Engineering Fundamentals: An Introduction to Engineering
Engineering Fundamentals: An Introduction to Engineering
6th Edition
ISBN: 9780357112311
Author: Saeed Moaveni
Publisher: Cengage Learning US
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Chapter 9, Problem 45P
To determine

Find the average density of the gas exiting the engine.

Expert Solution & Answer
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Answer to Problem 45P

The average density of the gas exiting the engine in kgm3, slugsm3, and lbmft3 are 0.155kgm3, 3×104slugsm3 and 0.0097lbmft3 respectively.

Explanation of Solution

Given data:

Consider that the inlet area of the engine as 5ft2.

Ain=5ft2 (1)

Consider that the outlet area of the engine as 4ft2.

Aout=4ft2 (2)

Formula used:

Consider the following expression.

(airmass flow rate)in+(fuelmass flow rate)in=(combustion mass flow rate)out

In this problem, the fuel mass flow rate is neglected since it is negligible value when compared air mass flow rate.

Consider that the mass flow rate of air enters is equal to the mass flow rate of exists.

(mass flow rate)in=(mass flow rate)out (3)

Write the expression for the mass flow rate.

mass flow rate=(density)(volume flow rate) (4)

Calculation:

Convert the unit of the value in equation (1) from ft2 to m2.

Ain=5×(1(3.28084)2)m2[1m=3.28084ft]=0.464m2

Convert the unit of the value in equation (2) from ft2 to m2.

Aout=4×(1(3.28084)2)m2[1m=3.28084ft]=0.372m2

Substitute equation (4) in (3),

[(density)(volume flow rate)]in=[(density)(volume flow rate)]outρin(volume flow rate)in=ρout(volume flow rate)out(ρin)(Vin)(Ain)=(ρout)(Vout)(Aout)[volume flow rate=(velocity)(area)]

Substitute 0.45kgm3 for ρin, and 180ms for Vin, 650ms for Vout, 0.464m2 for Ain, and 0.372m2 for Aout,

(0.45kgm3)(180ms)(0.464m2)=(ρout)(650ms)(0.372m2)

ρout=0.155kgm3 (5)

Convert the unit of the value in equation (5) from kgm3 to slugsm3.

ρout=0.155(114.5939)slugsm3[1slug=14.5939kg]=3×104slugsm3

Convert the unit of the value in equation (5) from kgm3 to lbmft3.

ρout=0.155kgm3(2.20462lbm1kg)1m3(3.28084)3ft3[1kg=2.20462lbm,and1m=3.28084ft]=0.0097lbmft3

Conclusion:

Thus, the average density of the gas exiting the engine in kgm3, slugsm3, and lbmft3 are 0.155kgm3, 3×104slugsm3 and 0.0097lbmft3 respectively.

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