WATER HAMMER

[JackofallMech]

How does the equation for water hammer surge pressure take into account the mass of the fluid being stopped? I would think that the greater the body of water being stopped the greater the pressure. yet the formula only seems to consider the change in velocity regardless of the mass of fluid being stopped. Can someone help me understand this a litte better please.

 

[BigInch]

The quick answer is that head is potential energy per unit of mass.

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"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[sailoday28]

The basic water hammer equations (highly incomressible fluid and sound speed nearly constant) are derived from conservation of mass and momentum.

 

[JackofallMech]

It appears as though there are two different formula's for water hammer. One considers the pressure wave that travels down the pipe due to an instantaneous shock and the other considers pressure rise due to rate of closure of a valve which does directly take into consideration the mass of the fluid. I'm not entirely sure when you would choose one over the other unless it has to do with the difference between instantaneous and less instantaneous valve closure

 

[sailoday28]

What are the two formulas?

 

[JackofallMech]

instantaneous a=4720/[1+(K(DR-2)/E)]^2 to go into deltP=density*a*deltaV where K=bulk modulus of fluid, DR dimension ratio HDPE, E modulus of elasticity
versus
noninstantaneous P=(0.070*V*L/t)+Pi where V=velocity, L=piple length, t=valve closure time, Pi=initial pressure.

Regards

 

[BigInch]

An instantaneous equation assumes that the fluid is incompressible and the pipe is not expandable. A more realistic method evaluates the resulting pressure as a function of both the fluid's equation of state, defining the density and hence its volume at any pressure, the pressure required to expand the pipe in order that it can hold the fluid's compressed mass within a volume that such a pressure will expand the pipe.

In a noncompressible fluid and rigid pipe scenario, there are no pressure waves because when the fluid is noncompressible, stopping the head of the column also stops the tail of the column instantaneously, just like a train. With a compressible fluid, stopping the head of the column causes trailing fluid packets to compresses up against each other when they "collide" which causes a wave of increasing pressure to travel back to the beginning of the pipeline.

I'll suggest you read Chaper 13, then come back if you still have any questions,

http://www.haestad.com/books/pdf/awdm.pdf

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[FredRosse]

“How does the equation for water hammer surge pressure take into account the mass of the fluid being stopped? I would think that the greater the body of water being stopped the greater the pressure. yet the formula only seems to consider the change in velocity regardless of the mass of fluid being stopped. Can someone help me understand this a little better please?”

The reason why the equation does not recognize the mass of fluid being stopped is because this is a wave process, and indeed does not depend on the total mass of the pipeline fluid.

Consider the classic example where a pipeline is flowing at some initial velocity, and a valve is suddenly closed. The upstream velocity is suddenly interrupted, and an increased pressure wave travels upstream. The basic equation is formulated on a wave interface, where velocity interruption is “traded” for pressure. The wave travels up the pipeline at sonic velocity, so the duration of unbalanced forces has a longer duration for a longer pipeline, however the magnitude of the pressure increase has nothing to do with the length of the pipeline.

The fundamental waterhammer equation is:

DP = Density X C X DV

Where:

DP = Differential pressure caused by a velocity interruption, Force per unit Area

Density = Fluid Mass per unit Volume

C = Sonic wave velocity for the fluid system, Length per unit time.

The sonic velocity in any system depends on the elastic properties of the fluid, plus the elastic properties of the pipeline. For ordinary water applications and steel pipe, the sonic velocity is around 4000 feet per second. Plastic pipes (more elastic) typically result in a lower sonic velocity.

DV = The velocity interruption, for example, if the pipeline is flowing at 10 feet per second, and the valve suddenly closed, then DV = 10 ft/sec

This equation is dimensionally consistent in any rational system of units.

Complications arise when the valve closure time is longer than the sonic travel time within the pipeline, for example, in a pipeline with a sonic velocity of 4000 ft/sec, and a length of 4000 ft, then any valve closure time of 1 second or less will produce the full waterhammer pressure. If the pipeline is shorter, then only a part of the full waterhammer pressure is realized. Dealing with this analytically is beyond what can be presented here, but it is generally treated as several small steps of valve closure, each small step creating a small wave, with additive pressure increase.

In fact , there are not two formulas, only one fundamental equation. The fundamental equation is sometimes modified for special conditions.

 

[BigInch]

That should be "complications arise when the valve closure time is shorter than the sonic travel time within the pipeline". Assuming complications mean maximum pressure.

In a shorter pipeline, full water hammer pressure can still be reached, as long as the valve closing time is made less than the time needed for the wave to run down that shorter line length.


**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/