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Darci's
Equation - Fluid Flow
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[ Fluid
Flow Table of Contents]
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:
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: 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 10 7
and a relative roughness
of 0.00008.
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