Consider the flow of a fluid with viscosity μ through a circular pipe. The velocity profile in the pipe is given as u(r) = u_max(1 - rⁿ/Rⁿ), where u_maxis the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; and u(r) is the flow velocity at any position r. Develop a relation for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of the pipe.

Transcribed Image Text:

u) = Umax(1- n/R") 'R 'max