BIZOMAT MAKEOS · Hydraulics
Water Hammer Pressure Surge
How big a pressure surge will closing this valve cause?
Pressure wave speed in a pipe, the Joukowsky surge for a fast valve closure, the critical closure time, and the reduced surge for slower closure.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Velocity change | m/s | Change in flow velocity caused by the valve (the full velocity for a complete closure). |
| Pipe length to the reservoir or open end | m | Length of pipe between the valve and the nearest reservoir, tank or open end. |
| Valve closing time | s | Time the valve takes to close. |
| Pipe inside diameter | mm | Inside diameter of the pipe. |
| Pipe wall thickness | mm | Pipe wall thickness. |
| Pipe elastic modulus | GPa | Elastic modulus of the pipe material (steel 200 GPa, PVC about 3 GPa). |
| Fluid bulk modulus | GPa | Bulk modulus of the liquid (water 2.2 GPa, hydraulic oil about 1.5 GPa). |
| Fluid density | kg/m³ | Liquid density. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Velocity change
- What it is
- How much the flow velocity in the pipe changes when the valve operates; for a complete closure, the full flow velocity before closure.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 100 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The surge pressure rises in direct proportion to the velocity change.
- Get it right
- This is a velocity in metres per second, not a flow rate; divide the flow by the pipe bore area to get it.
What this means: Pipe length to the reservoir or open end
- What it is
- The length of pipe from the valve back to the reservoir, tank or open end where the pressure wave reflects.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 1000000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer pipe lengthens the critical closure time, so a given valve closure is more likely to produce the full surge.
What this means: Valve closing time
- What it is
- The time the valve takes to go from open to closed.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 100000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Closing slower than the critical time reduces the surge in proportion to the closing time.
- Get it right
- Many valves shut off most of the flow in the last part of their stroke, so the effective closing time can be shorter than the full stroke time.
What this means: Pipe inside diameter
- What it is
- The inside diameter (bore) of the pipe, used with the wall thickness to allow for the pipe stretching under the surge.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the bore, not the outside or nominal diameter.
What this means: Pipe wall thickness
- What it is
- The wall thickness of the pipe, which with the pipe modulus sets how much the pipe expands under the pressure wave.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Pipe elastic modulus
- What it is
- The elastic (Young’s) modulus of the pipe material, which governs how stiff the pipe wall is against the pressure wave.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A stiffer pipe gives a faster pressure wave and a higher surge.
- Get it right
- Enter gigapascals. Plastic pipes are far more flexible than steel, which greatly lowers the wave speed.
What this means: Fluid bulk modulus
- What it is
- The bulk modulus of the liquid, its resistance to compression, from fluid property data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 10 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.2 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher bulk modulus raises the wave speed and so the surge.
- Get it right
- Enter gigapascals. Entrained air lowers the effective bulk modulus of a liquid considerably.
What this means: Fluid density
- What it is
- The density of the liquid in the pipe, from fluid property data at the operating temperature.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 998 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter kilograms per cubic metre.
Method and formulas
- Wave speed a = √((K/ρ) ÷ (1 + K D ÷ (E t))).
- Fast closure (tc ≤ 2L/a): Δp = ρ a Δv.
- Slow closure: Δp ≈ ρ a Δv × (2L/a) ÷ tc.
- Example: stopping 2 m/s of water in a 100 mm steel pipe gives up to 26.245 bar.
Limitations
- Simple estimate; valve characteristics, column separation and branches need a transient analysis.
- Add the surge to the steady operating pressure.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check pipework for surge when a valve shuts
- Choose a valve closing time
- Decide whether surge protection is needed
Who it is for
- Process engineers
- Maintenance engineers
- Design engineers
What you get
- Wave speed
- Critical closure time
- Joukowsky surge
- Estimated surge for the actual closing time
Interpreting the result
- If the surge plus working pressure exceeds the pipe or component rating, slow the closure or add surge protection.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3024–3027. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
What a pressure surge is and why it travels
In Water Hammer by the Numbers
What it covers: See why stopping a water column is a wave problem rather than a force problem, meet the 900 m rising main used throughout, and list the events that start a surge.
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