A liquid delivery system is being designed such that ethylene glycol flows out of a hole in

the bottom of a large tank. The designers need to predict how long it will take for the ethylene

glycol to completely drain. Since it would be very expensive to run tests with a full$-$scale

prototype using ethylene glycol, they decide to build a one$-$quarter scale model for experimental

testing, and they plan to use water as their test liquid. The model is geometrically similar to the

prototype as shown in the Figure.

$($a$)$ Temperature of the ethylene glycol in the prototype tank is $60C,$ at which $v=4\mathrm{.}75{10}^{-6}\frac{m^2}{s}.$

At what temperature should the water in the model experiment be set in order to ensure complete

similarity between model and prototype?

$($b$)$ The experiment is run with water at the proper temperature as calculated in part $($a$).$ It takes

$3\mathrm{.}27$min to drain the model tank. Predict how long it will take to drain the ethylene glycol from

the prototype tank.