At Whale World Amusement Park, guests are given the opportunity to be lifted by

Question

At Whale World Amusement Park, guests are given the opportunity to be lifted by a stream of water shot from the blowhole of a concrete whale. A horizontal 2.0-inch diameter pipe runs into mouth of the whale, and then narrows to a 1.0-inch diameter as it bends upward, shooting a stream of water into the air. Park visitors may stand on a board that is held in the air by the impact of the stream.

(a) In the diagram below, a 30-kg child is on a 3-kg board held aloft by the stream. What is the speed of the water as it strikes the board? Assume that the speed of the water immediately after striking the board is zero, and that the distance between the end of the pipe and the board is negligible. Begin your analysis with a free-body diagram for the board.
(b) What is the flow speed in the horizontal part of the pipe?
(c) The horizontal part of the pipe is 5.0m below the board. What is the gauge pressure in the horizontal part of the pipe?

Please answer with complete diagram with all required details. I will not reward anything less than that.

Explanation / Answer

Let v be the velocity of water as it strikes the board.

Force=Rate of change of momentum=rho*v*A*v=(M+m)g

v^2=(M+m)g/rho*A=33*9.8/(1000*pi*0.0127^2)=638.2

v=25.26m/s

b)v1*A1=v2*A2

v2=v1*(A1/A2)

v2=25.26*(1/4)=6.32m/s

c)Applying bernoull's theorem between the horizontal pipe and the point of exit of water,

guage pressure =P-P0=rho*g*H+0.5v1^2/2g=1000*9.81*5+0.5*1000*25.26^2=3.68*10^5Pa

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