### Darcy Equation Fluids Flow Equation

**Fluid Flow Table of Contents**

Hydraulic and Pneumatic Knowledge

Fluid Power Equipment

*Darcys Equation Fluids Flow Equation
- also called Darcy–Weisbach equation. *

In fluid dynamics , the **Darcy–Weisbach equation **is a phenomenological equation, which relates the head loss — or pressure loss — due to friction along a given length of pipe to the average velocity of the fluid flow.

The Darcy–Weisbach equation contains a dimensionless friction factor, known as the **Darcy friction factor **. This is also called the **Darcy–Weisbach friction factor **or **Moody friction factor **. The Darcy friction factor is four times the Fanning friction factor , with which it should not be confused.

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

where:

f = friction factor (unitless)

L = length of pipe (ft)

D = diameter of pipe (ft)

v = fluid velocity (ft/sec)

g = gravitational acceleration (ft/sec^{2})

Example: Darcys Head Loss Equation

A pipe 100 feet long and 20 inches in
diameter contains water at 200F flowing at a mass flow
rate of 700 lbm/sec. The water has a density of 60 lbm/ft^{3}
and a viscosity of 1.978
x 10^{-7}
lbf-sec/ft^{2}.
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 Darcys equation to determine the head loss.

Use the Moody Chart for a Reynolds number of
8.4 x 10^{7}
and a relative roughness
of 0.00008.