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Pipe Head Loss

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Type:

Input Variable

Units:

%

Symbol:

fh

The pipe head loss is the frictional loss in the hydro pipeline, expressed as a fraction of the available head.

Water (like any viscous fluid) flowing through a pipe experiences a loss in pressure due to friction. We can express this pressure loss in terms of a loss of head, where head is the vertical drop through which the fluid flows. In HOMER, you specify the pipe head loss as a percentage of the available head.

Small high-head, low-flow hydro systems typically experience pipe head losses of between 10% and 20%. With low-head systems, pipe head losses are typically only a few percent.

The head loss percentage is defined in terms of the absolute head loss hl and the total available head h:

equations_head_loss

The Darcy–Weisbach equation can be used to predict frictional losses in a circular pipe:

equations_DarcyWeisbach

where:


 

 

hl

= Absolute head loss due to friction, given in units of length

 

fD

= Darcy friction factor

 

L

= Pipe length

 

D

= Pipe diameter

 

V

= Flow velocity (where Q-dot is volumetric flow rate):

 


equations_pipe_inner_flow_velocity

 

g

= Gravitational acceleration (i.e. 9.81 m/s2)

The Darcy friction factor fD can be calculated several different ways, including the well-known Moody diagram (below) or one of many on-line calculators. For laminar flows (Reynolds number, Re, less than 2300), you can use the following:

fD = 64/Re

The friction factor can vary for transition flows (2300 < Re < 4000), and a number of correlations are possible. The Moody diagram provides a good estimate in this method. For turbulent flows, the Moody diagram is a good reference, or you can compute fD by solving the Colebrook–White equation:

equations_ColebrookWhite

where:

 

 

 

?

= Roughness height

 

Dh

= Hydraulic diameter (inside diameter for circular tubes)

 

graphics_Moody_diagram