Parameters
Presets
Inner Diameter D
100 mm
Wall Thickness t
5.0 mm
Pipe Material
Fluid
Initial Flow Velocity V₀
2.0 m/s
Valve Closure Time t_c
0.0 s
0 = instant closure (maximum water hammer)
Pipe Length L
500 m
Static Pressure P_static
300 kPa
—
Wave Speed a [m/s]
—
ΔP Joukowsky [kPa]
—
P_max [kPa]
—
t_cr = 2L/a [s]
—
P_max / P_static
Theory
Pressure wave speed (with pipe wall elasticity):
$$a = \frac{\sqrt{K/\rho}}{\sqrt{1 + KD/(Et)}}$$Joukowsky pressure rise (sudden closure, $t_c \le t_{cr}$):
$$\Delta P = \rho \, a \, V_0$$Gradual closure ($t_c > t_{cr}$) approximation:
$$\Delta P = \rho \, a \, V_0 \cdot \frac{t_{cr}}{t_c} = \rho \, a \, V_0 \cdot \frac{2L}{a \, t_c}$$Critical closure time: $t_{cr} = 2L/a$
Engineering note: Used for preliminary design checks before detailed Method of Characteristics (MOC) or CFD-FSI analyses in ANSYS Mechanical/Fluent. Applicable to water supply, plant piping, steam line and HVAC systems.