In regions far from the entrance, fluid flow through a circular pipe is one dimensional, a...

In regions far from the entrance, fluid flow through a circular pipe is one dimensional, and the velocity profile for laminar flow is given by u(r) = u_max(1 − r²/R²), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and u_max is the maximum flow velocity, which occurs at the center. Obtain (a) a relation for the drag force applied by the fluid on a section of the pipe of length L and (b) the value of the drag force for water flow at 20°C with R = 0.08 m, L = 30 m, u_max = 3 m/s, and μ = 0.0010 kg/m·s.