Water Hammer Calculator (Pressure Surge Estimate)

What is water hammer?

When flowing liquid is stopped suddenly, its kinetic energy turns into pressure. The pressure that builds up at the valve travels along the pipe as a wave at close to the speed of sound. This is water hammer. It can crack pipes, flanges and pump casings and tear supports loose.

Formulas

For rapid closure the pressure rise follows the Joukowsky relation: Δp = ρ × a × Δv, where ρ is the density, Δv the change in velocity and a the speed of the pressure wave. The wave speed depends on the bulk modulus of the liquid and the elasticity of the pipe:

a = √(K / ρ) / √(1 + (K / E) × (D / e))

The wave travels to the end of the line and back in 2L / a. If the valve closes faster than that, the closure counts as rapid. For slower closure the rise is roughly Δp = 2 × ρ × L × Δv / tc (Michaud).

Example

Water flows at 2 m/s in a steel pipe with a 200 mm bore and 5 mm wall. The wave speed comes out at 1236 m/s. Rapid closure raises the pressure by 24.7 bar. For a 600 metre line the critical time is 0.97 seconds. Closing the valve over 6 seconds cuts the rise to about 4 bar. Flexible pipe sees a much smaller surge: in heavy wall polyethylene pipe the wave speed falls to a few hundred m/s and the pressure rise drops in proportion.

Limits

This is a preliminary calculation. Pump trip, column separation, branched networks, air vessels and the real closing characteristic of the valve need transient analysis. Air in the line changes the wave speed. Final design belongs with a qualified engineer.