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Water hammer

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niallmacdubhghaill

niallmacdubhghaill

Chemical
May 2, 2006
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Hi,

Im looking into water hammer at the moment. I am trying to figure out whether or not my lines are at risk from water hammer stresses.

I have found a design guide which tells me that if t>3L/Vsound then water hammer is not a problem.

t = valve closing time
L = length of column of fluid (pipe length)
Vsound = velocity of sound in fluid

then Vsound is given as sqrt(k/rho) where rho is fluid density, and k is the bulk modulus of the fluid where the bulk modulus is given by k = -V dP/dV.

This is pretty much where I get lost.

If my fluid is an oil, with density 840 kg/m3 and is essentially incompressible (=> Zl=0) haw do I calculate k and thus Vsound to find out if I have a water hammer problem?

Any and all help appreciated!!

Thanks

Niall

 
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You have to get compressibility data of the fluid. If your fluid is considered "essentially incompressible", that means k is infite and your calc won't work out.
 
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The modulus of elasticity being typically about 14,000 kg/cm[sup]2[/sup] at ambient temperature, the celerity of the pressure wave (sound) in your oil would be, approximately:

(14,000 kg/cm[sup]2[/sup][×]10,000 cm[sup]2[/sup]/m[sup]2[/sup][×]9.8 m/s[sup]2[/sup][÷]840 kg/m[sup]3[/sup])[sup]0.5[/sup] = 1280 m/s.
 
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Coming at it from another direction: Assume the fluid IS incompressible. Assume the PIPE is infinitely stiff.
Remember F=MA
What is the flowing velocity of the fluid in the pipe? V
How long does it take for the valve to close? T
What is the density of the fluid? G
What is the cross sectional area of the pipe? A
How long is the pipe? L

So you have a MASS of fluid coming at the valve ADL
And it will be accelerated at V/T
So it will take a force AGLV/T to do that.

Force is Pressure times area, so pressure is Force divided by Area P=GLV/T

Since this disregards compressibility or elasticity, it is not absolutely correct, but it will put you in the ball park to estimate the pressures. It also assumes the valve has a linear characteristic and closes at a continuous rate. Therefore it might be prudent to double the force and pressure numbers.
 
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OIL IS NOT INCOMPRESSIBLE WHEN IT COMES TO SURGE ANALYSIS. By the way, you probably need the adiabatic bulk modulus.

Please have a look on my webpage... Surge "Blog" for when you sould do a waterhammer analysis. Note, if it is a code design, a "waterhammer" analysis is required... not optional.



Going the Big Inch! [worm]
 
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All fluids to my knowledge are compressible.
"Then Vsound is given as sqrt(k/rho) where rho is fluid density, and k is the bulk modulus of the fluid where the bulk modulus is given by k = -V dP/dV".... UNDER ISENTROPIC CONDITIONS.

MORE LATER
 
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U.S. DEPT OF ENERGY
OFFICE OF ELECTRICTIY DELIVERY AND ENERGY RELIABILITY

ENERGY ASSURANCE DAILY
Wednesday, August 16, 2006


Update: BP Prudhoe Pipeline Shutdown
[COLOR=white red]Pressure Surge Forces BP to Shut Point McIntyre Field in Alaska [/color]
On August 11 a pressure surge during a repressurizing of the pipeline serving the Point McIntyre field in Alaska led to BP shutting down the 20,000 b/d field. [COLOR=white red]The surge caused the pipeline to shift from some of its supports. [/color]
BP will inspect the line for damage and remount it on the supports before restarting the system. No oil was spilled
as a result of the surge.
Reuters, 10:51 August 16, 2006


Going the Big Inch! [worm]
 
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Quote from an article appearing in "World Pumps", by one of the frequent posters on this site, G. Stone

read the whole article here,

Commonly, the use of the Joukowsky formula (dH = c*dV/g: where dH is the increase in head in metres, c is celerity, dV the change in velocity in m/s, and g the acceleration due to gravity; Equation 1.1 in Ref. 1) is advocated to determine the worst case of surge. Unfortunately, it does not always indicate the highest transient pressure that will occur in a system for all scenarios. In practice, this equation is usually only directly applicable to quite simple pipe systems and when rapid collapse of vapour cavities occurs. In a complex system, the pressure transients reflect off boundaries and can combine to produce even greater surges than for a simple valve closure or other boundary change. The equation makes no allowance for vacuum events that may result in buckling failure.
Click to expand...




Going the Big Inch! [worm]
 
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BigInch For Information only--
The referenced equation is for frictionless one dimensional flow of a highly incompressible fluid. The referenced equation should have a + or - between the two terms and in reality is therefore two equations. Along with these equations are two additional ones
Dv/dt=u+/- a,
where a is the sound velocity and u local veloity.

Solution of these 4 equations and not one equation is required for the most basic problem.
Of course other factors, such as friction, elevation should be included in more sophistacted analyses.


Misuse or misunderstanding of the basic equations leads to errors in practical applications.
GITGO or garbage in=garbage out is the result of using programs in which the user is not knowledgable about the basic formulations in a program.

The Joukowsky equation or water hammer equation came about in the early 1900s. Integration of the equation was really solved in the mid 1800s by the mathematican Reimann.

Regards
 
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Correction to my previous post
Dv/dt=u+/- a,
where a is the sound velocity and u local veloity.
SHOULD READ
Dx/dt= u+/- a where x is distance.
regards
 
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