I just need help understanding this math. I'm unsure of the math behind the integral and how they got the final relation for momentum thickness "=-cos(pi/2*y/delta)*(2*delta/pi)...."
I just dont understand how they're integrating the sin^2 term in the momentum thickness equation. It's integration, I thought the exponent in the sin^2 should get higher??? Pls help, I'm just trying to learn the process and move on.
Analysis
First, we set U(x) = V = constant for a flat plate. We integrate using the definition of *
ay=[y+o]
We integrate only to y = &, since beyond that, the integrand is identically zero. After substituting t
limits of integration, we obtain * as a function of &,
* =0.36348
Similarly,
2T
where we obtained the integral for sin? from integration tables. After substituting the limits
integration, we obtain as a function of &
20
0 = 0.13668
The ratios are */S = 0.363, and 0/5 = 0.137, to three significant digits. We compare the approximate results to those obtained from the Blasius solution, i.e., */S= 1.72/4.91 = 0.350, and / 0.664/4.91 = 0.135. Thus, our approximate velocity profile yields */Sto less than 4% error, and 0/S
about 1% error.