Joukowsky Water Hammer Surge Pressure Calculator
For pipeline engineers who need a defensible first-pass surge number before running a full transient study — sized for valve closure, pump trip and ESD checks on steel, ductile iron and PVC mains, using the Joukowsky surge ΔP = ρ·a·ΔV with the pressure wave speed computed from the pipe (Korteweg) and the critical closure time 2L/a.
Water Hammer Surge Analyzer
How to Use This Calculator
- Enter fluid density ρ in kg/m³ and bulk modulus K in Pa (defaults 998 and 2.2e9 are water).
- Enter pipe inside diameter D, wall thickness e, and pick the pipe material (or choose custom and type E in Pa).
- Enter the velocity change ΔV in m/s, the pipe length L in m, and the valve closing time tc in s.
- Read the wave speed a, the surge pressure in Pa/bar/psi, and the critical closure time Tc, then check the verdict badge to see whether tc exceeds 2L/a and the Joukowsky value is only an upper bound.
FAQ
Q: What is the Joukowsky equation for water hammer surge pressure?
A: ΔP = ρ·a·ΔV, where ρ is fluid density, ΔV is the change in flow velocity and a is the pressure wave speed computed from the pipe (Korteweg) — the calculator applies that formula directly and reports the result in Pa, bar and psi.
Q: How do I know if my valve closing time counts as rapid closure?
A: Compare your closing time tc with the critical closure time Tc = 2L/a; if tc > Tc the closure is slow and the Joukowsky value is only an upper bound. For L = 1000 m with a ≈ 1286 m/s, Tc ≈ 1.56 s.
Q: Why does the pipe material change the surge pressure?
A: The Korteweg term a = √[(K/ρ)/(1 + K·D/(E·e))] puts the pipe wall stiffness in the denominator: a stiffer wall (steel E = 2.0e11 Pa) carries a faster wave than PVC (E = 3.0e9 Pa), and ΔP = ρ·a·ΔV rises in direct proportion to a.
Q: What surge pressure does a 0.3 m steel pipe with a 2 m/s velocity change produce?
A: With water in a steel pipe of D = 0.3 m and wall e = 0.01 m, ΔV = 2 m/s gives a ≈ 1286 m/s and ΔP ≈ 25.7 bar.