BIZOMAT MAKEOS · Hydraulics
Valve Closure Surge (Water Hammer against Pipe Rating)
How big a pressure surge does closing this valve cause, does working pressure plus surge stay within the pipe rating, and how slowly must the valve close to keep it there?
Water-hammer check of a pipeline: pressure wave speed from the liquid bulk modulus and the pipe diameter, wall and modulus, the critical closure time 2L ÷ a, the Joukowsky surge for fast closure and the reduced surge for the closing time used (as the water hammer tool), working pressure plus surge against the pipe or component rating, and the slowest-needed closing time that keeps the total within the rating.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Change in flow velocity | m/s | Velocity change when the valve closes (the full flow velocity for a full closure). |
| Pipe length to the reflection point | m | Length of pipe from the valve to the tank or reservoir where the wave reflects. |
| Valve closing time | s | Time the valve takes to close. |
| Pipe inside diameter | mm | Inside diameter of the pipe. |
| Pipe wall thickness | mm | Wall thickness of the pipe. |
| Pipe elastic modulus | GPa | Elastic modulus of the pipe (about 200 steel, 1–3 plastics). |
| Liquid bulk modulus | GPa | Bulk modulus of the liquid (2.2 for water). |
| Liquid density | kg/m³ | Density of the liquid. |
| Working pressure | bar | Steady working pressure at the valve. |
| Pipe or component pressure rating | bar | Pressure rating of the weakest pipe, fitting or instrument. |
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: Change in flow velocity
- What it is
- How much the liquid velocity in the pipe changes when the valve closes: the full flow velocity for a complete stop, or the difference for a partial closure.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 50 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 Joukowsky surge rises in direct proportion.
- Get it right
- Velocity is flow divided by the bore area; work it out from the flow rate rather than estimating it.
What this means: Pipe length to the reflection point
- What it is
- The length of pipe from the valve back to where the pressure wave reflects, usually an open tank, reservoir or large header.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 100000 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 slow closure produces more surge.
What this means: Valve closing time
- What it is
- The time the valve takes to move from its starting opening to fully shut.
- Units and format
- Enter a number in s: seconds. The form accepts 0.001 s to 3600 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 2L ÷ a reduces the surge in proportion; at or below it the full surge applies.
- Get it right
- Most of the flow change often happens near the end of the stroke, so the effective closing time can be shorter than the full stroke.
What this means: Pipe inside diameter
- What it is
- The internal bore of the pipe. With wall thickness and modulus it sets how much the pipe stretches under the pressure wave, which slows the wave.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 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 inside diameter, not the nominal size or outside diameter.
What this means: Pipe wall thickness
- What it is
- The thickness of the pipe wall, which with the pipe modulus sets how stiff the pipe is against the pressure wave.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 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.
- Effect on the result
- A thicker wall stiffens the pipe, raising wave speed and surge.
What this means: Pipe elastic modulus
- What it is
- The elastic (Young’s) modulus of the pipe wall material, from the pipe maker or material data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 400 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.
- Get it right
- Entered in GPa. Plastic pipes have far lower moduli than steel, which lowers the wave speed considerably.
What this means: Liquid bulk modulus
- What it is
- The bulk modulus of the liquid, its resistance to compression, from fluid property data at the operating temperature.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 5 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.
- Get it right
- Entrained air or gas greatly lowers the effective bulk modulus and the wave speed.
What this means: Liquid density
- What it is
- The density of the liquid in the pipe at its operating temperature, used for the wave speed and the surge pressure.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 2000 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.
What this means: Working pressure
- What it is
- The steady pressure in the pipe at the valve before it closes. The surge is added to it and the total compared with the rating.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same basis as the rating, normally gauge pressure.
What this means: Pipe or component pressure rating
- What it is
- The maximum pressure the weakest pipe, fitting or valve in the line is rated for, from its marking or data sheet.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 2000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the rating at the operating temperature; it must exceed the working pressure for the tool to run.
Method and formulas
- Wave speed a = √[(K ÷ ρ) ÷ (1 + K D ÷ (E t))].
- Critical time 2L ÷ a; Joukowsky surge Δp = ρ a Δv for closure within it; slower closure reduces it roughly in proportion, Δp × (2L ÷ a) ÷ t_c (as the water hammer tool).
- Closing time needed so working + surge ≤ rating: t = (2L ÷ a) × Δp_J ÷ (rating − working).
- Example: the wave travels at 1,314.9 m/s; closing in 1 s gives 7.984 bar surge, 13.984 bar in total against 16 bar.
Limitations
- Simple rigid-column estimate for a single pipe; networks and column separation need a transient analysis.
- Linear valve closure assumed; most valves cut flow mainly at the end of their stroke.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a pipeline for a fast-closing valve
- Set an actuator closing time
- Decide whether a surge vessel is needed
Who it is for
- Hydraulic engineers
- Plant engineers
- Maintenance engineers
What you get
- Wave speed and critical closure time
- Surge for fast and actual closure
- Total pressure against the rating and the closing time needed
Interpreting the result
- Slowing the last part of the valve stroke does most of the good: the flow changes fastest near closure.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3024–3027. Topic reference; no source tables or recommended settings are reproduced.
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Open the Valve Closure Surge (Water Hammer against Pipe Rating) calculator