水水撃圧力surgeにおける配管

Overview

Water hammer (hydraulic shock) is a pressure surge caused by sudden changes in fluid velocity in a pipe system. It occurs when:

• Valves close rapidly
• Pumps start or stop suddenly
• Check valves slam shut

Joukowsky Equation

The maximum pressure rise from instantaneous valve closure:

$\Delta p = \rho \cdot c \cdot \Delta v$

where:

• $\Delta p$ = pressure surge (Pa)
• $\rho$ = fluid density (kg/m³)
• $c$ = speed of sound in the pipe-fluid system (m/s)
• $\Delta v$ = change in velocity (m/s)

The wave speed in an elastic pipe:

$c = \sqrt{\frac{K/\rho}{1 + (K \cdot D)/(E \cdot t)}}$

where $K$ = fluid bulk modulus, $E$ = pipe elastic modulus, $D$ = pipe diameter, $t$ = wall thickness.

Typical Wave Speeds

Prevention Methods

Method	Mechanism
Slow-closing valves	Extend closure time > $2L/c$
Surge tanks / air vessels	Absorb pressure waves
Pressure relief valves	Vent excess pressure
Pump soft-start / VFD	Gradual velocity change
Air chambers	Compressible volume buffer
Check valve with dashpot	Prevent slamming