Consider the same flat plate boundary layer as described in Problem 4.64. Along each strea...

Consider the same flat plate boundary layer as described in Problem 4.64. Along each streamline within the boundary layer, there is a loss of total pressure due to frictional dissipation. Assume that the velocity profile across the boundary layer is given by

where Ve is the velocity at the edge of the boundary layer, equal to the freestream velocity. (Note: The velocity profile given here is only a crude approximation in order to have an analytic expression to use in this problem. Do not use it for any other application.) Using some of the results from Problem 4.64, calculate the loss of total pressure (per unit span) integrated across the boundary layer at the downstream edge of the plate. Compare your result with the total skin friction drag per unit span exerted on the plate as obtained in Problem 4.64.

Problem 4.64

Consider the incompressible laminar flow over a flat plate of length 3 m at standard sea level conditions. The flow velocity is 100 m/s. For the laminar boundary layer, calculate:

(a) The boundary layer thickness at the downstream edge of the plate.

(b) The total skin friction drag coefficient.

(c) The drag per unit span.