A pipe is set in the bottom of a vessel containing water so that it can rotate freely about its own axis. Two nozzles are soldered to the upper end of the pipe and bent as shown in Fig. The whole system is a sort of inverted Segner's wheel. What will happen to the pipe when water flows out of the vessel through the pipe?

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Sol. Unlike a Segner's wheel, the tube will not revolve when water flows out of it. In fact the law of conservation of the moment of momentum tells us that in a system which initially has no rotation and to which no moment of force is applied from outside, the overall moment of momentum must remain equal to zero
In the case of an ordinary Segner’s wheel the water which flows out of the bent tubes has a certain moment of momentum. Therefore the vessel of water begins to rotate in the opposite direction, since the sum of the moments of momentum will remain equal to zero. In the case of the inverted Segner’s wheel which we are considering, the water which flows out of the straight pipe below has no moment of momentum relative to the axis of rotation of the pipe (since the water is flowing along that axis) and consequently the pipe should not rotate.
It may seem that the liquid as it flows into the bent tubes exerts pressure on the walls of the tubes and so should cause a rotation of the pipe. But besides the pressure, exerted by the water flowing in, on the inside walls of the tubes, there is also a pressure exerted by the surrounding liquid on the outside walls. This pressure is greater than at the openings of the tubes (where the pressure is reduced), and it in fact compensates the turning moment created by the liquid flowing into the tubes.
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