In June $1985$ a gas explosion occurred in $N{H}_3-$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 $5c{m}^2.$ As shown in the figure below this pump was feeding water to a wash tower. The wash tower was a $C{O}_2-$ scrubber, separating $C{O}_2$ 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 $4\mathrm{.}5m3.$ The height of the water$-$washer tower was approximately $20m.$ We can assume that the pressure was $30$ bar abs$)$ and the temperature was $10C$ in the water$-$washer were constant. Assume that $H2$ gas has the following properties: $MW=2k\frac{g}{k}$mol,$\frac{c_p}{c_v}=1\mathrm{.}41$ and $R=\frac{R_u}{M}W=4157\frac{m^2}{K}{s}^2.$

a$)$ Estimate the time before $H_2$ started to leak out through the flange?

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b$)H_2$ leaked for $20sec.$ before an explosion occurred. How many $kgs$ of $H_2$ had leaked out at the time of the explosion.

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