You are trying to calculate the size of a PRV needed to protect a tank. This PRV would allow for the outflow of gas. The tank has a maximum set pressure of $1\mathrm{.}5$ barg and a maximum accumulation pressure of $1\mathrm{.}65$ barg. Initial temperature and pressure are $298$ K and $85$ kPa respectively. The volume of the tank is $50$ m$3.$ Water flows into the tank at $298$ K and $5$ kg$/$s$.$ The tank is sealed and initially $48$ m$3$ of it was full of air and the remaining space was with water. The initial design was that water would flow out through the bottom through a valve. But, then the valve got plugged so the gases were getting to compress.

You may also assume that P$\_$atm is $101325$ Pa$,$ Cd of the valve is $0\mathrm{.}95,$ and gamma $($heat capacity ratio$)$ is $1\mathrm{.}4$