For laminar flow in a pipe, wall shear stress ( 0 ) causes the velocity distribution to

For laminar flow in a pipe, wall shear stress (τ₀) causes the velocity distribution to change from uniform to parabolic as shown. At the fully developed section, the velocity profile is u = u_max[1 – (r/r₀)²]. Derive a formula for the force on the wall due to shear stress, F_τ, between 1 and 2 as a function of U (the mean velocity in the pipe), ρ, p₁, p₂, and D (the pipe diameter).

Transcribed Image Text:

(1) to ro 2