I am working on a piping system which caries petroleum products. The piping is not supported well laterally, and in the past when the pipe has experienced sudden increases in flow rate, it has caused the piping to move on it's supports. I think the simple solution is to provide adequate lateral restraint, which is also designed to permit thermal expansion. However, I have been asked to estimate the magnitude of the forces that will occur due to various flow rates. I'm more of a stress and strain guy, can anyone direct me to a way to relate flow rate to force acting on a piping system of s specific geometry?
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Pipe Forces due to Flow
- Thread starter meca
- Start date
meca,
As a starting point, I advise you refer to "Momentum Balance" on page 6-6 of the 7th Edition of Perry's Handbook. Example 1 on page 6-8 is very pertinent. The 6th edition has this information too, but probably on different pages.
Good luck,
Latexman
As a starting point, I advise you refer to "Momentum Balance" on page 6-6 of the 7th Edition of Perry's Handbook. Example 1 on page 6-8 is very pertinent. The 6th edition has this information too, but probably on different pages.
Good luck,
Latexman
Tremolo
Nuclear
- Feb 26, 2003
- 77
meca,
Since you said that the pipe moves when the "pipe has experienced sudden increases in flow rate," it also sounds like you are experiencing a temporary force imbalance due to transient flow.
Typically, for steady state flow, the force acting on a 90-degree elbow can be characterized as w*u, where w is the mass flow rate and u is the fluid velocity.
Consider, for example, that you have a straight pipe segment with a 90-degree elbow at either end. Then, at steady state the flow rate is the same at both ends of the pipe, so the forces balance out. During transient flow, two things happen. First, the flow rate may be different at each end of the pipe and for sudden changes in flow, a transient pressure wave may move through the pipe causing the pressure at either end of the pipe to be significantly different.
The pressure force is simply P*A, where P is the pipe internal pressure and A is the pipe cross sectional area. The pressure force acts in opposite directions at either end of the pipe segment (the momentum force also acts in opposite directions at either end of the pipe segment).
The duration of the force imbalance, the impulse, may also be of interest to you. The impulse is dependent on the pipe segment length, fluid sonic velocity, and the acceleration rate.
So, my point is that if you are asked to calculate forces for a variety of flow rates, you may actually want to calculate forces for various changes in flow rate.
Have a nice day.
TREMOLO
Since you said that the pipe moves when the "pipe has experienced sudden increases in flow rate," it also sounds like you are experiencing a temporary force imbalance due to transient flow.
Typically, for steady state flow, the force acting on a 90-degree elbow can be characterized as w*u, where w is the mass flow rate and u is the fluid velocity.
Consider, for example, that you have a straight pipe segment with a 90-degree elbow at either end. Then, at steady state the flow rate is the same at both ends of the pipe, so the forces balance out. During transient flow, two things happen. First, the flow rate may be different at each end of the pipe and for sudden changes in flow, a transient pressure wave may move through the pipe causing the pressure at either end of the pipe to be significantly different.
The pressure force is simply P*A, where P is the pipe internal pressure and A is the pipe cross sectional area. The pressure force acts in opposite directions at either end of the pipe segment (the momentum force also acts in opposite directions at either end of the pipe segment).
The duration of the force imbalance, the impulse, may also be of interest to you. The impulse is dependent on the pipe segment length, fluid sonic velocity, and the acceleration rate.
So, my point is that if you are asked to calculate forces for a variety of flow rates, you may actually want to calculate forces for various changes in flow rate.
Have a nice day.
TREMOLO
Regarding the momentum variation forces , they are applied to the elbows as well, and to its center at 45°.
When you have waterhammer,the delta P calculated should be applied simultaneously to all the fittings if a static analisis is performed with a stress analysis program as Cessars , AUTOPIPE, etc..
