Aude equation or T.R Aude equation is used in industry to calculated the pressure drop in pipelines. The equation is used for petroleum products transported in pipelines. It was name after the engineer who conducted experiments on pipelines sized between 8 in (203 mm) to 12 in (305 mm) in 1950s.

The equation doesn’t use pipe roughness however it requires the use of Aude K-factor to represent the pipeline efficiency.

## What is the K-factor and how do I obtain it?

As above the Audi equation K-factor is based on the experiments that was conducted in 1950s to represent pipeline efficiency. Assuming that this valued does take into account the internal condition of the pipe, the value is determined by field measurement and calibration of an existing pipe. If the field values are not available; engineers assume a value between 0.90 to 0.95. A higher value of K-factor will result in a lower pressure drop.

## Any usage limitations?

Yes, as mention above, the equation was deducted on the pipe sizes below. So using the equation with larger pipelines is cautioned!

– | From | To |
---|---|---|

Pipe size | 8 in (203 mm) | 12 in (305 mm) |

## Aude equation

The equation can be expressed in the following format

### English/US Units

`\[P\ =\ \left[\frac{Q\cdot v^{0.104}\cdot Sg^{0.448}}{0.871\cdot K\cdot D^{2.656}}\right]^{1.812}\]`

Where; P = Pressure drop due to friction, psi/mile Q = Volumetric Flow rate, bbl/h D = Pipe internal diameter, in Sg = Liquid Specific gravity v = Liquid viscosity, centipoise K = Aude K-factor (between 0.90 to 0.95)

### SI Units

`\[P\ =8.888\cdot10^8\cdot\left[\frac{Q\cdot v^{0.104}\cdot Sg^{0.448}}{K\cdot D^{2.656}}\right]^{1.812}\]`

Where; P = Pressure drop due to friction, kPa/km Q = Volumetric Flow rate, m3/h D = Pipe internal diameter, mm Sg = Liquid Specific gravity v = Liquid viscosity, centipoise K = Aude K-factor (between 0.90 to 0.95)

## References

E. Shashi Menon, Liquid Pipeline Hydraulics, Marcel Dekker, Inc. 2004

## Useful Software

Process engineering calculator by Webbusterz engineering software