How to calculate built up back pressure?

[johcatrac]

How to calculate built up back pressure when hot water relieves and flashes into steam in the discharge piping?
Relief Valve is 1/2"x3/4" with a set pressure of 1000 psig. The water temperature is 107°C.

 

[apetri]

it depends from the (equivalent) length (and characteristics) of discharge piping...
for a short tailpipe terminated to atmosphere one may presume critical flow (or calculate fluid speed / pressure drop) but considering the small size of the PSV probably that is not required,
for flashing liquids there are different models, see for example

https://www.cheresources.com/invision/topic/21654-hem-vs-hne-for-two-phase-flow-psv-design-rating/

but, as said, probably that is not required in this case.

 

[johcatrac]

The discharge piping is around 20 meters and with a few bends and leading to the floors below.

 

[apetri]

assume max (rated) PSV flow, estimate tout and define fluid state and density, for vapor test mach number, start from the end (atm) and proceed, not too different from other dp calc's...
at 107 C you are close to saturation line (atm) and considering the dt across PSV and piping possibly it's liquid (to verify)

 

[chicopee]

Is the set pressure really 1000psig? It seems to me more like 100 psig.