Water Hammer Pressure Surge (Joukowsky)
Wave celerity from pipe-fluid coupling, pressure surge dP = rho × a × dV, and rapid-closure flag against 2L/a.
Example
You enter
- Pipe material copper
- Pipe size (nominal) 1
- Velocity at closure (fps) 8
- Closure time (s) 0.05
- Run length (ft) 100
- Fluid water
You get
- Wave celerity 4130 fps
- Surge ΔP 445.1 psi
- Reflection time 2L/a 48.4 ms
- Closure category slow closure (surge attenuated)
Checked against published worked examples from: Spears Manufacturing Co.
Details, formula, and sources
Formula or tableJoukowsky surge: a = sqrt(K/rho) / sqrt(1 + (K × D)/(E × t)), D the INSIDE diameter (outside diameter less two walls); dP = rho × a × dV. Reflection time = 2L/a; rapid closure when t_close <= 2L/a.
Source and editionJoukowsky (1898) classical-fluids result by name; ASCE Manual of Practice 49 by name; manufacturer pipe-elastic-property values from data/plumbing/pipe-elastic-properties.json.
Free accessJoukowsky derivation free in published fluid-mechanics texts. ASCE MOP-49 licensed.
What governsEstimate. AHJ and licensed plumber / gas fitter govern. Verify against the IPC / IFGC edition adopted in your jurisdiction.
API field namesmaterial, pipe_size, velocity_fps, closure_time_s, run_length_ft, fluid, celerity_fps, surge_psi, reflection_time_s, rapid_closure
- Water bulk modulus K 2.19 GPa ≈ 317 800 psi at 60 °FNIST
- Water density rho 1.940 slug/ft³physical fact at 60 °F
- Wall D / t by material copper ASTM B88 Type L; PEX SDR 9 and CPVC SDR 11 (copper tube size); PVC Schedule 80; steel and ductile iron Schedule 40 (ductile iron as a proxy)ASTM B88 / F876 / F441 / D1785