Darcy’s Equation

The frictional head loss can be calculated using a mathematical relationship that is known as Darcy’s equation for head loss. The equation takes two distinct forms. The first form of Darcy’s equation determines the losses in the system associated with the length of the pipe.

where:

Example: Darcy’s Head Loss Equation

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

Solution:

The sequence of steps necessary to solve this problem is first to determine the flow velocity. Second, using the flow velocity and the fluid properties given, calculate the Reynolds number. Third, determine the friction factor from the Reynolds number and the relative roughness. Finally, use Darcy’s equation to determine the head loss.

Use the Moody Chart for a Reynolds number of 8.4 x 107 and a relative roughness of 0.00008.