A fluid flows between two plates separated by a distance, \(d\). The velocity profile is measured, and the data can be fit to the following function. The fluid viscosity is a constant, \(\mu\), and the system length is \(L\).

\[v_{z}(x)=C_{1}(x-d)+C_{2}(x-d)^{2}+C_{3}(x-d)^{3}\]

a. Determine an expression for the pressure drop \((d P / d z)\) driving the flow.

b. What is the force exerted on the fluid at \(x=0\) ?