In regions far from the entrance, fluid flow through a circular pipe is one-dimensional, and the velocity profile for laminar flow is given as u(r) = umax(1 - r^2/R^2), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and umax is the maximum flow velocity, which occurs at the center. Obtain the following:
A relation for the drag force applied by the fluid on a section of the pipe at length L
The value of the drag force for water flow at 20°C with R = 0.07 m, L = 35 m, umax = 4 m/s, and μ = 0.0010 kg/m·s