Water Hammer Pressure Surge Calculator – Joukowsky Equation | Pipeline Surge Analysis
Water Hammer Pressure Surge Calculator (Joukowsky)
Pipeline surge pressure • Critical closure time • Pressure rise • Surge arrestor sizing • Joukowsky equation
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📐 1. Water Hammer – Joukowsky Equation & Pipeline Protection
Sudden valve closure or pump trip generates a pressure wave (water hammer) that can exceed pipe design pressure. The Joukowsky equation calculates the instantaneous pressure rise:
ΔP = ρ · a · ΔV
where: ρ = fluid density (kg/m³), a = wave celerity (m/s), ΔV = velocity change (m/s).
Critical closure time Tc = 2L / a – if valve closes faster than Tc, full Joukowsky pressure occurs.
🚀 2. Water Hammer Surge Calculator
📊 3. Pipeline & Pressure Wave Schematic
📈 4. Surge Pressure vs Velocity & History
📘 5. How to Use the Calculator
- Enter pipe length, flow velocity, diameter, and material.
- Provide wall thickness (for wave celerity calculation).
- Specify valve closure time (use 0 for instantaneous closure).
- Click "Compute" – wave celerity, critical time, surge pressure (ΔP and total P), and surge arrestor recommendation are shown.
- 2D schematic shows the pipeline and pressure wave reflection.
- Batch CSV: upload multiple designs to compare surge pressures.
- PDF report includes all inputs, results, and sketch.
❓ Frequently Asked Questions
❓ What is the Joukowsky equation?
It relates pressure rise to fluid density, wave speed, and velocity change. For instantaneous closure, ΔP = ρ·a·ΔV. If closure time > 2L/a, pressure is reduced.
❓ How to reduce water hammer?
Increase valve closure time, install surge tanks, air vessels, or use slow-closing check valves.
❓ What is wave celerity a?
Speed of pressure wave: a = √(K/ρ) / √(1 + (K/E)·(D/e)) for elastic pipes. Typical values: steel ~1000 m/s, PVC ~300 m/s.
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