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: usingMoodyFriction factor - h(friction) =f(M)* (L/D) * v^2 / (2 * g) usingFanningFriction factor - h(friction) =4*f(F)* (L/D) * v^2 / (2 * g) where, h(friction) = head loss by friction in feetf(M)= Moody Friction factorf(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 TheColebrook-Whiteequation is an iterative method that calculatesFanningfriction 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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