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Classical Mechanics

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Moderate

Density and Pressure: Pressure Drop

CLMECH-D7GGLF

Water from a water tower is distributed through a variety of pipelines. Consider water delivered through pipes of different diameters.

Suppose that originally, a $4.00\ cm$ pipe delivered water to a downtown building, but as time progressed the needs for water in this downtown building increase. To compensate, a second pipe $3.00\ cm$ in diameter is added.

Each of the pipes traverses the same path $200\,m$ long and both start out with the same initial pressure of $5.00\times 10^5\,Pa$. Also, assume that the flow speed (in m/s) of the water as it enters each pipe is the same. (Note: While we can show, using Bernoulli's equation, that this would be true in the absence of any viscosity or friction, here we take it as an assumption to make the problem easier; in reality, the viscosity would affect the flow speeds).