Immediately after graduation, you get a chance to work a harvest in the cellar at a

well$-$known, high end wine producer in the Napa Valley. The winemaker is new to the winery,

but very experienced. On your first day, she shows you around the cellar, especially the $16$ rectangular tanks that line the walls $-$ half concrete and half stainless steel, but otherwise identical in dimensions $(6ft6ft8ft$ tall$).$ This design would not be the winemaker's choice, but the owner is not interested in buying new ones, so this is what the winery has.

$($a$)$ You know that the concrete tanks could be problematic from a cleaning point of view, but you are hopeful on the stainless tanks. The winemaker asks you to look in the tank and tell her three design issues that are likely to make this fermentor difficult to clean. What would you list as the issues, given the photo above? Briefly explain.

$($b$)$ Mostly, this winery is producing Cabernet Sauvignon, and you crush the grapes into this stainless steel tank. About $8$ tons of crushed, destemmed fruit yields $1616$ gal of must which gives you a must height of $6$ feet. At the peak of fermentation, the winemaker expects the cap to take up about half of this height, and the maximum sugar utilization rate to be $5\mathrm{.}5$ Brix per day. You would like to maintain the liquid in the fermentor at $92F$ using the stainless steel coil shown in the diagram and photo. If you are using chilled water at $40F$ with an outlet temperature of $80F,$ how much heat transfer area is needed? The manufacturer of the cooling coil tells you that the overall heat transfer coefficient, $U,$ should be $25Bt\frac{u}{h}rf{t}^{2}F.$

$3\mathrm{.}41Bt\frac{u}{h}r=1W$

$1f{t}^3=7\mathrm{.}48$ gal

$3\mathrm{.}78L=1$ gallon

$($c$)$ This cooling coil is made up of a continuous $0\mathrm{.}5$ inch diameter stainless pipe and the diameter of the coil is $2\mathrm{.}3$ feet. Upon counting, you find that the coil is composed of $20$ complete turns. Does this coil provide enough area?

$($d$)$ What volumetric flow rate of chilled water is needed to maintain this temperature? The heat capacity and density of water are $1Bt\frac{u}{l}{b}_{m}F$ and $62\mathrm{.}4l\frac{b_m}{f}{t}^3,$ respectively.