For fully developed flow in a pipe the contributions to viscous dissipation are from \(\tau_{r z}\) and \(d v_{z} / d r\). What is the form of the viscous generation term for a fully developed laminar flow of a Newtonian fluid in a pipe? How does it vary with radial position?

Calculate this for

(a) water and

(b) crude oil flowing in a pipe of diameter \(2 \mathrm{~cm}\) at a velocity of \(5 \mathrm{~cm} / \mathrm{s}\).