A laminar flow occurs between two horizontal parallel plates under a pressure gradient dp/ds (dp/ds is a constant and the sign of dp/ds is negative.). The upper plate moves left with a speed ut. The expression for local velocity u is given as

a. Is the magnitude of the shear stress greater at the moving plate (y = H) or at the stationary plate (y = 0)?

b. Derive an expression for the y position of zero shear stress.

c. Derive an expression for the plate speed ut required to make the shear stress zero at y = 0.

1 dp -(Hy y') u, u = 2 ds H