What is a hydraulic transient (water hammer) and state the Joukowsky equation for surge pressure.

A transient surge due to sudden changes in flow velocity; ΔP = ρ c ΔV

Hydraulic transient, or water hammer, is a rapid change in pressure that occurs when the flow velocity in a pipeline changes suddenly. This happens, for example, when a valve shuts quickly or a pump trips, and the moving water cannot adjust its velocity instantly. The resulting surge pressure travels as a wave along the pipe, with its magnitude tied to how abruptly the velocity changes and how stiff the system is.

The surge pressure is described by the Joukowsky relation: ΔP = ρ c ΔV. Here ρ is the fluid density, c is the speed of the pressure wave in the pipe (a function of the fluid and the pipe’s elasticity), and ΔV is the sudden change in flow velocity. This equation shows why a small sudden change in velocity can produce a large pressure spike in longer or more rigid systems.

Other options describe steady or gradual pressure changes or effects due to temperature, which do not characterize a hydraulic transient.

A steady-state pressure drop; ΔP = 0

A gradual pressure rise; ΔP = ρ g ΔV

A transient surge due to temperature change; ΔP = μ ΔV

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