Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 2, Problem 42P
To determine

The height of the building.

Expert Solution & Answer
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Explanation of Solution

Given:

Barometer reading at the bottom of the building (hbottom) is 695mmHg.

Barometer reading at the top of the building (htop) is 675mmHg.

Density of air (ρ) is 1.18kg/m3.

Density of mercury (ρHg) is 13,600kg/m3.

Acceleration due to gravity (g) is 9.81m/s2.

Calculation:

Calculate the pressure at the top of the building (Ptop).

  Ptop=ρHgghtop=(13600kg/m3)(9.81m/s2)(675mmHg)=(13600kg/m3)(9.81m/s2)(675mmHg)(1mHg1000mmHg)=(13600kg/m3)(9.81m/s2)(0.675m)=(90055.8kgm/s2)(1N1kgm/s2)(1kPa1000N/m2)=90.06kPa

Calculate the pressure at the bottom of the building (Pbottom).

  Pbottom=ρHgghbottom=(13600kg/m3)(9.81m/s2)(695mmHg)=(13600kg/m3)(9.81m/s2)(695mmHg)(1mHg1000mmHg)=(13600kg/m3)(9.81m/s2)(0.695m)=(92724.12kgm/s2)(1N1kgm/s2)(1kPa1000N/m2)=92.72kPa

Calculate the height of the building (h) using the force balance per unit base area relation.

  WairA=PbottomPtop(ρgh)air=PbottomPtop(1.18kg/m3)(9.81m/s2)(h)=92.72kPa90.06kPa(11.5758kgm/s2)(h)(1N1kgm/s2)(1kPa1000N/m2)=2.66kPah=231m

Thus, the height of the building is 231m_.

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Chapter 2 Solutions

Fundamentals of Thermal-Fluid Sciences

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