At a large fish hatchery the fish are reared in open, water-filled tanks. Each tank is approximately square in shape with curved corners, and the walls are smooth. To create motion in the tanks, water is supplied through a pipe at the edge of the tank. The water is drained from the tank through an opening at the center. A model with a length scale of 1:13 is to be used to determine the velocity, \(V\), at various locations within the tank. Assume that \(V=f\left(\ell, \ell_{i}, ho, \mu, g, Q\right)\) where \(\ell\) is some characteristic length such as the tank width, \(\ell_{i}\) represents a series of other pertinent lengths, such as inlet pipe diameter, fluid depth, etc., \(ho\) is the fluid density, \(\mu\) is the fluid viscosity, \(g\) is the acceleration of gravity, and \(Q\) is the discharge through the tank.

(a) Determine a suitable set of dimensionless parameters for this problem and the prediction equation for the velocity. If water is to be used for the model, can all of the similarity requirements be satisfied? Explain and support your answer with the necessary calculations.

(b) If the flowrate into the full-sized tank is \(250 \mathrm{gpm}\), determine the required value for the model discharge assuming Froude number similarity. What model depth will correspond to a depth of 32 in. in the fullsized tank?