In June $1985$ a gas explosion occurred in NH$3-$plant NI at Hydro Porsgrunn $($now Yara$).$ A flange gasket in a by$-$pass line of a water pump was blown out. The leaking area was $5$ cm$2.$ As shown in the figure below this pump was feeding water to a wash tower. The wash tower was a CO$2$scrubber$,$ separating CO$2$ from H$2$ gas. The pressure in the water$-$washer was $30$ bar. The pressure in water main line was $5$ barg. Since the pump was not operating the leak in the flange was resulted in backflow of water in the line between the pump and the water$-$washer. The volume of this line was $4\mathrm{.}5$ m$3.$ The height of the water$-$washer tower was approximately $20$ m$.$ We can assume that the pressure was $30$ bar $(3*106$ Pa abs$)$ and the temperature was $10$ in the water$-$washer were constant. Assume that H$2-$gas has the following properties: MW $=2$kg$/$kmol$,$ cp$/$cv $=1\mathrm{.}41$ and R $=$ Ru$/$MW $=4157$ m$2/$Ks$2.$

a$)$ Estimate the time before H$2$ started to leak out through the flange?

b$)$ H$2$ leaked for $20$ sec$.$ before an explosion occurred. How many kgs of H$2$ had leaked out at the time of the explosion.