Axial thrust due to pressure reduction 1

[sbnz]

Hi,

We have a 400NB water supply pipeline where a direct acting pressure reducing valve is to be installed to reduce the pressure of 130m of water to 50m of water.

Question is, is there an axial thrust generated inherently due to the pressure reducing valve functioning which needs to be considered in designing the downstream pipe restraint? If yes, why is that and how is that calculated? Is it the differential pressure (80m of H2O or 800 kPa) acting on the whole pipe cross section?

thanks,

 

[BigInch]

If you consider a free body of the valve and include some pipe upstream and downstream, you see there is a net axial and unbalanced force that is equal to P_in * Pipe_Area - P_out * Pipe Area.

Since the pressure differential is across the valve, the valve must transfer that force into the wall of the pipe, where it results in the net tension stess (F_net/A_up) being added to any existing stress in the upstream pipe and the net tension stress (F_net/A_down) being subtracted from any existing stress in the downstream pipe.

For Valve Installation design, it would be prudent to consider that some movement = F_net/A * (L_up + L_down)/2 * E might occur to the downstream direction, in addition to any movement caused by pre-existing stress.
Where L is the upstream pipe length and downstream pipe length. If you do not want that movement, then anchor the valve sufficiently to hold the force increase + any pre-existing forces.

http://virtualpipeline.spaces.msn.com

"What gets us into trouble is not what we don't know, its what we know for sure" - Mark Twain

 

[KevinNZ]

Big Inch

If i draw a free body diagrame and include elbows upstream and down stream then there no force.

The upstream pressure is balanced by the elbow and the valve. The downstream pressure is balanced by the valve and down stream eblow.

I acpect that is not the case for long pipelines and dynamic changes in pessure.

Kevin

 

[BigInch]

Its not so much about what you can see that holds any given free body diagram in place. What really controls the stress distribution, after a closed valve or something else sets up a force imbalance is how the pipe is allowed to move as the unbalanced forces convert to stress and then to strain and what and where the strains (elongations) are prevented from occuring by earth, supports, anchors and guides.

Consider a pressure reduction valve as above at the top of a tall expansion loop coming up deep from out of the ground at both vertical pipe segments. As you say, starting at the valve, you draw a free body of the valve and the horizontal segments and you get to the elbows. The upstream portion of the horizontal segment has a higher tension force than the downstream segment. When you arrive at the els with that tension force/stress, it gets converted to shear force in the vertical pipe segments. Shear in the vertical segments becomes bending moment as it moves down the vertical segments. The pipes bend in response to the tension bending stress on one side of the neutral axis and the compression bending stress on the other side of the neutral axis. OK, so now that we know what's going on, lets see how much is where. Tension stress is higher on the upstream side of the valve, so there's more shear and more bending on the upstream vertical leg, it must bend more than the downstream leg. If it bends more than the downstream leg, it deflects more than the downstream leg and now finally forces/stress and axial strains and bending deflections all balance. That's the secret to pipe stress. You can't look at pipe stress from the one sided prespective of stress alone. You must also consider how strains and bending deflections are resisted in order to understand how stresses are finally distributed. Every time you resist a strain or bending deflection, stress increases somewhere. Every time you can allow more movement, stress reduce somewhere.

http://virtualpipeline.spaces.msn.com

"What gets us into trouble is not what we don't know, its what we know for sure" - Mark Twain

 

[sbnz]

BigInch,

I am trying to follow your logic and must admit am somewhat confused.

I agree that with a pressure reducing valve (or for that matter with a shut isolation valve) in the pipeline, the tension in the pipe segments upstream and downstream sides of the valves will be different. But overall, I can not underestand how could there be a net unbalanced external force in the system which needs to be restrained by the anchors. Hypothetically, if the pipeline did not have any longitudinal restraint (and we ignore any thermal movement), do you mean the line will start moving under the action of the axial unbalanced force due to the differential pressure?

If there is actually an unbalanced force in a closed pipeline resulting from differential pressure on two sides of a valve, why do the pressure piping codes (B31.1 or B31.1) guidelines do not cover that and calculate the longitudinal stresses in the pipelines only due to the absolute internal pressure and other sustained loadings. As per the codes, the longitudinal stresses in the pipelines upstream and downstream of the pressure reducing (or closed isolation) valve will be different but there should not be net axial horizontal force exerted on the end restraint. I still can not see how in a rigid closed pipeline, an anchor can be subjected to a statically unbalanced force due to differential pressure within different sections in the pipeline.
I have not done any waterworks pipe design, but thought that the thrust blocks and anchors are designed to take the dynamic unbalanced forces (eg, water hammer)- may be I am wrong. Would appreciate more light thrown into the topic for clarifying our understanding.

thanks,

 

[BigInch]

That's exactly what I mean. Get one of those long balloons and start blowing it up. The end of the balloon that you're not blowing into moves away from your nose.

In the case of a two pressured pipe segments on each side of a closed valve with different pressures on each side of the valve, each far end of the pipe segments will move away from the valve according to the net axial stress in each segment.

Codes don't directly place a limit on the axial stress component because of its effect on maximum shear stress. Maximum Shear Stress is responsible for failure and axial tension from "closed end stress" reduces maximum shear stress. Remember Mohr's stress circle? However codes do address and limit the MAXIMUM COMBINED (shear) STRESS, which DOES include the both axial stresses and hoop stress.

What a pipe stress engineer must not forget is that AXIAL COMPRESSION increases maximum shear stress and you must be sure to check that maximum shear stress is not exceeded.

Codes don't address everything either, buckling stress for example. A very tall vertical segment of pipe with zero pressure will pass code check, but will fail totally under its own accord due to the buckling stress being exceeded for its buckling mode length. Flagpole buckling mode length is 2 x its actual length. Even though the codes don't address that particular mode directly, the engineer must know to check for that condition or the pipe will obviously fail. Codes don't guarantee the design works. They only guarantee that they meet code requirements.

OK, now for the last question, how do anchor loads form up from pressure stress? Taking the closed pipes on two ends of the valve example again,

We have different elongations from the different pressures in each segment, so lets try anchoring these displacements and totally restricting movement. What happens to stress?

Since those movements were elongations, if we anchor at both far ends of pipe right on the end caps, and at the valve, the all movements are now restricted to 0. The resulting net axial compressive stress resisted by the anchors are found from setting the negative of the pressure elongations to = F * L / MaterialA / E, the axial deflection of a material subject to axial stresses.

where L = pipe lengths
F = Anchor Force

[

http://img207.imageshack.us/img207/9922/stressmohrcirclela3.png

]

<whops.. stick a minus sign on the resultant anchor force at the valve>

These are absolute anchors, NO movement allowed. If the anchors completely deflected to accomodate all movement (we free the system again) only the end cap force would transfer to axial tension stress in the pipe segments again.

So everything seems to balance. Mohr's circle even agrees. I believe you have your answers. Right?

-------------------------------------------
Retracing back to my first response, I realize that I didn't finish very well. As those vertical segments go into the ground, if the ground is firm, the bending and shear loads will be resisted by the first few feet of embedment in the soil. Additionally after the pipeline travels 1000 feet away from the loop, that is usually sufficient for the total of all the soil's relatively small cohesive and friction resistance acting on each square inch of pipe surface area to collectively add together and resist any further movements. That is termed a "virtual anchor", which is just a very long anchor made from soil contact alone.

http://virtualpipeline.spaces.msn.com

"What gets us into trouble is not what we don't know, its what we know for sure" - Mark Twain