Question

The Von Karman Momentum Integral (VKMI): dU can be a very powerful tool for generating approximate solutions for boundary layer problems. Recall that To is the shear stress at the wall, U00 is the free stream velocity, while 0 and are the momentum and displacement boundary layer thicknesses, respectively. consider a laminar zero-pressure gradient flat plate boundary layer (Le, U” is constant), and assume the following mean profile: u=U,0 sin( ) for y for y > δ(x), 6(x), where δ (x) is a nominal boundary layer thickness. Based on this assumed profile: a. Compute το, δ., and θ as functions of U, and δ. [3] b. Use the above expressions for wall shear stress and boundary layer thicknesses in the VKMI to get an ordinary differential equation governing the evolution of δ(x). [1] c. Solve the equation obtained in part b) to yield an expression for 5(x). You can use the initial condition 80 atx0. [1 Compare your estimates for το (x), δ. (x), and θ(x) obtained via the procedure above with those obtained via Blasius' full similarity solution. [1 d.

Answer 1