# Pipeline flow rate

Online civil engineering calculator to calculate pipeline flow rate by using colebrook white equation method.

## Calculator of Pipeline Flow Rate

## Formula

Q = \frac{{\pi D^2}}{{4}} \cdot \frac{{\sqrt{{2g(S - h_f)}}}}{{\sqrt{{\frac{{K_s}}{{v}}}}}}

- S - hydraulic gradient,
- v - kinematic viscosity of water,
- D - internal diameter,
- Ks - roughness coefficient,
- g = 9.81 m/s
^{2}, - A - area of the section.

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.

## 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 m
^{2}/s - kinematic viscosity of water (v) = 0.00000101 m
^{2}/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 m
^{2}

### 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 m
^{3}/s