Proportionality
Classical Mechanics
Level
3
A large volume of water is gushing through a pipe which narrows at the outlet. At which point, the water will flow fastest?
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B
D
C
A
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1 solution
The total quantity of water flowing through unit volume in unit time is constant , Therefore , V/t is constant , rearranging it we get Av = constant This is the principle of continuity . It is a consequence of conservation of mass .
In the above figure , for example , A 1 > A 2 , therefore , it follows that v 1 < v 2
Similarly , in this problem , as the area at C is the smallest. However, after the water gains its maximum speed due to flow at C, it accelerates due to gravity, thus it is traveling fastest at D.