Pressure Surge Calculations
How to Perform Pressure Surge (Water Hammer) Calculation in a Piping Network
Pressure surge (or water hammer) occurs when there is a sudden change in velocity (valve closure/opening, pump trip, etc.). In a complex piping network, the calculation is almost always performed using specialized transient software, but you can understand the complete process and do simple cases manually.
Step-by-Step Procedure
1. Choose the Calculation Method
| Network Complexity | Recommended Method | Software Examples |
|---|---|---|
| Single pipeline | Joukowsky + Method of Characteristics (MOC) | Manual or simple Excel |
| Branched / looped network | Method of Characteristics (full transient) | Mandatory software |
| Any real network | Implicit or explicit MOC + surge protection | Bentley HAMMER, AFT Impulse, WANDA, Pipenet, Flowmaster, BOSfluids, KYpipe Surge, HYTRAN |
2. Collect Required Input Data
| Parameter | Typical Source / How to Get |
|---|---|
| Pipe geometry (length, diameter, thickness) | Design drawings |
| Pipe material & wall thickness | To calculate wave speed (a) |
| Fluid properties (density ρ, bulk modulus K) | Water at temperature → usually 1000 kg/m³, K = 2.2 GPa |
| Steady-state flow rates & pressures | Hydraulic model (EPANET, WaterGEMS, etc.) |
| Valve characteristics & closure time | Valve data sheet (Cv vs. stroke, closure law) |
| Pump data (inertia I, 4-quadrant curve) | Pump manufacturer |
| Air valves, surge tanks, check valves locations | Design documents |
| Elevation profile | Topographic survey |
3. Calculate the Wave Speed (a) – Critical Parameter
Joukowsky formula requires the celerity (speed of pressure wave):
a = √[ K / ρ × (1 + (K×D)/(E×e)) ]⁻¹
Where:
- a = wave speed (m/s) → usually 900–1300 m/s for steel/DI/GRP
- K = bulk modulus of fluid (2.19 × 10⁹ Pa for water @ 20°C)
- ρ = density (998 kg/m³)
- D = internal diameter (m)
- e = wall thickness (m)
- E = Young’s modulus of pipe material (210 GPa steel, 110 GPa DI, ~20 GPa GRP)
4. Maximum Theoretical Surge Pressure (Joukowsky)
For instantaneous full closure (the worst case):
ΔP = ρ × a × ΔV
ΔH = (a × ΔV) / g
Typical values:
- ΔV = 2 m/s → ΔP ≈ 2 × 1200 × 2 = 4.8 bar (48 m head) in steel pipe
- Closing in < 2L/a (critical time) → treat as instantaneous
5. Perform Full Transient Analysis (Software Steps)
Typical workflow in Bentley HAMMER / AFT Impulse / WANDA:
- Build steady-state model (same as EPANET/WaterGEMS).
- Define transient event(s):
- Pump trip (power failure)
- Fast valve closure/opening (specify closure time or stroke vs. time)
- Check valve slam, demand change, etc.
- Enter wave speed for every pipe (or let software calculate).
- Add surge protection devices (if any):
- Air valves (inflow/outflow orifice size)
- Surge tanks / one-way tanks
- Air vessels (pre-charge pressure, volume)
- Pressure relief valves
- VFD ramp-down, flywheels
- Set simulation duration = 5–10 × (2L/a) for longest path.
- Run transient simulation.
- Check envelopes:
- Maximum pressure (MAOP check)
- Minimum pressure (avoid column separation → vapor pressure < –10 m)
- Iterate protection design until pressures are within limits (usually class rating × 1.5 or 2.0).
6. Quick Hand Calculation for Simple Pipeline (No Software)
Example: 1000 m steel pipe, DN300, 8 mm wall, flow 300 l/s, valve closes in 8 seconds.
- Wave speed a ≈ 1150 m/s
- 2L/a = 2×1000/1150 ≈ 1.74 s → since 8 s > 1.74 s → not instantaneous
- Use Allievi’s chart or approximate: N = (ρ L ΔV) / (P₀ × t_c)
τ = t_c / (2L/a) Then look up pressure ratio from Allievi diagram (or use formula): ΔP / ΔP_Joukowsky ≈ 1 / (1 + N) Or use simple linear closure approximation: ΔP_max ≈ ρ a ΔV × (2L/a) / t_c if t_c > 2L/a
7. Rules of Thumb for Design
| Situation | Maximum Acceptable Surge |
|---|---|
| Steel / DI pipe | ≤ 1.5 × PN rating |
| PVC / GRP | ≤ 1.3 × PN (more brittle) |
| Minimum pressure | > –0.5 bar gauge (avoid vapor pockets) |
| Valve closure time | > 10 × (2L/a) for longest pipe to keep surge low |
8. Recommended Software (2024–2025)
| Software | Best For | License Cost |
|---|---|---|
| Bentley HAMMER | Water distribution networks | High |
| AFT Impulse | Industrial/process piping | Medium |
| WANDA (Deltares) | Large transmission lines | Medium |
| KYpipe Surge | Very user-friendly, academic use | Low |
| Pipenet Transient | Firewater & complex oil/gas | High |
| BOSfluids | Detailed structural interaction | High |
Summary Checklist Before Final Design
- Wave speed calculated for every pipe material
- Steady-state verified
- Transient event clearly defined (worst credible scenario)
- Surge protection sized and located optimally
- Max & min pressure envelopes plotted along entire network
- Vacuum/column separation avoided
- Report includes HGL envelopes, air valve air flow rates, tank levels, etc.
If you have a specific network (even a small one), send me the layout, pipe data, and event, and I can walk you through the actual numbers or build a quick HAMMER/Impulse example.