Energy Loss due to Friction (in turbulent or laminar flow)

The Darcy-Wesibach equation can be used in either turbulent or laminar flow (this will be factored into the variable f).

Below you will find the Darcy equation:

h_L = {{fLv^2}\over {2Dg}}


hL = Total head loss
f = Darcy friction factor
L = Length
v = Velocity of fluid
D = Diameter of pipe
g = Gravitational acceleration

Note: These equations will work as long as you keep your units straight. That way you can use either SI or US as long as you keep everything in order. Your hL should end up in units of length (e.g. feet, meters, etc.)

How to solve for the Darcy fluids friction factor:

A complete explanation of the Darcy friction factor can be found here. This section will sum up how the friction factor can be found in a majority of situations. A friction factor (f) of a pipe is not a constant value, but will decrease as the Reynolds number (Re) increases (up to a certain point; obviously friction exists in any system).

For Laminar Flow (Re < 2100):

f = {{64}\over {Re}}

For Turbulent Flow (3000< Re < 100,000):

f = {{0.316}\over {Re^{0.25}}}


Note: In situations where Re falls between 2100 and 4000 (an area between laminar and turbulent flow) eddies will be present which cause critical flow. It is difficult to design for this region since fluid behavior is not consistent.

Other Variations of the Continuity Equation:

Solve for head loss:

h_L = {{fLv^2}\over {2Dg}}
Solve for friction factor:
f = {{2h_LDg}\over {Lv^2}}
Solve for pipe length:
L = {{2h_LDg}\over {fv^2}}
Solve for pipe diameter:
D = {{fLv^2}\over {2h_Lg}}
Solve for flow velocity:
v = \sqrt{{2h_LDg}\over {fL}}
Solve for gravitational acceleration:
g = {{fLv^2}\over {2h_LD}}


  1. To be inserted.



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