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

Hydraulic and Pneumatic Knowledge
Fluid Power Equipment

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.

Δph = ρ · cs · V / gc

Where:

Δph = pressure rise caused by water hammer, lbf /ft2
ρ = fluid density, lbm/ft3
cs = velocity of sound in fluid, fps
V = fluid flow velocity, fps
gc = gravity ft/sec2

The cs 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:

Δph = 62.4 lbf/ft3 x 4720 fps x 10 fps / 32.2 ft/sec2 = 91,468 lb/ft2 = 635 psi

Conversion:

1 lb/ft2 = 0.0069444444 psi
1 psi = 144 lb/ft2

• ASHRAE Handbook of Fundamentals, 2021 Inch-Pound Edition