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Water Hammer — Surge Calculator

Enter the pipe geometry and material, the water's bulk modulus, and the velocity change — the calculator returns the pressure-wave celerity, the Joukowsky surge pressure and head, the critical closure time, and whether your valve closure counts as rapid or gradual.

a = √(K/ρ) / √[1 + (K/E)(D/e)] Δp = ρaΔV ΔH = aΔV/g t_c = 2L/a

a	pressure-wave celerity (m/s) — the elastic-pipe form; a rigid pipe gives the ceiling √(K/ρ)
ΔV	magnitude of the velocity change, V_initial − V_final (m/s)
t_c	critical closure time (s): closures faster than this see the full Joukowsky surge
Gradual-closure estimate	for t > 2L/a: ΔH ≈ 2LΔV/(g t) (simplified Michaud approximation)

Pipe length, L (m) Internal diameter, D (mm) Wall thickness, e (mm) Pipe material Water bulk modulus, K (GPa) Velocity change, ΔV (m/s) Valve closure time, t (s) — 0 = instant

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook. Surge protection design for real systems needs a qualified engineer — this tool does not size protection devices.

Worked example: instant valve closure

A steel water main (L = 500 m, D = 300 mm, e = 8 mm, E = 200 GPa) carries water (K = 2.2 GPa, ρ = 1000 kg/m³) at 1.5 m/s. The valve is slammed shut (t ≈ 0). Find the surge head and pressure.

Wave celerity: a₀ = √(2.2×10⁹/1000) = 1483 m/s; (K/E)(D/e) = (2.2/200)(300/8) = 0.4125, so a = 1483/√1.4125 = 1248 m/s
Critical time 2L/a = 1000/1248 = 0.80 s — an instant closure is far shorter, so the full Joukowsky surge applies
ΔH = aΔV/g = 1248 × 1.5/9.81 = 191 m of head
Δp = ρaΔV = 1000 × 1248 × 1.5 = 1.87 MPa — stacked on top of the steady operating pressure

Exam tip: ΔV is the velocity change, not the flow velocity. If the valve only throttles the flow from 2.0 to 0.5 m/s, ΔV = 1.5 m/s — plugging in 2.0 overstates the surge.

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Preparing for exam day? The 110-question FE Civil practice exam is a full 5-hour-20-minute rehearsal with detailed solutions.