$13.$ A $1/50$ scale model is to be used in a towing tank to study the water motion near the

bottom of a shallow channel as a large barge passes over. Assume that the model is

operated in accordance with the Froude number criteria for dynamic similitude. The

prototype barge moves at a typical speed of $15$ knots. $($a$)$ At what speed $($in ft$/$s$)$ should

the model be towed? $($b$)$ Near the bottom of the model channel a small particle is found

to move $0\mathrm{.}15$ ft in one second so that the fluid velocity at that point is approximately $0\mathrm{.}15$

ft$/$s$.$ Determine the velocity at the corresponding point in the prototype channel.