I have seen many companies, in their design guide use an expression for rupture disk reaction force as 0.375.(1+k).A.P

where k= cp/cv , A and P have their usual meanings. I have also seen this expression in the book " Piping and Pipeline assessment guide " by Keith Escoe.

I have few questions on the derivation of the above expression:

As per my understanding, reaction force= P.A + W^2/(density X Area)


where W is the mass flow rate.

Using the expression for mass flow rate at sonic condition:
W^2= (density X Area)^2 .(kRT) and using the ideal gas equation ( P=density.R . T)

the above expression becomes: P.A + k.P.A = (1+k).P.A

I think my derivation is correct.

I am not sure how the factor 0.375 comes ( one can argue that it has to do with some unit conversion , but it is not as P is expressed in N/mm^2 and A is mm^2 and the above expression is in Newton)

I am looking forward to response from Mariog or other members of the forum.

Regards

Kind response from esteemed members of the forum will be highly appreciated.

Regards

Dear Anindya,

Frankly, I have no idea. The only speculation I can do is 0.375 may be a very conservative value for relief device discharge coefficient for case of rupture disk with vacuum support (I found a value as 60% * 0.625)... it's just a speculation, and may be my stupidity..

In my opinion the reaction force can be counted exactly as for every "free jet" isentropic critical (choked sonic) flow, without applying any correction.