### Water Hammer Pressure Spike Review, Equations and Calculator

**Fluid Flow Table of Contents
Hydraulic and Pneumatic Knowledge**

*Water Hammer Pressure Spike Review and Equations*

When any moving fluid (not just water) is abruptly stopped, as when a valve closes suddenly, large pressures can develop. Although detailed analysis requires knowledge of the elastic properties of the pipe and the flow-time history, the limiting case of rigid pipe and instantaneous closure is simple to calculate.

A *pressure spike *is the resulting rapid rise in pressure above static pressure caused by water hammer. The
highest pressure spike attained will be at the instant the
flow changed and is governed
by the following equation.

*Δp _{h} = ρ · c_{s} · V / g_{c}*

Where:

*Δp _{h}* = pressure rise caused by water hammer, lb

_{f}/ft

^{2 }

*ρ*= fluid density, lbm/ft

^{3 }

*c*= velocity of sound in fluid, fps

_{s}*V*= fluid flow velocity, fps

*g*= gravity ft/sec

_{c}^{2}

The *c _{s}* for water is 4720 fps, although the pipe’s elasticity reduces the effective value.

Example water hammer calculation:

What is the maximum pressure rise if water flowing at 10 fps is stopped instantaneously?

Solution:

*Δp _{h}* = 62.4 lb

_{f}/ft

^{3}x 4720 fps x 10 fps / 32.2 ft/sec

^{2}= 91,468 lb/ft

^{2}= 635 psi

Conversion:

1 lb/ft^{2} = 0.0069444444 psi

1 psi = 144 lb/ft^{2}

Related:

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- Water Hammer Accumulator Sizing Excel Spreadsheet Calculator
- Steam Hammer Review
- Water Hammer (Waterhammer) Review and Equation
- Operational Considerations Practical Applications Water Hammer
- Impact Loading Approximate Formulas
- Mass Impact Loading Equations

References

- ASHRAE Handbook of Fundamentals, 2021 Inch-Pound Edition