A liquid hydrogen$/$liquid oxygen thrust chamber has a constant bipropellant flow rate of $347k\frac{g}{sec}$ at a mixture ratio of $6\mathrm{.}0.$ It operates at full thrust for exactly $2$ min $.$ The propellants in the vehicle's tanks are initially vented to the atmosphere at the propellant boiling points and are assumed to be of uniform initial temperature at start. Use data from Table $7-1$ for the propellant specific gravities. Assuming no losses, find the masses of $($a$)$ fuel and $($b$)$ of oxidizer used to produce the thrust for the nominal duration. $($c$)$ What was the volume of the liquid hydrogen actually used? $($d$)$ Assuming $4\mathrm{.}0\%$ extra fuel mass $($for unusable propellant residual, evaporation, hardware cooling, or venting just prior to start, or propellant consumed inefficiently during start$-$up and shutdown$)$ and a $10\%$ ullage volume $($the void space above the liquid in the tank$),$ what will be the volume of the fuel tank? Assume other losses can be neglected.

Answer: $($a$)5941$ kg $,($b$)35,691kg,($c$)83\mathrm{.}83m^3($d$)95\mathrm{.}6m^3.$