A high-speed boat is powered by a water jet pump engine, similar to a jet engine

Question

A high-speed boat is powered by a water jet pump engine, similar to a jet engine on airplanes. The engine takes in water at the bow through a tube with diameter 1 ft, and the water is pumped out the stern of the boat through a 3-in diameter tube. The flow rate is 5000 gpm. Neglecting any frictional loss, find: (a) the thrust force of the engine; (b) the maximum speed of the boat, if the drag coefficient is 0.005 with a corresponding projected area of 500 ft2; (c) If the pump is 100% efficient, how many hp are required?

Explanation / Answer

Flow Rate, Q= 5000 Gallons/minute = 18.9270589 m^3/min = 0.315450982 m^3/s

Inlet Velocity, Vi = Q/(Inlet Area) = 0.315450982*4/(pi*0.3048^2) = 4.323 m/s

Exit Velocity, Ve= Q/(Exit Area) = 0.315450982*4/(pi*0.0762^2) = 69.172 m/s

Thrust Force, F = (mass flow rate of water)*(Ve - Vi) = rho*Q*(Ve - Vi) = 1000*0.315450982*(69.172 - 4.323)

                       = 20456.68 N

Drag Coefficient CD= 0.005

to get the max. speed, Thrust = Drag Force = 0.5*rho*V^2*CD*S= 0.5*1000*0.005*V^2*46.45152

or, V = sqrt {20456.68/(0.5*1000*0.005*46.45152)} = 13.272 m/s = 43.54 ft/s

Power Required by pump = F*V = 20456.68*13.272 = 271501.05696 W = 364.09 HP

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