A Bingham plastic is a fluid in which the stress \(\tau\) is related to the rate of strain \(d u / d y\) by

\[ \tau=\tau_{0}+\mu\left(\frac{d u}{d y}\right) \]

where \(\tau_{0}\) and \(\mu\) are constants. Consider the flow of a Bingham plastic between two fixed, horizontal, infinitely wide, flat plates. For fully developed flow with \(d u / d x=0\) and \(d p / d x\) constant, find \(u(y)\).