On some railways steam-locomotives take on water without stopping. For this purpose a pipe bent at a right angle is used, being lowered into a trough between the rails while the train is moving (Fig.). What must be the speed of the train v, if the water is to be raised through a height of h = 3 m?
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Sol. A mass of water m, on entering the horizontal part of the pipe has a velocity v relative to the pipe as a result of the engine’s motion and consequently it has a kinetic energy of ½mv 2 , at the expense of which it can rise through a height h; this height is determined by the condition that all this kinetic energy will be converted into potential energy. Thus
½ mv 2 = mgh
Hence
v = 
= 28 km/hr approx.
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