Chapter 14, Problem 51GP

& (a) Show that the work W done per unit time $\mathrm{**\#x0394;}t$ by viscous friction in a fluid with a flow rate Q across which there is a pressure drop $\Delta P$ is

$\frac{W}{\Delta t}=\Delta PQ=Q^{2}R=\frac{\Delta P^2}{R}$ where $R=8\eta l/\pi r^4$ is called the flow resistance of the fluid moving through a vessel of radius r. (b) By what percentage must the work per unit time increase if the radius of a vessel decreases by 10% and all other quantities including the flow rate remain constant (the pressure does not remain constant)?