I have a problem where a piping system is modelled and the effect of surge
due to pressure differential across elbow pairs is investigated.

The major pressure differential is existing between the elbows ( an example
) 10 and 20 where my pipe between the elbows is in Z direction. After
elbow 20, the next elbow is 30 where the pipe between the elbows is in X
direction. and length and differential pressure between elbows 20 and 30 is
much less than what is between 10 and 20.


My question is: Should the surge load on elbow 20 be equal to the pressure
differential between elbows 10 and 20 times the flow area , acting in Z
direction only or in both X and Z?


As per my understanding, under the action of pressure on elbow , the
loading should be in two directions, at the two weld points. However the
portion of pipe which is between elbows 10 and 20 is in Z direction and
the max. differential is between these two elbows . The distance between
elbow 20 and 30 is very less ( in comparsion to that between 10 and 20) and
the pipe is in X drection between these elbows and the unbalanced load in
20 in X direction should be balanced by that in 30 in X direction ( because
of small distance and small differential between them) and hence the
effective unbalanced force at 20 will be in Z only.

Would like comments on the above.

Regards

Dear Anindya,

I think your approach is correct, as far as I understand your little example.

When we transfer unbalanced forces based on pressure differences to the Caesar II model normally every piping segment will be subjected to its own force time-history. However, in case of very small distances between two elbows, the pressure difference (and the resulting forces) are sometimes negligible.

Force time-history direction is always identical with the centerline orientation of the pipe segment.

Please feel free to contact me in this matter in case of further questions.

Regards,
Veit Bockemühl
www.pipestressanalysis.com
www.surgeanalysis.com

Herr Bockemuhl,

Thanks for your response. First, I agree with you. Second: My doubt is based on two reasons:

1) Most consultancies , I have seen , use the forces in two directions, for the similar geometry and pressure vs time data.

2) The ASME paper Dynamic pipe stress during Water Hammer by Robert Leishear ( PVP Vol. 440 2002), shows the Forces in two directions.

Regards

I seems to me that either approach would work - either define the calculated load on every elbow where only one elbow load changes at a time or just apply the imbalance on each elbow-elbow pair. The first approach uses the steady-state plus the transient and the second applies only the transient. I think the second is simpler.

Dave sir,

Nice informative post....

I am still working on this topic.

Please find the attachment of the sample calculations of forces from both approaches.

In my calculation, first and second Approach force values are varies.

Please correct me, Where my calculations/understanding gone wrong.

Hi,

Transient force due to pressure difference is parallel to the axis of straight pipe while steady-state force due to momentum change of flow, which is mass flow rate times velocify of fluid, is in two direction. Seady-state force may not be considered as the force is not so big normally. (Sometimes it's considered for two-phase flow.)

I have a question. Do you have any devices such as quick closing valve which can cause surge effect in the piping? If not, why do you need to consider transient load. Ordinary pressure difference(pressure drop) due to friction is not considered as it's small enough. If yes, you can increase valve closing time to avoid surge.

In summary,
Check if transient force is really required to consider?
Transient force due to pressure difference is parallel to the axis of pipe
Steady-state force due to flow is in two-direction and normally not considered.

Parky thanks for your reply,

yes, quick closing valve is there.

No I cant increase valve closing time to avoid surge. Its a client requirement to do surge analysis.

Please find what Dave said " I seems to me that either approach would work - either define the calculated load on every elbow where only one elbow load changes at a time or just apply the imbalance on each elbow-elbow pair. The first approach uses the steady-state plus the transient and the second applies only the transient. I think the second is simpler."

Please find the attached document in above post in that I did calculations for both approaches What I understand from dave words.

Both approaches calculations gives different values of forces. I am unable to find out where I did a mistake.

As a general query , what if leg 20 to 30 is also long like leg 10 to 20 ? Now if we put the load at 20 in either direction, there is no way in any software to identify that the second set of loads starts acting after a time lag .That lag is the time required to reach the pressure wave from 10 to 20 . Also the software package shall be able to take care that at 20 , the X load will not act during first set of loads.
Then an option is needed to impose the second set on the displaced pattern at the end of time lag described above.