Air enters a diffuser operating at steady state at 540°R, 15 lbf/in.2, with a velocity of 600 ft/s, and exits with a velocity of 60 ft/s. The ratio of the exit area to the inlet area is 6.Assuming the ideal gas model for the air and ignoring heat transfer, determine the temperature, in °R, and pressure, in lbf/in.2, at the exit.

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Asked Oct 11, 2019
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Air enters a diffuser operating at steady state at 540°R, 15 lbf/in.2, with a velocity of 600 ft/s, and exits with a velocity of 60 ft/s. The ratio of the exit area to the inlet area is 6.

Assuming the ideal gas model for the air and ignoring heat transfer, determine the temperature, in °R, and pressure, in lbf/in.2, at the exit.

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Expert Answer

Step 1

Given:

Inlet pressure(p)=15lbf / in
Inlet temperature(T) = 540°R
Inlet velocity (V) 600 ft /s
Exit velocity (V,) 60 ft /s
A
Exit arearatio
8 =
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Inlet pressure(p)=15lbf / in Inlet temperature(T) = 540°R Inlet velocity (V) 600 ft /s Exit velocity (V,) 60 ft /s A Exit arearatio 8 =

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Step 2

For any ideal gas and steady flow,

Mass flow rate will remain constant at inlet and exit:

т 3 т,
AV
т
т 3 т,
4,V A,V,
V2
4,.V 8.4V
(A-8.4
8V
12
Substitute specific volume into 1 by using gas equation pv = RT;
12
Ир 8V,р.
RT2
RT
И
8=
Т,
X
(2)
X
Р.
Using energy balance equation
0-2-W(- ) )+8(-2)
m
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т 3 т, AV т т 3 т, 4,V A,V, V2 4,.V 8.4V (A-8.4 8V 12 Substitute specific volume into 1 by using gas equation pv = RT; 12 Ир 8V,р. RT2 RT И 8= Т, X (2) X Р. Using energy balance equation 0-2-W(- ) )+8(-2) m

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Step 3

Since, there is no work and n...

Since, there is no work and no heat transfer occur,
0-0-0+ m (4-A))+0
So, the value of enthalpy at the exit wili be;
1
From ideal gas table for enthalpy
at T 540°R
h 129.06Btu/ lb
h.
lbf
-(600)-(60) J
Btu
+129.06Btu/lb
32.174lb.ft/s 778.17 ft.1bf
h 136.18 Btu / lb
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Since, there is no work and no heat transfer occur, 0-0-0+ m (4-A))+0 So, the value of enthalpy at the exit wili be; 1 From ideal gas table for enthalpy at T 540°R h 129.06Btu/ lb h. lbf -(600)-(60) J Btu +129.06Btu/lb 32.174lb.ft/s 778.17 ft.1bf h 136.18 Btu / lb

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