Extend Prob. 3.96 to include a linear (laminar) average wall shear stress resistance of the form 8V/D,

Question:

Extend Prob. 3.96 to include a linear (laminar) average wall shear stress resistance of the form τ ≈ 8μV/D, where μ is the fluid viscosity. Find the differential equation for dV/dt and then solve for V (t), assuming an initial displacement z = zo, V = 0 at t = 0. The result should be a damped oscillation tending toward z = 0.