Colebrook Friction Loss Formula for Round Ducts

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Colebrook Friction Loss Formula for Round Ducts

Fluids Engineering Table of Contents
Hydraulic and Pneumatic Engineering

In the region of laminar flow (Reynolds numbers less than 2300),the friction factor is a function of Reynolds number only. For completely turbulent flow (fully rough), the friction factor depends on duct surface roughness and internal protuberances (e.g., joints). Between the bounding limits of hydraulically smooth behavior (laminar flow) and fully rough behavior is a transitional zone where the friction factor depends on both roughness and Reynolds number.

In both the transitional and fully rough regions (see Moody diagram ), the friction factor f is calculated by Colebrook’s equation (Colebrook 1938-1939).

Because Colebrook’s equation cannot be solved explicitly for f, use iterative techniques to determine f (Behls 1971).

Eq. 1
1/ f^1/2 = -2 log [ 12 ε / ( 3.7 D_h ) + 2.51 / ( Re ( f^1/2) ) ]

Reynolds number (Re) is calculated using the following equation.

Eq. 2
Re = D_h V / ( 720 v )

For standard air and temperature between 40 and 100°F, Re can be calculated by

Eq. 3
Re = 8.50 D_h v

Eq. 4
D_h = 4 A / P

Where:

ε = material absolute roughness factor, ft
D_h = hydraulic diameter, in
A = duct area, in²
P = preimeter of cross section, in
Re = Reynolds number,
V = velocity, fpm
v = kinematic viscosity, ft²s.
f = Darcy-Weisback Friction Factor

Reference:

ASME Code for Pressure Piping, B31.5, Refrigeration Piping and Heat Transfer Components