Question

1. (4 pts.) A large tank of diameter D is drained under the action of gravity through a hole of diameter d in its bottom. Of interest is the time it takes the tank to drain completely. diameter D An experimentalist wishing to model this system with a smaller tank has determined that the time ? that it will take to drain the tank is a function of the initial liquid depth ho, the diameters, D and d, the gravitational acceleration constant g, the fluid density p and viscosity u. Furthermore, she has determined through dimensional analysis that the dimensionless groups involved may be represented as diameter d Are the density and dynamic viscosity independently important here? Why or why not? The experimentalist has decided to build a scale model that is one-halfthe size of the actual prototype. In order to maintain dynamic similarity, what does this choice imply about the liquid to be used for the model experiments? Assuming such a liquid is actually available, what would be the relationship between the draining time for the prototype versus that measured for the model?

Answer 1

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