In fully-developed laminar pipe flow, consider the rate of work done on an annulus of thickness dr (hint: consider, for each face of the annulus, rate of work = power = force × velocity).

(i) Find an expression for the power (per unit volume) dissipated by the flow in the fluid annulus, and show that it is equal to µ(du/dr)

(ii) By using u(r) from 3(ii) above, and integrating this expression, show that the power dissipated across a length of pipe is Q∆P