Concept explainers
A parabolic velocity profile was used to model flow in a laminar incompressible boundary layer in Problem 5.11. 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.
5.11 A useful approximation for the .x component of velocity in an incompressible laminar boundary layer is a parabolic variation from u = 0 at the surface (y = 0) to the freestream velocity, U, at the edge of the boundary layer (y = δ). The equation for the profile is u/U = 2(y/δ) − (y/δ)2, where δ = cx1/2 and c is a constant. Show that the simplest expression for the y component of velocity is
Plot υ/U versus y/δ to find the location of the maximum value of the ratio υ/U. Evaluate the ratio where δ = 5 mm and x = 0.5 m.
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Fox and McDonald's Introduction to Fluid Mechanics
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