Let us assume a liquid film over an horizontal solid plate. the flow, with constant thickness ℎ and subject to the gravity, is driven by a constant shear stress at the top surface: �[\(ℎ) = �. assume that the liquid film is thin enough and flat and that the flow is fully developed with zero net flow rate. determine the velocity profile �(�) and the pressure gradient ��/��.

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?