# Friction Factor Expressions - Implicit and Explicit

Written by quark:

Friction factor is calculated, generally, by any one of the three implicit equations of Colebrook. The equation, I use, is of the form:

1/(f)1/2 = -2.0log((e/D)/3.7 + 2.51/Re(f)1/2)

Note: This is applicable for Re>3000. For laminar flows, Re<2100, Poiseuille’s law (f = 64/Re)is used

Engineers, who think that it is difficult to solve this equation, use Moody’s chart to get values of ‘f’. But, you will find out how easy it is to solve the implicit equation by some simple calculations in Excel.

To make our life easier, some great engineers developed explicit expressions for the friction factor. As I went on reading the subject, I came to know that there were many explicit expressions. Out of those, the following are the famous equations.

Serghides Equation (for Re>2100 and any e/D)

• f = [A – [(B-A)2/(C-2B+A)]]-2
• A = -2.0 log((e/D)/3.7 + 12/Re)
• B = -2.0 log((e/D)/3.7 + 2.51A/Re)
• C = -2.0 log((e/D)/3.7 + 2.51B/Re)

Moody Equation (4000<Re<107 and e/D <0.01)

• f = 5.5x10-3(1+ (2x104e/D + 106/Re)1/3)

Wood Equation (Re>4000 and any e/D)

• f = 0.094(e/D)0.225 + 0.53(e/D) + 88(e/D)0.44 x Rea
• a = -1.62(e/D)0.134

Jain Equation (for 5000<Re<107 and 0.00004<e/D<0.05)

• 1/f1/2 = 1.14 – 2.0 log (e/D + 21.25/Re0.9)

Churchill Equation (for all values of Re and e/D)

• f = 8((8/Re)12 + 1/(A+B)1.5)1/12
• A = (-2.457ln((7/Re)0.9 + 0.27e/D))16
• B = (37530/Re)16

Chen Equation (for all values of Re and e/D)

• 1/(f)1/2 = -2.0log((e/D)/3.7065 – 5.0452A/Re)
• A = log((e/D)1.1098/2.8257 + (5.8506/Re0.8981))

Zigrang and Sylvester Equation (for 4000<Re<108 and 0.00004<e/D<0.05)

• 1/(f)1/2 = -2.0log ((e/D)/3.7 – 5.02A/Re)
• A = log[(e/D)/3.7 – (5.02/Re)log((e/D)/3.7 + 13/Re)]