Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 14 - Fluids and Elasticity - Exercises and Problems: 65

Answer

(a) The air pressure above the roof is lower than the air pressure inside the house. (b) The pressure difference is $841~N/m^2$ (c) The force exerted on the roof is $75,700~N$ If the roof can not withstand this force, the roof will "blow out".

Work Step by Step

(a) The air above the roof is moving at high speed while the air inside the house is essentially at rest. Since the air pressure is lower when fluids move at higher speeds, the air pressure above the roof is lower than the air pressure inside the house. (b) We can convert the wind speed to units of m/s $v = (130~km/h)(\frac{1000~m}{1~km})(\frac{1~hr}{3600~s})$ $v = 36.1~m/s$ We can use Bernoulli's equation to find the pressure difference inside the house and above the roof. Let $P_1$ be the pressure inside the house and let $P_2$ be the pressure above the roof. $P_1 = P_2 + \frac{1}{2}\rho~v^2$ $P_1-P_2 = \frac{1}{2}\rho~v^2$ $P_1-P_2 = \frac{1}{2}(1.29~kg/m^3)~(36.1~m/s)^2$ $P_1-P_2 = 841~N/m^2$ The pressure difference is $841~N/m^2$ (c) We can find the upward force exerted on the roof from the pressure difference. $F = (P_1-P_2)~A$ $F = (841~N/m^2)(6.0~m)(15.0~m)$ $F = 75,700~N$ The force exerted on the roof is $75,700~N$ Since the pressure is lower above the roof, the force that is exerted on the roof is exerted upward. If the roof can not withstand this force, the roof will "blow out".
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