Surge pressure head increases linearly with velocity change at constant wave velocity (a = 1400 m/s, g = 9.81 m/s²). The green dot marks the current calculation.
Water hammer calculates the maximum pressure surge when fluid flow is suddenly stopped or redirected. The wave velocity (a) depends on pipe material and fluid properties; in steel water pipes it ranges from 900–1,400 m/s.
H = a × ΔV / g
Water hammer (H = a × ΔV / g) calculates the maximum pressure surge when fluid flow is suddenly stopped or redirected. The wave velocity (a) depends on pipe material and fluid properties; in steel water pipes it ranges from 900–1,400 m/s. The resulting pressure spike can burst pipes, so engineers use slow-closing valves, surge tanks, and arrestors to mitigate it.
A steel water pipe has a wave velocity of 1,200 m/s. A valve closes suddenly, stopping flow from 2 m/s to 0. What is the surge pressure head?
This extreme pressure can easily rupture unprotected piping.
Water hammer is a pressure transient caused by sudden changes in fluid velocity. The Joukowsky equation (H = aV/g) gives the maximum surge pressure for an instantaneous valve closure. The wave velocity depends on both the fluid bulk modulus and the pipe wall elasticity — stiffer pipes produce faster waves and higher surge pressures.
The banging sound is water hammer — a pressure shockwave created when moving water is suddenly stopped. The kinetic energy of the water converts into a pressure spike that travels through the pipe at 900–1,400 m/s in metal pipes. The pipe walls flex under this pressure, creating the characteristic hammering noise.
Use the Joukowsky equation: H = a × ΔV / g, where a is the wave velocity, ΔV is the velocity change, and g is gravity. To convert head to pressure: ΔP = ρ × g × H. For example, a 1,200 m/s steel pipe with 2 m/s flow stoppage produces H = 244.6 m, or about 24 bar (348 psi) above normal.
It depends on the fluid's bulk modulus and the pipe's elasticity. Steel pipes produce waves at 900–1,400 m/s; PVC pipes are slower at 300–600 m/s, which reduces surge pressure proportionally. Ductile iron falls between at 1,000–1,200 m/s.
Use slow-closing valves (closure time > 2L/a), install surge tanks or water hammer arrestors, maintain proper pipe support, and size pipes to keep velocities below 3 m/s. Variable-speed pumps with soft start/stop reduce transient pressures significantly.
The critical time is 2L/a, where L is the pipe length and a is the wave velocity. If a valve closes faster than this time, the full Joukowsky surge develops. Slower closures produce proportionally lower surges because the reflected pressure wave partially cancels the incoming wave.
Yes. Water hammer surges can exceed the pipe's pressure rating, causing joint failures, fitting blowouts, and pipe bursts. Even repeated moderate surges cause fatigue damage over time. The surge pressure is additive to the normal operating pressure — a 25 bar surge on a 10 bar system means 35 bar total.
Water hammer specifically refers to the rapid pressure transient from sudden flow stoppage (Joukowsky equation). Surge is a broader term covering all transient pressure events, including slow valve closures, pump startups, and air pocket compression. Water hammer is the most severe type of surge.
The Joukowsky equation gives the maximum pressure surge head from an instantaneous velocity change:
Where:
To convert surge head to pressure: ΔP = ρ × g × H, where ρ is fluid density. For water, each meter of surge head equals about 9.81 kPa (1.42 psi).
Municipal Water
A steel water main has a wave velocity of 1,200 m/s. A fire hydrant valve closes quickly, stopping flow from 2.5 m/s to 0. What is the surge head?
This extreme surge can burst unprotected fittings. Slow-closing hydrant valves and surge arrestors prevent this.
Power Plant
A hydroelectric penstock (steel, a = 1,100 m/s) experienced a 150 m surge head during an emergency turbine shutdown. What was the velocity change?
Even a moderate velocity change of 1.34 m/s produces dangerous surge in a high wave-speed penstock. Surge tanks absorb this energy.
Oil Pipeline
A PVC oil pipeline experiences a 69 m surge head during an emergency shutdown that stops flow at 1.5 m/s. Back-calculate the wave velocity.
This is typical for PVC pipe (300–600 m/s). The lower wave speed compared to steel (900–1,400 m/s) produces proportionally lower surge pressures.