A cubic velocity profile was used to model flow in a laminar incompressible boundary layer in Problem 5.12. Derive the stream function for this flow field. Locate streamlines at one-quarter and one-half the total volume flow rate in the boundary layer.

Data From Problem 5.12

Transcribed Image Text:

5.12 A useful approximation for the x component of velocity in an incompressible laminar boundary layer is a cubic variation from u =0 at the surface (y = 0) to the freestream velocity, U, at the edge of the boundary layer (y=6). The equation for the profile is u/U= (y/6)-(y/6), where = cx/2 and c is a constant. Derive the simplest expression for v/U, the y component of velocity ratio. Plot u/U and v/U versus y/8, and find the location of the maximum value of the ratio v/U. Evaluate the ratio where 6=5mm and x 0.5 m.