5. A liquid delivery system is being designed such that ethylene glycol flows out of a hole in the bottom of a large tank, as in Figure 5. 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) Based on the variables listed, find an expression for non-dimensional time in terms of other non-dimensional quantities. Clearly identify your choice of repeated variables, and also how many non-dimensional II groups you obtain. (b) The temperature of the ethylene glycol in the prototype tank is 60° C, at which v the-kinematic viscosity is 4.75 × 10-6 m²/s. What should be the kinematic viscosity of water in the model experiment in order to ensure complete similarity between the model and prototype? (c) Now the designers run the model experiment. If it takes 543.6 sec to drain ethylene-alcohol from the prototype tank, predict how long it will take to drain water from the model tank.