want to speed all of this part up I would just go ahead and start moving these key frames over to the left side so that each one of these is sped up and now this one I would move way out here to be slow let me show you what I got fast fast slow motion I'm just doing this through key frames through time remapping speed ramping that's all there's to it guys thanks for watching ton more stuff coming out


this person, does this artist, Shaky Grace for example, he has a song in the film, he's fantastic. The song was presented to me, I didn't love as much as the one I clicked on next and I said this is the one we need to put in the film, we need to go get this. And we had a budget for music and we were very lucky, we got the Revivalist for good and sake, I mean one of the hottest bands around. The music's fantastic. The music's fantastic. Really fantastic. And it really, I think it helps to tell the story of the movie too, it's not just music for the sake of music.