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Chapter 15: Problem 76

A plumber comes to your ancient apartment building where you have a part-time job as caretaker. He's checking the hotwater heating system, and notes that the pressure in the basement is 18 psi. He asks, "How high is the building?" "Three stories, each about 11 feet," you reply. "OK, about 33 feet," he says, pausing to do some calculations in his head. "The pressure is fine," he declares. On what basis did he come to that conclusion?

Short Answer

Expert verified
The plumber's conclusion can be verified by noting that the calculated building height, approximately 33 feet, matches the stated building height. This indicates the water pressure is at a suitable level for a building of that height.

Step by step solution

01

Conversion of Pressure Units

Firstly, convert the pressure measurement from psi to the SI unit of pascal (Pa). Note that 1 psi equals approximately \(6894.76\) Pa. So, \(18\) psi = \(18 * 6894.76\) Pa.
02

Setting up the equation

Next, set up the fluid column pressure equation \(P = ρgh\). Given that the density of water \(ρ\) is approximately \(1000 kg/m^3\) and the acceleration due to gravity \(g\) is approximately \(9.8 m/s^2\), the equation becomes \(18 * 6894.76 = 1000 * 9.8 * h\).
03

Calculate the height

Now, solve for the height \(h\) by dividing both sides of the equation by \(1000 * 9.8\).
04

Conversion of height units

Finally, convert the calculated height from meters to feet by multiplying by \(3.281\), since 1 meter equals approximately 3.281 feet.

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