$[$Crowl $4-14]$ The distillation column in the Michigan Tech Unit Operations Lab distills a mixture of isopropanol and water. The isopropanol product is delivered to tank T$-107$ for temporary storage. The tank is a vertical cylinder in geometry with a coneshaped bottom, as shown in the Figure below. A $2-$in$.$ schedule $40$ pipe is connected to the bottom of the tank to pump the tank back to the raw material tank. We want to determine the consequences due to the rupture of the pipe at the very bottom of the vessel and spillage and evaporation of the isopropanol.

Consider the tank to be $50\%$ full and the isopropanol to be $100\%$ pure. Assume turbulent flow in the pipe and a sharp break.

Assume ideal mixing due to lab ventilation.

$2-$in schedule $40$ pipe: ID$=2\mathrm{.}067$in$,OD=2\mathrm{.}375$ in

a$)$ What is the initial discharge rate when the pipe finally ruptures? The tank is padded with nitrogen at a regulated pressure of $4in.$ of water gauge.

b$)$ If the initial discharge rate is maintained, how long will it take to drain all of the material from the tank? If the total draining time is less than $10m,$ then the release can be considered instantaneous. Is this the case?

c$)$ If an isopropanol pool forms on the floor with an estimate liquid depth of $1cm,$ what is the pool area in $f{t}^2?$

d$)$ Estimate the evaporation rate of the isopropanol from the pool, in $l\frac{b_m}{s}.$ Assume a temperature of $80F$ and an ambient pressure of $1$atm.

e$)$ Estimate the concentration of the isopropanol vapors in the UO lab $($in ppm$)$ from this evaporation. Assume a lab volume of $74,300f{t}^3$ and a ventilation rate of $6$ air changes per hour.