A large open tank discharges water (ρ = 998 kg/m³, μ = 1.00×10⁻³ Pa·s) through a 40.0 m…

A large open tank discharges water (ρ = 998 kg/m³, μ = 1.00×10⁻³ Pa·s) through a 40.0 m length of 50 mm inside-diameter pipe to the atmosphere. The free surface in the tank is 6.50 m above the pipe exit. The line contains a sharp-edged entrance (K = 0.50), two regular 90° flanged elbows (K = 0.30 each), a fully open globe valve (K = 10.0), and a submerged-free exit (K = 1.00). A Moody evaluation at the expected Reynolds number gives f = 0.023. Using Darcy–Weisbach plus the stated minor-loss coefficients, determine the exit velocity and the volume flow rate.

Energy from the free surface to the discharge: elevation equals Darcy–Weisbach plus all minor losses, including the exit.