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 Fig. P7–99. 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 (Fig. P7–101). 

(a) The temperature of the ethylene glycol in the prototype tank is 60°C, at which ν = 4.75 × 10^–6 m²/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 3.27 min to drain the model tank. Predict how long it will take to drain the ethylene glycol from the prototype tank.

FIGURE P7–99

FIGURE P7–101

Transcribed Image Text:

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