What is the difference between Fanning and Moody friction factors?

Which is a correct equation of head loss, Equations 1 or 2?

hL = 4fLV2/2gD         (Equation 1)
hL = flv2/2gd         (Equation 2)

Equation 1 is applied Fanning equation and Equation 2 is applied Moody equation. For old books and tutorial, they like to use the Fanning equation. But, the recent books, they love to applied Moody equation. 😉

A good explanation for this issue as follows (source):

What is the difference between Fanning and Moody friction factors?

Many folks calculate 4 times greater head loss (or 4 times less) than the actual friction loss. This comes from confusion between Moody and Fanning Friction factors. Some friction factor graphs are for Moody Friction factor, which is 4 times Fanning friction factor. That is, f = 64/Re is Moody and f = 16/Re is Fanning.

Be careful with your hydraulic calcs. It is easy to mix the two and calculate 400% greater (or 25% less) head loss. The calculation for head loss in feet is:

using Moody Friction factor -
 h(friction) = f(M) * (L/D) * v^2 / (2 * g)

using Fanning Friction factor -
 h(friction) = 4*f(F) * (L/D) * v^2 / (2 * g)

where,
 h(friction) = head loss by friction in feet
 f(M) = Moody Friction factor
 f(F) = Fanning Friction factor
 L = length in feet
 D = pipe inside diameter in feet
 v = velocity in ft/s
 g = 32.174 ft/s^2, acceleration due to gravity

The Colebrook-White equation is an iterative method that calculates Fanning friction factor.
 f(F)^2 = 1 / ( -4 * Log(eps / (3.7 * D) + 1.256 / (Re * √f(F) )

where,
 eps = pipe roughness in feet
 Re = Reynold's number
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