# Summary

The Joukowsky equation is a method of determining the surge pressures that will be experienced in a fluid piping system. When a fluid in motion is forced to either stop or change direction suddenly a pressure wave will be generated and propagated through the fluid. This pressure wave is commonly referred to as fluid hammer (also known as water hammer, surge or hydraulic shock) and typically occurs in piping systems when a valve is suddenly closed, isolating the line. The resultant surge pressures are complex to characterise but for simple systems they may be calculated using the Joukowsky equation.

# Definitions

 : Speed of sound in a fluid : Fluid pressure : Fluid velocity : Fluid density

# Introduction

The Joukowsky equation is a simplified method for calculating the peak transient pressure experienced when a valve is closed against a fluid in motion and may be represented as follows:

The Joukowsky equation takes into consideration the elasticity of the pipe wall and the compressibility of the fluid itself through the calculation of the speed of sound , however assumes instant closure of the valve. This assumption of instant valve closure introduces several limitations to its application.

# Limitations of the Joukowsky Equation

The Joukowsky equation is a vast simplification of the characteristics of surge and is therefore only applicable to a limited sub set of fluid systems. It application should be limited to situations matching the following criteria:

• Simple 'linear' piping systems i.e. there are no branches by which pressure waves can be reflected back and cause constructive interference in the main line.
• Valve closure time is significantly shorter than the pressure wave communication time.
• System frictional losses are similar to that of a water transport system.

Additionally the Joukowsky equation does not consider column separation in its analysis of fluid hammer. Column separation can often result in surge pressures exceeding those predicted by the Joukowsky equation and therefore the Joukowsky equation should not be applied when analysing system in which the pipeline pressure can rapidly drop below the fluid vapour pressure.

# References

1. Fluid Transients in Pipeline Systems 2. Applied Hydraulic Transients 3. Fluid Transients in Systems 