Problem 10.1. Assume that a viscous fluid flows in a pipe with a circular cross section of radius

a. Choose the z axis to be the direction of motion of the fluid. Assume that the density of the fluid is constant and that the flow is steady. Starting from the hydrodynamic equations, find the equation relating pressure gradients to velocity gradients in the fluid. Describe what is happening in the pipe. (Note: For steady flow, the velocity is independent of time, but can vary in space. At the walls the velocity is zero due to friction.)