Hi Everybody,

With all humility, I'm asking for ur help.

I have to analysis a closed PSV system, I calculated the trust forces applicable(see attached file PSV1 4112).

1. I will like to know which one of the forces to use and in which direction( PSV discharging North)

2. I do have a propose support detial which I attached(0027 & 0028). Please, I will like to know how to model these to achieve a realistic situation.

Thanks for ur help

Your 220 kN upward force looks strange.

Check again.

Regards,

Oatty, as Damb said, the 220 kn looks high.
Please check the value of W1, because it looks a little high if compared to the selected area and the set pressure.

Your pdf shows the directions and the application points of the force, so your question has an answer in itself.
Your spreadsheet is valid for closed systems only. Be careful because some customers/companies ask not to the consider the forces on the elbows before and after short legs.
Best regards

Corrado Vannella
tech@vannella.com

Peng's book suggests to read an old paper by Moody "Pipe forces caused by a fluid density change through a discharge safety/relief valve" Asme Special Publication PVP-Vol.98-7.

I am searching for this paper but I can't find it? Does somebody know where I can find and/or buy it?

Thank you.

Chakot

What Happens after the piping heats up?????

They will not be there to witness

Welcome back!

To understand the "F2" expression and numerical result in "PSV1 4112" doc, I propose to make a short trip through some fluid mechanics results. Just hope it is quite easy to be understood.

We may consider a steady state adiabatic flow evolution of a perfect gas,
FROM resting state (p0, density0, T0, speed=0, sonic speed=a0)
--->
TO choked state (p*, density*=rho*, T*, speed=critical speed=a*)

Here a* is the critical speed in choked section (where the flow speed equals the "sound" speed at Mach=1) and a0 is the sonic speed for resting fluid.
By similitude with the "well known" expression a0= sqrt(kRT0), we can fix the expression of "critical" speed as a*= sqrt(kRT*).
Now it is a little more complicated to enter in fluid mechanics details about T*; however there is a simple correlation between T* and T0 (or, if you prefer, between a* and a0), based on energy conservation of one dimensional adiabatic evolution:
T*/T0=a*^2/a0^2=2/(k+1)

And here it can be made a consistent simplification in theory: if we are able to know/ calculate the mass flow-rate W (lets say by theory combined with experiments), we can consider the continuity equation of the steady state flow as
W=rho* A*a* where A* is choked area.
so
rho*=W/( A*a*)
If we are interested (are we?) to evaluate p*, we can consider the gas state equation
p*= rho* R T*= WRT*/( A*a*)
We can manipulate by math the p* expression as
p*= WkRT*/( kA*a*)= W [a*^2] /(kA*a*)= W a* /(kA*)
(or a*= p*kA*/W, if you prefer this form).

And that’s all, we just succeeded to correlate all critical "*" parameters by knowing "W".

In case we have an ONE DIMENSIONAL FLOW (is this assumption closed to reality for the flow through PSV orifice ?) we have to evaluate the reactive force of the jet flow.

The momentum component of reactive force in one-dimenional flow is
[mass flow-rate] x [jet_velocity]= Wa*
which is the basic of API formula. However, I would remark that never API said this is the formula of the reactive force of flow through the PSV orifice.

The same evaluation of reactive force would lead to something presented in other way (and obviously leading to the same numerical result):

[mass flow-rate] x [jet_velocity]=
=Wa*=W [a*^2]/a*=W [kRT*]/[(p*kA*)/W]= W^2 RT*/(p*A*)

This form of reactive force evaluation is a nice one ... in practice good for nothing, because you don’t know the p* value.

Exactly for this reason, "somebody" decided to "improve" it and pretended this formula is valid for PSV orifice, in both "pop condition" and "flow condition", applying it with p*=p0 and T*=T0, and here is what you have as F2 evaluation in some Companies papers.

In "PSV1 4112" doc you can see the numerical consequences of this "approximation"; F2 is 220 kN while F1= 16 kN.

F2 = W² R T/(0.1xPs A) = 38.92² x 0.5 x 375.15/ (0.1 x 14 x 830) = 220.199 kN
(the coefficient 0.1 is here because Ps unit is bar).

Best regards.

please, can you tell me from which document or book you obtained the formulas used in "PSV1 4112"?

Best regards.

Juan