Discharge Piping

Dear All

I am currently checking the adequacy of existing relief valves along with its Inlet & Outlet line sizing (& it has become one of my favourite subjects now).

For steam we normally have discharge line open to atmosphere. And invariably many of the times the flow at the end of discharge pipe is Sonic.

In normal cases, since we know the discharge pressure as atmospheric, we estimate the pressure at the outlet of PSV by calculating the pressure drop through pipe & fittings.

In one of the calculations, I got the velocity at the discharge pipe above 1 Mach. I adjusted the inlet & out let pressure so that the velocity is in the Sonic range. But the outlet pressure goes above atmospheric. I discussed in the department & I was told to change the lin size (Agreed)

But the question is, now since the system is already in place, how is the relief valve going to act in case the pressure rises. What would be the discharge pressures & what would be the back pressure at the outlet of PSV. Is it right to assume the line frictional pressure drop as backpressure???
(maybe the excess energy goes as sound that we hear when PSV pops up)