$3($b$)\_$#$2$: A propane company worker arrives and begins filling your $15f{t}^3$ rigid storage tank

which currently contains $12\%$ liquid propane at $40F.$ The propane worker adds saturated liquid

propane to the tank at a flowrate of $20l\frac{b}{m}in$ with a velocity of $15i\frac{n}{s}$ through a line whose

temperature is $45F.$ After $10$ minutes of filling the heat pump kicks on causing saturated liquid

propane to begin exiting the tank at a flowrate of $11l\frac{b}{m}in$ through a $3"$ diameter pipe. When

the propane company worker leaves the tank is $97\%$ full $($by volume$)$ of saturated liquid propane.

a$)$ Determine the diameter, in$,$ of the pressurized inlet line.

b$)$ Determine the velocity, $f\frac{t}{s},$ of the flow out through the exit pipe.

c$)$ Determine the amount of mass added to the tank, in lb$.(462\mathrm{.}86lb)$

d$)$ Determine the time required to complete the filling process, min $.$