 So when looking at the drag characteristics on a cylinder, it turns out that the nature of the boundary layer plays a very big role in the drag coefficient on the cylinder. So what I'm going to do is draw two different cylinders, one with the laminar boundary layer and the second one with a turbulent boundary layer and then we'll look at the drag coefficient and the characteristics. Okay, so what we have drawn here, on the left we have a cylinder that has a laminar boundary layer forming from the front stagnation point and then the cylinder on the right, we have a boundary layer that becomes turbulent and so it could become turbulent due to the Reynolds number. It could also become turbulent if you were to put surface roughness on the front of the boundary layer. Again, that would depend upon the Reynolds number of the flow over the cylinder, but if you have the turbulent boundary layer, it will have an impact upon the separation characteristics from the body and so if you recall, we had the lecture about how pressure gradients are very important to the performance of boundary layers and you can have either favorable or adverse pressure gradients. In this case, you would have an adverse pressure gradient on the cylinder and so the flow in the laminar boundary layer has less energy, I guess you could say, or less momentum right along the wall region and consequently you get to the zero shear point earlier than you would with the turbulent boundary layer, which is what we have on the right. So the implication of all of this for drag characteristics, if you look at the drag coefficient for a cylinder with a laminar boundary layer, the drag coefficient is 1.2. Now if we look at the drag coefficient of a cylinder with a turbulent boundary layer, the drag coefficient is much lower at 0.3 and the reason is because the boundary layer is energized and it's able to make it past where it would normally separate and continue on the body and then it separates aft of the 90 degree point and that results in a narrower wake, a lower form drag and so that is a characteristic of the cylinder and so I just want to make a comment about that. So what happens, we have less drag due to the fact that the boundary layer is energized when it is turbulent and this is actually, I'm sure you're aware of this, if you're not, it's the reason why golf balls have dimples in them and what the dimples do is they cause the boundary layer to transition and when it transitions it goes from laminar to turbulent and so it would be the dimples on the front of the ball that are the ones that are causing the effect but it's basically surface roughness and that causes the boundary layer to become turbulent and consequently the separation is much further downstream than it would be if you had a laminar boundary layer on the golf ball and this causes the golf ball to travel much further than if you had the laminar boundary layer on the golf ball so that's something that we use for those of you who are avid golfers, you can now explain to your golf partners why the golf ball travels as far as it does so when there we have something from sports that can be applied to fluid mechanics now what I'm going to do in the next slide here is I'm going to plot the pressure distribution around the cylinder and that will provide a little bit more information in terms of why this process is occurring okay so what we have there I've drawn on an inviscid pressure distribution so we have CP plotted in the vertical here and that is the pressure with respect to the free stream pressure theta is the angle with respect to the free stream velocity going from 0 to 180 degrees so we're going from the leading edge over to the back of the cylinder 90 degrees would be up here and I plotted in the inviscid pressure distribution inviscid would be what you would get out of potential flow and we haven't done that in this course but you would basically do superposition of elementary solutions and then put them together and they satisfy you use the Laplace equation for that and you can then compute the flow over a cylinder and so we can come up with an analytic expression for the pressure distribution around a cylinder now in reality what happens no flow is inviscid because inviscid would assume that we have symmetric streamlines going around like that which we don't because we have separation now in the case of a laminar flow shown in red we have the separation is up around 80 degrees so some place up in here is when you start getting into the separation zone with the boundary layer starts to lift off and then for turbulent flow it would be up a little higher around 120 degrees where you start to encounter separation so again this is just a little bit of a artist conception of a very poor artist conception please do look in your textbook or other things in order to see the pressure distribution on cylinders but the main point is you can see that when you have a turbulent boundary layer it more closely approximates the inviscid characteristic where you have no separation on the cylinder and consequently with lower pressure drag on the back of the cylinder that or lower you don't have as much of a form drag on the back of the cylinder and that reduces the drag coefficient for the turbulent boundary layer so that is flow over a cylinder what we're now going to do we're going to move in and look a little bit at streamlining so streamlining is something that we use in order to reduce the drag on objects and so let's just look at an example so let's assume that we have a cylinder and i'm going to say the thickness is t but it's also the diameter of the cylinder uh the chord sometimes we will use c to denote the length but that is a cylinder so we could say t over c is equal to one and then if we have an airfoil i'm going to try to draw a symmetric airfoil that's not perfect again the thickness would be somewhere here the chord is the length of the airfoil so let's say this airfoil has a t over c of 0.15 NACA 0015 would be an example of something like that uh looking at the drag coefficient we saw for the cylinder uh about 1.2 and if you look at the drag coefficient for NACA 0015 it's actually 0061 significantly significantly less now granted it is thinner uh much thinner than the cylinder but there are other things going on and and mainly what's happening here uh the boundary layer is is very very different on these two bodies obviously especially in relation to where it may separate from the body when you have streamlining the purpose is to cause the flow to go all the way around the body without separating so that's really the goal that we have in drag reduction uh sometimes you do get a little bit of a separation zone down in here now you contrast that to the cylinder and at 1.2 that would mean that we have a laminar boundary layer so we separate around 82 degrees we get this massive wake forming and form drag coming there so what we're going to do next um we're going to take a look at some video clips showing us a flow over different bodies some of them bluff bodies some of them streamline bodies and then we're going to measure the wakes and we're going to compare that to the drag coefficient just to kind of highlight the advantages of streamlining before we do that however i should make the comment that essentially uh a streamlined body for the same frontal area will have a much lower drag coefficient and so that's really one of the main things for streamlining so for the same frontal area drag on a streamlined body is much less okay so let's move on and take a look at the videos so what we start with is flow over a cylinder circular cylinder diameter d we're going to look at any ellipse so here we have an elliptical body thickness 1.15 d so it's thicker than the cylinder and finally this is an aca 0015 it's thinner 0.77 d is the thickness now let's take a look at the wake widths occurring on these bodies so here we have the cylinder wake width i just crudely measure at 2.1 d here is the ellipse wake width about 0.770 thinner than its thickness and then finally the aca 0015 wake width about 0.28 d and and that's a fairly crude estimate uh with just me looking at the video and trying to estimate what those values would be let's write those down and compare them to the drag coefficients for these objects okay so there we have the three objects that we've looked at in the video we had our cylinder wake width we said it was 2.1 times the diameter of the cylinder the ellipse uh wake width was 0.77 times the diameter of the cylinder although it was a thicker body at 1.15 d and finally the aca we estimated the wake width about 0.28 that was a fairly far downstream of the airfoil uh for a thickness that is on the same order of magnitude 0.77 versus the 1 d for the cylinder so looking at the drag coefficients now so we've already seen the cylinder the cylinder has a drag coefficient of 1.2 for the ellipse the ellipse that we looked at has a uh length to thickness ratio of five and with that experimentally those have been determined to be 0.25 would be the drag coefficient so significantly less than what we saw uh with the cylinder and then going to the naka 0015 uh we saw 006 so really really low and and part of this is due to the fact that we have a reduction in the wake width but it's also due to the fact of the nature of the boundary layer forming around the object uh and and consequently the skin friction characteristics that would result but obviously naka airfoils have been designed for high lift and low drag uh always what you're after with those but what this highlights is that uh the width of the weight does have a fairly big impact upon the drag characteristics and and consequently streamlining is used in order to reduce the drag on bodies