Question

Water towers store water above the level of consumers for times of heavy use, eliminating the need for high-speed pumps. How high above a user must the water level be to create a gauge pressure of $3.00 \times 10^5 \textrm{ N}$?

Final Answer

$30.6 \textrm{ m}$

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Video Transcript

This is College Physics Answers with Shaun Dychko. We want to know what height of a water tower is needed to create a gauge pressure in somebody’s water tap of three times ten to the five Pascals. So gauge pressure will be the density of the water multiplied by <i>g</i> multiplied by the height above the water tap. And we can solve for <i>h</i> by dividing both sides by <i>rho g</i> so that’s going to be pressure divided by density times <i>g</i>. So three times ten to the five Pascals divided by one times ten to the three kilograms per cubic meter, that’s the density of water at four degrees Celsius, times 9.8 Newtons per kilogram, and this gives 30.6 meters is the height needed for the water tower.