Pressure surge

Flowing fluid carries kinetic energy. If it is suddenly slowed or accelerated – by a closing valve, a tripping pump, a slamming check valve – that energy is converted into pressure. The pressure change travels through the line as a wave at the speed of sound and is reflected at vessels, branches and closed ends.

Pressure surge is the general term for such events. In liquid lines it is also called water hammer; in steam lines, slugs of condensate can cause similarly violent impacts.

The magnitude of the surge for an instantaneous change in velocity is given by the Joukowsky equation: Δp = ρ · a · Δv, where ρ is the density of the fluid, a the wave speed in the pipe and Δv the change in flow velocity.

An example: water at 1000 kg/m³, a wave speed of 1000 m/s and a velocity change of 2 m/s give 2,000,000 Pa – that is, 20 bar on top of the operating pressure. The wave speed depends on the fluid, the pipe material and the wall thickness; in steel pipes carrying water it is in the order of 1000 m/s, in plastic pipes considerably lower.

Whether the full Joukowsky surge occurs depends on the closing time. The pressure wave runs from the valve to the nearest reflection point and back; this takes the reflection time 2 · L / a, with L as the length of the line. If the valve closes faster, the full surge develops. If it closes much more slowly, the returning wave already relieves the pressure while closing is still in progress.

Long lines are therefore more sensitive than short ones: a closing time that is harmless over twenty metres can trigger the full surge over two kilometres.

The pressure peak loads the pipe wall – that is the obvious part. The more dangerous part is often the force on the line itself: while the wave passes through a straight section between two elbows, the pressure at the two ends differs. The difference acts as an unbalanced force along the pipe axis, displaces the line and loads supports and anchors.

Verification takes two steps: a fluid transient calculation provides pressure against time, and a dynamic structural analysis derives stresses and support loads from it.

The most effective measure addresses the cause, not the consequences.