Solve using conservation of Momentum. Tugboats provide assistance to large ships

Question

Solve using conservation of Momentum. Tugboats provide assistance to large ships for maneuvers such as docking. As an alternative, bow thrusters may be used for the same purpose. The thruster consists of a ducted propeller mounted at right angles to the fore/aft axis of the ship. Water is drawn in from one side of the bow and ejected as a jet on the other side. The momentum flux of this jet produces a starboard or port force on the ship for maneuvering. Consider the boat shown, which is stationary in still water. Its bow thruster produces a 12-inch diameter jet of water. What velocity must the exiting jet have if the force produced by the thruster is 20,000 lb_f?

Explanation / Answer

Force produced = rho * Area * V^2

20000                        = 62.43 * pi * 1^2 / 4 * V^2

Velocity = sqrt(20000*4 / (62.43 *pi)   = 20.196 ft/s

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