Mariog,

Thanks for the input.

Reaction force should be equal to

= Mass flow rate times velocity at Relief valve outlet + ( Exit pressue-atmospheric pressure) x exit area. This is precisely what API 520 expression says.

The flow process to bring the fluid from the vessel stagnation condition to the nozzle throat can be assumed to be isentropic i.e adiabatic and reversible, the flow from nozzle throat to the relief valve can be considered to be adiabatic only but irreversible and finally the flow through the outlet nozzle can be considred to be isentropic.

The first part of API 520 expression is = mass flow rate times exit velocity.There can be three different scenarios.

1) flow through the relief valve is choked at the relief valve nozzle and relief valve exit plane.

2) Flow through the relief valve nozzle is still choked but the flow at the relief valve exit plane remains unchoked.

3) flow throughout the relief valve is unchoked.

It can be shown that the API 520 equation fits case 1 and the velocity at exit is the sonic velocity. API expresses it in terms of stagnation temp. in the vessel which can be coverted to temp. at exit and this conversion shows the well known expression for sonic velocity ( SQRT GAMMA X R X T/M)in terms of exit temperature.

My doubt is: the expression mentioend in my original post is sonic velocity. So if this one used along with the first part i.e. momentum part of API 520 eqn. is not not a doubling of momentum expression and secondly how do we justify this expression as a substitute for the second term of API expression?

Regards