Water Hammer Calculator

What is Water Hammer?

Water hammer (hydraulic shock) is a pressure surge caused by the sudden change in fluid velocity — typically when a valve is quickly closed or a pump trips. The kinetic energy of the moving fluid converts to pressure, sending a shock wave through the pipe that can burst pipes, damage fittings, and loosen joints.

Joukowsky's Equation (Instantaneous Closure)

ΔP = ρ × a × ΔV

Where:

• ΔP = pressure surge (Pa)
• ρ = fluid density (kg/m³)
• a = pressure wave speed (m/s) — depends on pipe material and wall thickness
• ΔV = change in fluid velocity (m/s)

Wave speed in rigid pipes: a = √(K/ρ) where K = bulk modulus of water ≈ 2.15 GPa → a ≈ 1,460 m/s. For elastic pipes: a = √(K/ρ × 1/(1 + D×K/(E×t))) where E = pipe material Young's modulus.

Practical Examples

Example: Water flowing at 2 m/s in a steel pipe, valve closes instantly. ΔP = 1000 × 1,200 × 2 = 2,400,000 Pa = 2.4 MPa = 24 bar — far above typical pipe ratings.

Example with PVC pipe (a ≈ 400 m/s): ΔP = 1000 × 400 × 2 = 800 kPa = 8 bar.

Prevention

• Slow-closing valves: Closing time > 2L/a seconds eliminates hammer.
• Surge tanks / accumulators: Absorb the pressure wave.
• Air vessels: Compress to buffer the shock.
• Pump bypass valves: Prevent pump trip hammer.