Example: Darcy's Head Loss Equation

A pipe of 100 feet long and 20 inches in diameter have water at 200°F flowing at a mass flow rate of 700 lbm/sec. The water contains a density of 60 lbm/ft³ and a viscosity of 1.978 x 10^-7 lbf-sec/ft². Relative roughness of the pipe is 0.00008. Compute the head loss for the pipe.

Solution:

The series of steps essential to resolve this problem is initially to determine the flow velocity. Secondly, by using the flow velocity and the fluid properties given, compute the Reynolds number. Thirdly, establish the friction factor from the Reynolds number and the relative roughness. Lastly, employ Darcy's equation to establish the head loss.

m = ρAv

v = 5.35 ft/sec

By using the Moody Chart for a Reynolds number that is, 8.4 x 10⁷ and a relative roughness of around 0.00008.

f = 0.012

H_f = 0.32 ft