In that case the loads are :
- At an elbow : 2. Delta P.pipe cross area . sine (alfa/2)
- Reducer
elta P.Delta cross area.- Blind flange = 2. Delta P.pipe cross area
A dinamic analysis can be done as well with those programs.
Regards,
SPLIT
Dear meca,
Please be aware that it is very difficult to evaluate fluid loads without any knowledge of the plant operating scenarios that cause the flow variations.
Typically, the first step would be the definition of various scenarios (opening of valves, starting of pumps etc.) The next step would be the investigation of these transient hydraulics by using suiteable software to identify the loads to be used in a dynamic analysis of the structural piping system.
The last step would be to transfer the piping restraint loads to the civil department for the design of the pipe rack etc.
Best regards,
VBHMBG
Please be aware that it is very difficult to evaluate fluid loads without any knowledge of the plant operating scenarios that cause the flow variations.
Typically, the first step would be the definition of various scenarios (opening of valves, starting of pumps etc.) The next step would be the investigation of these transient hydraulics by using suiteable software to identify the loads to be used in a dynamic analysis of the structural piping system.
The last step would be to transfer the piping restraint loads to the civil department for the design of the pipe rack etc.
Best regards,
VBHMBG
This is an easy problem, very well discussed in most textbooks on Fluid Mechanics.
You need to apply a control volume analysis using the Reynolds Transport Theorem. Using momentum as the system property, (i.e. the partial derivative of momentum with respect to time equals the property of force) you can set up the control volume, in your case, around the pipe support. Following through on the mathematics and making allowances for system contraints: pipe pressure P, internal pipe area A, mass flow m', upstream velocity V1 and downstream velocity v2 you will arrive at the euation:
F = PA - m'(V1 - V2)
In other words, the force exterted by the pipe which is equal and opposite the force delivered from the supports is that force induced by static pressure force less dynamics of the fluid.
Interestingly enough, you can see the effects of pressure drop in the equation. Remember that for subsonic flow, pressure drop is at the expense of fluid flow increase, another aspect of energy conservation. If for example, pressure drop is very small, then V1 is almost V2 and the second term approaches zero.
I would consult elementry textbooks in fluid mechanics and model a few of the problems posted with known solutions. This will give you the confidence in the correct approach to the analysis. Good luck!
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada
You need to apply a control volume analysis using the Reynolds Transport Theorem. Using momentum as the system property, (i.e. the partial derivative of momentum with respect to time equals the property of force) you can set up the control volume, in your case, around the pipe support. Following through on the mathematics and making allowances for system contraints: pipe pressure P, internal pipe area A, mass flow m', upstream velocity V1 and downstream velocity v2 you will arrive at the euation:
F = PA - m'(V1 - V2)
In other words, the force exterted by the pipe which is equal and opposite the force delivered from the supports is that force induced by static pressure force less dynamics of the fluid.
Interestingly enough, you can see the effects of pressure drop in the equation. Remember that for subsonic flow, pressure drop is at the expense of fluid flow increase, another aspect of energy conservation. If for example, pressure drop is very small, then V1 is almost V2 and the second term approaches zero.
I would consult elementry textbooks in fluid mechanics and model a few of the problems posted with known solutions. This will give you the confidence in the correct approach to the analysis. Good luck!
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada
Oops...I said "static pressure less dynamics of fluid". What I meant to say is "stagnation pressure less static pressure or dynamics of fluid".
First morning coffee hasn't kicked in yet. Sorry for the confusion!
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada
First morning coffee hasn't kicked in yet. Sorry for the confusion!
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada
sailoday28
Mechanical
Cockroach (Mechanical)
I believe the force you have stated is for steady state flow. For transients, a wave force also contributes to a force imbalance.
If the volume of the elbow is small compared to the piping to which it is connected, I would disregard the transient term.
I believe the force you have stated is for steady state flow. For transients, a wave force also contributes to a force imbalance.
If the volume of the elbow is small compared to the piping to which it is connected, I would disregard the transient term.
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