What is the Joukowsky equation for pressure rise due to water hammer, and what do the symbols represent?

• A. ΔP = ρ c ΔV; ρ is fluid density, c is wave speed in the pipe, ΔV is the change in velocity of the fluid.
• B. ΔP = γ h; γ is the specific weight, h is head.
• C. ΔP = μ ΔL / A; μ is viscosity, ΔL is length change, A is area.
• D. ΔP = ρ g h; ρ is density, g is gravity, h is head.

Answer: (A)

When flow is changed suddenly, such as a valve closing quickly, the moving fluid carries momentum and a pressure wave propagates along the pipe. The Joukowsky equation links that dynamic pressure rise to the speed of the pressure wave and the change in fluid velocity: ΔP = ρ c ΔV.

Here, ρ is the fluid density, c is the wave speed (celerity) of the pressure wave in the pipe, and ΔV is the abrupt change in the fluid’s velocity. This relation shows that a larger density, a faster pressure wave, or a bigger change in velocity all push the pressure rise higher.

The other forms describe static or different phenomena (like hydrostatic pressure from height or effects of viscosity and pipe deformation) and do not capture the rapid dynamic surge caused by water hammer.