The velocity profile in fully developed laminar flow of

Question

Question: The velocity profile in fully developed laminar flow of water at 40°F in a 140-ft-long horizontal circular pipe, in ft/s, is given by u(r) = 0.8(1 - 625r²) where r is the radial distance from the centerline of the pipe in ft. Determine

(a) the volume flow rate of water through the pipe,

(b) the pressure drop across the pipe, and

(c) the useful pumping power required to overcome this pressure drop.