Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 15 - Fluids and Elasticity - Exercises and Problems: 31

Answer

The air pressure at the floor is greater than the air pressure at the ceiling by 0.20%

Work Step by Step

The pressure at the floor of the gym is $1 ~atm$. The pressure at the gym floor is greater than the pressure at a height $h$ by $\rho~g~h$. Let $P_f$ be the pressure at the floor. Let $P_c$ be the pressure at a height of 16 meters. $P_c+\rho~g~h = P_f$ $P_c = P_f - \rho~g~h$ $P_c = (1.013\times 10^5~N/m^2)-(1.29~kg/m^3)(9.80~m/s^2)(16~m)$ $P_c = 1.011\times 10^5~N/m^2$ We can find the percent increase of the air pressure at the floor compared to the air pressure at the ceiling. $\frac{P_f-P_c}{P_c}\times 100\% = \frac{(1.013\times 10^5~N/m^2)-(1.011\times 10^5~N/m^2)}{1.011\times 10^5~N/m^2} \times 100\% = 0.20\%$ The air pressure at the floor is greater than the air pressure at the ceiling by 0.20%.
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