Please advise me if, I can use the following equation for calculating steam hammer forces at down stream of a stop valve, we use this approach in calculating steam hammer forces at up-stream of a stop valve and that seems correct to me:

F=(DLF) x K x m x a

Where:

m= mass flow rate of steam; a= speed of sound
DLF = 2
K= (pipe length/valve closure time x speed of sound) if length is less than critical length otherwise it’s equal to 1

What worries me is that, perhaps the pressure at the downstream of valve may reduce to zero (vacuum) as the valve shuts down. As such the pressure difference between the adjacent elbows of the run would be same as operating pressure of pipe and steam hammer force might be calculated as:

F= (DLF) x K x (operating Pressure) x (Cross sectional area of pipe)

Both these approch will give very different results

hi! please provide your suggestions.

Pressure at the downstream of valve in case of water hammer reduces to vapor pressure as the valve shuts down. As such the pressure difference between the adjacent elbows of the run would be (Operating pressure-Vapor pressure) hence, hammer force might be calculated as:

F= (DLF) x K x (Operating pressure-Vapor pressure) x (Cross sectional area of pipe)

But I doubt, what would happen in case of steam hammer as the medium is already in gaseous phase

Dear KSR

i have the same doubt

The dynamic event look so :
At beginn you become a high pressure on the valve.
This pressure (phigh)are higher as on the next elbow so you have a delta p in this pipe segment.
phigh can calculated with joukowski formula.
The pressure wave to travel in the pipe until the source.
Maybe on the source you can become to beginn this event a vacuum.
This vacuum collaps at this time pressure wave come to the sourge.
So the pressure wave go return to the valve and so forth...
until damping ( friction etc..)the pressure wave reduced at zero.

Calculation Methods :
1. Static with DLF = 2
2. Response
3. Time Historie
Normaly this 3 Methods to consider once pressure wave (vale to source)and not consider forwards and backwards pressure waves.
This szenario can to escalate the pipe with i higher dyn. result.

Sorry my english is from 1970.

Dear Mr Ohlinger

Thanks for your reply.

I agree with you on the nature of the wave. My only worry is if, i can use the joukowski formula in portion of pipe after a closing valve like i use it in portion of pipe before the valve.

Please see drawing attached below:

Please see the drawing

On the right side the valve is the same case as a pump drop fast down.
Also here a you become a delta p with another sign.

Dear Mr Ohlinger

Thank you very much.

So, I believe that Joukowsky equation can be used for calculation of pressure difference downstream of the closing valve, if the pressure difference calculated by Joucowsky formula is less than, operating pressure in pipe.

So, I think force will be calculated as the lesser of:

(Pressure as per Joucowsky X area of pipe) or
(Operating pressure before valve closure X area of pipe)