At steady state, air at 148 kPa, 52°C and a mass flow rate of 0.48 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. At the duct exit, the pressure of the air is 117 kPa, the velocity is 297.09 m/s,the temperature is 82.25°C, and the cross-sectional area is 2 × 10-3 m2. Assuming the ideal gas model, determine the velocity of the air at the inlet, in m/s.

Question
Asked Nov 15, 2019
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At steady state, air at 148 kPa, 52°C and a mass flow rate of 0.48 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. At the duct exit, the pressure of the air is 117 kPa, the velocity is 297.09 m/s,the temperature is 82.25°C, and the cross-sectional area is 2 × 10-3 m2. Assuming the ideal gas model, determine the velocity of the air at the inlet, in m/s.

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Expert Answer

Step 1

Consider the diagram showing an insulated duct in through which the air is flowing in a steady state.  All the variables define the characteristic of the flow of the air at inlet and out let of the insulated duct.

 

The subscript 1 on every variable parameter are for the inlet side and subscript 2 is for the outlet side of the duct.

A2
A1
-82-25
Insulated Duct
T52c
P-148kfa
V, To fiud
2297.09
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A2 A1 -82-25 Insulated Duct T52c P-148kfa V, To fiud 2297.09

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Step 2

Here, the mass flow rate of the air flow is given. Now, use the expression for steady state flow.

Q-W =m(h-) + m|
+mg (-2)
2
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Q-W =m(h-) + m| +mg (-2) 2

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Step 3

In the steady state equation, under the ideal conditions the value of the Q and work, W will be same and since t...

0= m (0-4)+
+0
2
т(h, - h)+т
2
= (4-1h)
2
V2(4-)
.. (1)
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0= m (0-4)+ +0 2 т(h, - h)+т 2 = (4-1h) 2 V2(4-) .. (1)

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