What Is Water Hammer?
Water hammer is a pressure surge or shock wave that travels through a pipe when a moving fluid is suddenly forced to stop or change direction — for example when a valve closes quickly or a pump trips. The momentum of the fluid is converted into a spike in pressure that can be many times the normal operating pressure, potentially bursting pipes, damaging valves and shaking pipework. This calculator estimates the magnitude of that surge using the classic Joukowsky equation.
How to Use This Calculator
Enter three values: the fluid density (about 1000 kg/m³ for water), the pressure wave speed \(c\) (the speed at which the shock wave travels through the fluid-pipe system, often 1000–1400 m/s for water in steel pipe), and the velocity change \(\Delta v\) (the difference between the initial flow velocity and the final velocity, typically the full pipe velocity for instant valve closure). The tool returns the peak pressure surge in pascals, kilopascals, bar and psi.
The Formula Explained
The Joukowsky equation is $$\Delta P = \text{Density } \rho \cdot \text{Wave Speed } c \cdot \left| \Delta v \right|$$ It assumes an instantaneous valve closure (faster than the pipe’s critical time, \(2L/c\)). The surge is independent of pipe length and depends only on density, wave speed and how much the velocity changes. Slower closures produce smaller surges, so this gives a conservative worst-case estimate.
Worked Example
Water (\(\rho = 1000\) kg/m³) flows at 2 m/s and is stopped instantly. With a wave speed of 1200 m/s: $$\Delta P = 1000 \times 1200 \times 2 = 2{,}400{,}000 \text{ Pa} = 2400 \text{ kPa} = 24 \text{ bar} \approx 348 \text{ psi}$$ That surge is added on top of the static line pressure.
FAQ
Does pipe length matter? Not for the peak surge in the Joukowsky equation, but length sets the critical closure time \(2L/c\); longer pipes give more time for valves to close gradually.
What wave speed should I use? Use ~1480 m/s for water in a rigid pipe, but real elastic pipes lower it — steel pipes are often 1000–1300 m/s, plastic pipes 300–500 m/s.
How do I reduce water hammer? Close valves slowly, use surge tanks or air chambers, install pressure-relief valves, and select pipe materials with lower wave speed.
