Surge Pressure Computations

What is a Surge

• A pressure surge or a water hammer A pressure surge or a water hammer is a pressure wave caused by a is a pressure wave caused by a sudden change in water velocity. sudden change in water velocity.

• The word “water hammer” The word “water hammer” originates from the hammering originates from the hammering sound which plumbing makes inside sound which plumbing makes inside a house when faucets are turned on a house when faucets are turned on or off quickly.or off quickly.

Why do Surge analysis?

• Protect the pipeline and its Protect the pipeline and its appurtenancesappurtenances

• Protect human lifeProtect human life• Reduce pipe costsReduce pipe costs

When do Surge analysis?

• Consideration should be given to Consideration should be given to performing a surge analysis when any performing a surge analysis when any of the following conditions existof the following conditions exist– the maximum change of fluid velocity the maximum change of fluid velocity

could exceed 4 fpscould exceed 4 fps– the length of the pipeline exceeds 1000 the length of the pipeline exceeds 1000

feetfeet– there are fast acting valves in the systemthere are fast acting valves in the system– there are pumps in the systemthere are pumps in the system

What are the Maximum Allowable Pressures?

• The various standards for PVC pipe are The various standards for PVC pipe are not in total agreement regarding the not in total agreement regarding the “safety factor “for PVC pipe.“safety factor “for PVC pipe.1 The pipeline shall have a pressure class rating The pipeline shall have a pressure class rating

greater than the static or working pressure greater than the static or working pressure plus surge at any point in the system.plus surge at any point in the system.

2 For low pressure systems, “Pressure relief For low pressure systems, “Pressure relief valves shall be large enough to pass the full valves shall be large enough to pass the full pump discharge with a pipeline pressure no pump discharge with a pipeline pressure no greater than greater than 50 percent above the permissible 50 percent above the permissible working head of the pipe.”working head of the pipe.”

Allowable Pressures cont..

3 For high pressure systems, “Pressure For high pressure systems, “Pressure relief valves shall be set to open at a relief valves shall be set to open at a pressure no greater than 5 psi above the pressure no greater than 5 psi above the pressure rating of the pipe or the lowest pressure rating of the pipe or the lowest pressure rated component in the system.pressure rated component in the system.

4 The Handbook of PVC Pipe (Uni-bell, 1977) The Handbook of PVC Pipe (Uni-bell, 1977) states that “In general, system operating states that “In general, system operating pressure (static pressure plus surge pressure (static pressure plus surge pressure ) should not exceed 150% of the pressure ) should not exceed 150% of the pipe pressure rating or pressure class.”pipe pressure rating or pressure class.”

What causes varying velocity?

• Closing a valveClosing a valve• Opening a valveOpening a valve• Rhythmic valve operationRhythmic valve operation• Starting a pumpStarting a pump• Stopping a pumpStopping a pump• Movement of air pocketsMovement of air pockets• Sudden release of airSudden release of air• Sudden halt in flow when air has been Sudden halt in flow when air has been

exhaustedexhausted• Recombination after water-column separationRecombination after water-column separation

Critical time

• Critical time = 2L/aCritical time = 2L/a• Valve or pump closure should be Valve or pump closure should be

greater than criticalgreater than critical• The last 20% of valve closure most The last 20% of valve closure most

critical. Very dependent on type of critical. Very dependent on type of valve.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 thingsWave speed based on two things– Bulk modulus of elasticity of the fluid, Bulk modulus of elasticity of the fluid,

usually water.usually water.– Bulk modulus of elasticity of the pipe Bulk modulus of elasticity of the pipe

walls.walls.

How to compute surge pressures

h ag

v *h = change in pipe pressure heada = wave speedg = speed of gravityv = change in velocity

akEDe

u

4720

1 1 2* *( )

K = bulk modulus elasticity of fluid ( water = 300,000 psi)E = modulus of elasticity of pipe materialD = 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

La

La

La

La

La

n

n

n

n1

1

1

2

2

.....

Branching Pipelines

P P a a Aa a A a a A a a A

3 1 1 2 12 3 1 1 3 2 1 2 3

(2 )

( )

Effects From Air Movement

• When an air pocket becomes When an air pocket becomes suddenly dislodged, as by a stream suddenly dislodged, as by a stream of flowing water, the extent of of flowing water, the extent of changes in “local” fluid velocities changes in “local” fluid velocities and the consequent waterhammer and the consequent waterhammer pressures are often much in pressures are often much in excess of instantaneous closure.excess of instantaneous closure.

Pressure Rating

• Pressure rating can changed Pressure rating can changed based on hoop stress and number based on hoop stress and number of cyclesof cycles

Pressure Rating Over TimePVC PIPE Hoop Stress vs Cycles to Failure

1000

10000

1000 10000 100000 540000 10000000 100000000

Cycles to Failure

Hoo

p St

ress

(psi

)

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? HHss=P*D/2*t=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 Actual surge analysis is generally much more

complicated than the simple example.complicated than the simple example.• The most practical method of solutions is to The most practical method of solutions is to

understand the available protection hardware understand the available protection hardware and to install that equipment at enough and to install that equipment at enough locations and with reasonable settings.locations and with reasonable settings.

• A fact of life which makes this approach A fact of life which makes this approach almost necessary is that irrigation systems almost necessary is that irrigation systems tend to be added to or changed with time tend to be added to or changed with time until they may only vaguely resemble the until they may only vaguely resemble the original design.original design.