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 87RQ
To determine

The gage pressure of the gasoline line.

Expert Solution & Answer
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Explanation of Solution

Given:

Gage pressure (Pgage) is 180kPa.

Height of the water in the manometer (hw) is 45cm.

Height of the mercury in the manometer (hHg) is 10cm.

Height of the oil in the manometer (hoil) is 50cm.

Height of the gasoline in the manometer (hgasoline) is 22cm.

Density of the water (ρw) is 1000kg/m3.

Specific gravity of the oil (SGoil) is 0.79.

Specific gravity of the mercury (SGHg) is 13.6.

Specific gravity of the gasoline (SGgasoline) is 0.70.

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

Calculation:

Calculate the density of the oil (ρoil).

  ρoil=(ρw)(SGoil)=(1000kg/m3)(0.79)=790kg/m3

Calculate the density of the mercury (ρHg).

  ρHg=(ρw)(SGHg)=(1000kg/m3)(13.6)=13,600kg/m3

Calculate the density of the gasoline (ρgasoline).

  ρgasoline=(ρw)(SGHg)=(1000kg/m3)(0.70)=700kg/m3

Calculate the gage pressure of the gasoline line (Pgasoline).

  Pgageρwghw+ρoilghoilρHgghHgρgasolineghgasoline=Pgasoline

  Pgasoline=Pgageρwghw+ρoilghoilρHgghHgρgasolineghgasoline=Patmg(ρwhwρoilhoil+ρHghHg+ρgasolinehgasoline)=180kPa(9.81m/s2)[(1000kg/m3)(45cm)(790kg/m3)(50cm)+(13,600kg/m3)(10cm)+(700kg/m3)(22cm)]=180kPa(9.81m/s2)[(1000kg/m3)(0.45m)(790kg/m3)(0.50m)+(13,600kg/m3)(0.10m)+(700kg/m3)(0.22m)]=180kPa(9.81m/s2)[(1000kg/m3)(0.45m)(790kg/m3)(0.50m)+(13,600kg/m3)(0.10m)+(700kg/m3)(0.22m)](1kN1000kgm/s2)(1kPa1000kN/m2)=164.6kPa

Thus, the gage pressure of the gasoline line is 164.6kPa_.

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Chapter 2 Solutions

Fundamentals of Thermal-Fluid Sciences

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