# How to Solve Pipeline Flow Rate Using Colebrook White Equation - Tutorial

## How to Solve Colebrook White Equation - Definition, Formula and Example

### Definition:

The Colebrook White equation is used to find the pipeline flow rate of liquids like water, oil, etc., in smooth and rough pipes.It is also used to estimate the friction factor when the liquid flows in filled pipes.

### Formula: Where, S - hydraulic gradient v - kinematic viscosity of water, D - Internal diameter, Ks - Roughness coefficient, g = Gravity = 9.81 m/s2, A - Area of section. Q - Pipe Flow Rate.

### Example:

Find the Pipe Flow rate, where hydraulic gradient is 4%, kinematic viscosity of water is 0.00000101 m2/s, Internal diameter is 300mm, Area of section is 0.071 m2 and Roughness coefficient is 0.015 mm.

### Given,

Gravity (g) = 9.81 m2/s kinematic viscosity of water (v) = 0.00000101 m2/s Colebrook-White roughness coeff (Ks)= 0.015 mm = 0.000015 m Inside diameter (D)= 300mm = 0.300m Hydraulic Gradient (S)= 4.000% = 0.0400 m/m = 4.000 m/100m = 1:25 Area of section (A) = 0.071 m2

### To find,

Pipeline flow rate (Q).

### Solution:

Substitute the values in the formula, Q = (-2) √2 (9.81) x (0.3) x (0.04) x log [ (Ks)/(3.7 x (D) + (2.5 x v)) / √2 g D S] x A Q = -0.970443198 x log [ (Ks)/(3.7 x (D) + (2.5 x v)) / √2 g D S] x A Q = -0.970443198 x log [ (0.000015)/(3.7 x (0.30) + (2.5 x 0.00000101)) / √2 g D S] x A Q = -0.970443198 x log [ 0.000013514 + (0.000002525)) / 0.485221599] x A Q = 4.38 x 0.071 Q = 0.31098 m3/s