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# Unbalanced pressure

## Unbalanced pressure

(OP)
Dear Friends,

I modeled a line in CAESAR II that is not a practical one but it is a conceptual one(See attachment). Can you guide me?

I modeled a simple line with a reducer at the middle of two elbows in CAESAR II. As we know, after a reducer, the pressure of the fluid drops. Therefore [pressure thrust at downstream elbow(=P2*A2)] + [pressure at the reducer*the reducer projection] is lower than [pressure thrust at upstream elbow(=P1*A1)] and Unbalanced pressure thrust causes movement of the piping in -X direction. But CAESAR II shows no movement in X direction. After I turned on Bourdon effect, CAESAR II showed negligible movement in +X direction.

Do you agree with me that the Unbalanced pressure thrust causes movement in -X direction?
Why does CAESAR II gives these results?

As I told before it is not a practical model.
Inputs:
Differential temperature=0
friction coefficient=0
fluid density=0
P1=50 barg
P2=2 barg
The reducer size:78"*42"

### RE: Unbalanced pressure

You may have unbalanced forces, however any resulting movement is still dependent on frame stiffness. With that short length of large diameter pipe, it's a very stiff frame in which there may be no, or very little movement.

Independent events are seldomly independent.

### RE: Unbalanced pressure

1. Pressure may not be less at a diameter change, that depends upon flow conditions.

2. Caesar II is not a CFD package and it does not know about flowing state in a static analysis.

3. I guess that you entered the differing pressures into the respective spreadsheets.

4. Caesar II conducts a structural / mechanical analysis of the pipe system, on an elemental basis. Thus each element with differing diameter, presumably wall thickness and pressure will produce a specific axial and hoop stress in that pipe element. If you set the 'Bourdon' option to 'no', you will see no axial extension. Set it to anything else and you will see axial pressure elongation, which will normally be small, as you have observed.

5. Since axial pressure causes axial stress in the wall, you should not expect to find axial pressure thrust acting extenally. In your system it will act on the inner wall of the elbows and the reducer inner wall. To see the external effects of pressure, include an un-restrained expansion joint in your model.

### RE: Unbalanced pressure

(OP)
Dear C2it,

As you told, I inserted different pressure into the respective spreadsheets.
But as I know, CAESAR II is a FEM software for calculating displacement and forces; therefore actual behavior of the pipe should be specified by CAESAR II(Correct me if I'm wrong).
Does my understanding of the actual behavior of the pipe(movement in -X direction) is true?

### RE: Unbalanced pressure

Caesar II applies beam theory in finite element modelling.

To convince yourself what is going on, draw a free-body diagram for each element.

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