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.
f = friction factor (unitless)
L = length of pipe (ft)
D = diameter of pipe (ft)
v = fluid velocity (ft/sec)
g = gravitational acceleration (ft/sec2)
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/ft3
and a viscosity of 1.978
The relative roughness of the pipe is 0.00008. Calculate the
head loss for the pipe.
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
Use the Moody Chart for a Reynolds number of
8.4 x 107
and a relative roughness