Butane liquid is stored in a large vertical insulated tank. A refrigeration unit maintains the temperature of the liquid butane at $28$oF$.$ The tank is pressurized with nitrogen to atmospheric pressure. A $14-$inch $($actual$)$ inside diameter pipe located at the bottom of the tank is used to remove or add butane to the tank. You have been asked to analyze the incident of separation of the $14-$inch pipe from the bottom of the tank. The plant is interested only in the realistic release incident, not the worst$-$case incident.a$.$ Use table $4-6$ in the textbook or the table provided in the lecture to determine the release area for the $14-$inch pipe for this realistic release incident. What hole diameter is this equivalent to$?$b$.$ If the maximum height of the butane liquid in the tank is $75$ feet, what is the discharge rate, in gal$/$sec$,$ thru this hole when the hole first forms? The density of the butane at these conditions is $37\mathrm{.}5$ lbm$/$ft$3$ and its molecular weight is $58\mathrm{.}123.$