Cities across the U.S.supply fresh water to the residents at constant pressure by the use of water towers.If the diameter,d₂,of the pipe coming out of the tower is 25 cm,and the diameter,d₁,of the pipe at your home is 2.0 cm,what is the ratio of the velocity of the water at d₁ compared to d₂? Assume that all the taps are off except yours.

Question

Quizplus · Accepted Answer

The velocity ratio can be found using the principle of conservation of mass, which in the context of fluid dynamics is often represented by the equation A1V1 = A2V2, where A1 and A2 are the cross-sectional areas of the pipes and V1 and V2 are the velocities of the water in these pipes. The cross-sectional area of a pipe is given by the formula π(d/2)^2. Therefore, the ratio of the velocities (V2/V1) is equal to the ratio of the areas (A1/A2) = (π(25/2)^2) / (π(2/2)^2) = (625/4) / (1) = 156.25. Since the question asks for the ratio of the velocity at the home compared to the tower, and given the choices do not include decimals, the correct answer is rounded or approximated to the nearest whole number provided in the options, which is 156.

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