# Water Hammer

## Joukowski's equation

Where

DH = change in pressure head, m

a = celerity, m/s

DV = change in velocity, m/s

g = acceleration due to gravity, m2/s

Valid for

0<m<=2L/a

m = return period of wave, s

L = length of pipeline, m

## Celerity

In this estimate, the following simplifying assumptions apply:

1. The bore of the cement mortar lining is used as the internal diameter of the section.
2. The appropriate wall thickness is approximated as the sum of the thickness of the DI wall plus the transformed thickness of CML. The CML thickness is transformed using the ratio of Young's Modulus for CML divided by that for DI.

The wave speed or celerity is also adjusted to incorporate differences in installation restraint:

1. pipe anchorage only at upstream end
2. full pipe restraint from axial movement
3. longitudinal expansion joints along the pipeline

Wylie & Streeter (1993) show the equation for wave speed can be conveniently expressed in the general form:

a = (K/ρ)0.5 / (1+K/Ed/teC)0.5

Where

case a)
5/4-m
case b)
1-m2
case c)
1.0
DN
Y mm
t mm
tC mm
d = Y-2*(t + tc) mm
ECML/EDI
tc transformed, mm mm
te = t + tc transformed, mm
µ= mm
C case a)
case b)
case c)
Celerity, a =
case a) m/s
case b) m/s
case c) m/s
ΔH = aΔV/g
ΔV = change in velocity m/s
g gravity, m/s/s/ m/s
case a) m
case b) m
case c) m