a. The volume flow rate for flow through an annulus is found by integrating the velocity profile…

a. The volume flow rate for flow through an annulus is found by integrating the velocity profile over the cross section: Q = ? 0 2p ? ?R R Vz rdrd? b. Substitute the velocity profile for laminar flow through an annulus, namely, Vz = ? ? ? – ? dp dz ? ? ? ? R2 4µ ? ? ? 1 – ? ?? ? ? r R 2 – 1 – ?2 ln(?) ln r R ? ? ? ? laminar flow annular duct into the volume flow rate equation and integrate. Show that Q = ? ? ? – ? dp dz ? ? ? ? pR4(1 – ?2) 8µ ? ? ? 1 + ?2 + ? 1 – ?2 ln(?) c. With the average velocity found with V = Q A show that V = ? ? ? – ? dp dz ? ? ? ? R2 8µ ? ? ? 1 + ?2 + ? 1 – ?2 ln(?)