# 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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 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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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.

Step 2

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

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...

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