Water hammer is the pressure surge that appears in a pressurized pipeline when a valve closes or a pump stops: the decelerated water compresses the fluid and expands the pipe, and a pressure wave travels along the pipeline at the wave speed a.
How it works
How to use the calculator
- Choose the situation: closure of a valve or a pump trip.
- Enter the length, the internal diameter and the wall thickness; choose the material (or type its modulus E) and give the steady-state velocity or discharge.
- Give the valve closure time or, for a pump trip, the total pump head: if you do not know the stoppage time, it comes from the Mendiluce formula.
- For the pressures along the pipeline, give the static level and the centerline elevations (start, end and up to two intermediate points) and, if you wish, the PN.
- Press “Calculate”: you will see the wave speed, the critical time, the formula applied, the surge head and the envelopes.
Method: wave speed, critical time, Joukowsky, Michaud and Mendiluce
Pressure wave speed (Korteweg)
a = √(K/ρ) / √(1 + K·D/(E·e))
It depends on the water (K = 2.1 GPa, ρ = 1000 kg/m³) and on the elasticity of the pipe (D, e, E). In rigid pipes, such as steel, it is around 1000–1300 m/s; in plastic ones, such as HDPE, about 200–400 m/s.
Critical time
tc = 2L / a
It is the time the wave takes to travel to the reservoir and back. If the maneuver is shorter, the surge head is the highest possible, that of an instantaneous closure.
Joukowsky and Michaud
T ≤ tc: ΔH = a·v0/g
T > tc: ΔH = 2·L·v0/(g·T)
They are not alternative methods: they are the two branches of the classical method, and the calculator chooses the one that applies. They coincide when the maneuver time equals the critical time.
Pump stoppage time (Mendiluce)
T = C + K·L·v0 / (g·Hm)
C depends on the hydraulic gradient Hm/L: it is 1 up to 15 % and drops to 0 towards 40 %. K depends on the length: 2 in short rising mains, down to 1 in those longer than 1 500 m. With gradients above 50 % the stoppage is very rapid and Joukowsky applies.
Static line and envelopes
The static line is the water elevation in the highest reservoir. The surge head ΔH is added to it and subtracted from it: it is maximum at the valve or at the pumps and zero at the reservoir. If the pipeline is short compared with a·T/2, the envelope is a triangle; if it is long, a trapezoid, with the full surge head over the reach farthest from the reservoir. The pressure at each point is the envelope elevation minus the centerline elevation: the maximum is compared with the PN; the minimum, with the vapor pressure (about −10 m H2O).
Typical moduli of elasticity
Indicative short-term values, the ones that apply to transients (Wylie and Streeter, 1993; Chaudhry, 2014). For your project, use the manufacturer’s value.
| Material | E (GPa) |
|---|---|
| Steel | 206 |
| Ductile iron | 170 |
| Reinforced concrete | 30 |
| GRP | 20 |
| PVC | 3 |
| HDPE (PE100) | 1 |
Frequently asked questions
Why does the surge head not depend on the closure time when it is shorter than the critical time?
Because the wave reflected at the reservoir has not yet returned to the valve when the closure ends: the valve “sees” an instantaneous closure, and the surge head is the Joukowsky value.
How is a pump trip calculated?
With the Mendiluce stoppage time, which depends on the length, the velocity and the total pump head, or with the one you have measured. Rising mains with an air vessel or a surge tank need a full transient analysis.
What happens if the minimum pressure falls below the vapor pressure?
The water may vaporize and the column separate; when it rejoins, surges higher than those of the classical model occur. The calculator warns you when this happens.
Which modulus of elasticity should I use for PVC or HDPE?
The short-term one, which corresponds to rapid phenomena such as water hammer; the long-term modulus is lower and is used for sustained loads.
References
- Chaudhry, M. H. (2014). Applied Hydraulic Transients (3rd ed.). Springer.
- Wylie, E. B., and Streeter, V. L. (1993). Fluid Transients in Systems. Prentice Hall.
- Mendiluce Rosich, E. (1987). El golpe de ariete en impulsiones (2nd ed.). Bellisco.