Surge Pressure Computations
What is a Surge
• A pressure surge or a water hammer is
a pressure wave caused by a sudden
change in water velocity.
• The word “water hammer” originates
from the hammering sound which
plumbing makes inside a house when
faucets are turned on or off quickly.
Why do Surge analysis?
• Protect the pipeline and its
appurtenances
• Protect human life
• Reduce pipe costs
When do Surge analysis?
• Consideration should be given to
performing a surge analysis when any
of the following conditions exist
– the maximum change of fluid velocity
could exceed 4 fps
– the length of the pipeline exceeds 1000 feet
– there are fast acting valves in the system
– there are pumps in the system
What are the Maximum
Allowable Pressures?
• The various standards for PVC pipe are not in
total agreement regarding the “safety factor
“for PVC pipe.
1 The pipeline shall have a pressure class rating
greater than the static or working pressure plus
surge at any point in the system.
2 For low pressure systems, “Pressure relief valves
shall be large enough to pass the full pump
discharge with a pipeline pressure no greater than
50 percent above the permissible working head of
the pipe.”
Allowable Pressures cont..
3 For high pressure systems, “Pressure relief
valves shall be set to open at a pressure no
greater than 5 psi above the pressure rating
of the pipe or the lowest pressure rated
component in the system.
4 The Handbook of PVC Pipe (Uni-bell,
1977) states that “In general, system
operating pressure (static pressure plus
surge pressure ) should not exceed 150% of
the pipe pressure rating or pressure class.”
What causes varying velocity?
•
•
•
•
•
•
•
•
Closing a valve
Opening a valve
Rhythmic valve operation
Starting a pump
Stopping a pump
Movement of air pockets
Sudden release of air
Sudden halt in flow when air has been
exhausted
• Recombination after water-column separation
Critical time
• Critical time = 2L/a
• Valve or pump closure should be
greater than critical
• The last 20% of valve closure most
critical. Very dependent on type of
valve.
What Really Happens?
Simple Valve Closure
Wave Diagram t=0 to 2L/a
Wave Diagram t= 2L/a to 4L/a
How fast is the pressure
wave?
• Wave speed based on two things
– Bulk modulus of elasticity of the fluid,
usually water.
– Bulk modulus of elasticity of the pipe
walls.
How to compute surge
pressures
h = change in pipe pressure head
a
speed
h 
* v ag == wave
speed of gravity
g
v = change in velocity
4720
a
k D
1 * *(1 u 2 )
E e
K = bulk modulus elasticity of fluid ( water = 300,000 psi)
E = modulus of elasticity of pipe material
D = inside pipe diameter (in)
e = Pipe wall thickness (in)
u = Poission’s ratio (PVC = .45)
Another way is nomographs
What happens if there are
multiple pipes?
The Procedure here is to convert the series pipe
to an equivalent uniform pipe
L
L1 L2
Ln

 .....

a1 a1 a2
an
Ln
a
n
Branching Pipelines
P3
P1(2a1a2 A1)
(a2a3 A1a1a3 A2 a1a2 A3)
Effects From Air Movement
• When an air pocket becomes suddenly
dislodged, as by a stream of flowing
water, the extent of changes in “local”
fluid velocities and the consequent
waterhammer pressures are often much
in excess of instantaneous closure.
Pressure Rating
• Pressure rating can changed based on
hoop stress and number of cycles
Pressure Rating Over Time
PVC PIPE Hoop Stress vs Cycles to Failure
Hoop Stress (psi)
10000
1000
1000
10000
100000
540000
Cycles to Failure
10000000
100000000
Example
• Compute the head increase due to instantaneous
stoppage of water initially flowing at 5.0 fps in an 10
inch, 80 psi, PIP pieline, a = 860
• If the static head at the point of stoppage is 55.0 psi,
what is the total pressure acting on the pipe at the
moment of stoppage?
• What is the hoop stress developed at the moment of
stoppage? Hs=P*D/2*t
• If this Hoop stress will occur twice each day, and at
each occurrence there are 8 stress cycles of this
approximate magnitude, and if the irrigation season
is 90 days long, how many years can this pipe be
expected to last before failure due to stress cycles?
Summary
• Actual surge analysis is generally much more
complicated than the simple example.
• The most practical method of solutions is to
understand the available protection hardware
and to install that equipment at enough
locations and with reasonable settings.
• A fact of life which makes this approach
almost necessary is that irrigation systems
tend to be added to or changed with time
until they may only vaguely resemble the
original design.