PROBLEM3: Two-dimensional, laminar boundary-layer flow along a flat plate. The boundary- layer velocity profile is for

And for

Find: (a) , (b) , and (c) Total friction force on a plate of length L and width b.

SOLUTION:

For flat plate flow, U= constant, dp/dx = 0, and

.......................................................... (1)

Assumptions: (1) Steady flow

(2) Incompressible flow

Substituting in eq.1

Now,

Therefore

Separating variables gives

Integrating, we obtain

But c=0, since δ=0 at x = 0, so

Or

................................................................... (a)

The displacement thickness, , is given by

Since, from part (a)

then

The total friction force on one side of the plate is given by

Since dA = bdx and , then

Again we know, β=0.137 and , so