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. ðŸ˜‰

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 * âˆšf(F) )
where,
eps = pipe roughness in feet
Re = Reynold's number

## About zulkarnainh

I was born in Melaka (1987), holds the degree in B.Eng.(2010), M.Eng (2012) and Ph.D. (2016) in Civil Engineering at Universiti Teknologi Malaysia. I have been the UniMAP since 2016 and currently serving as Senior Lecturer. Feel free to contact me if you are interested to collaborate or pursuit a study (Master or Ph.D.) with me. Thank you!