Question

Air at 80 kPa, 27°C, and 220 m/s enters a diffuser at a rate of 2.5 kg/s and leaves at 42°C. The exit area of the diffuser is 400 cm². The air is estimated to lose heat at a rate of 18 kJ/s during this process. Determine (a) the exit velocity and (b) the exit pressure of the air. Answers: (a) 62.0 m/s, (b) 91.1 kPa.

Answer 1

Air is decelerated in a diffuser from 220 m/s. The exit velocity and the exit pressure of air are to be determined. 

Assumptions:

1. This is a steady-flow process since there is no change with time. 
2. Air is an ideal gas with variable specific heats. 
3. Potential energy changes are negligible. 
4. There are no work interactions. 

Properties: The gas constant of air is 0.287 kPa.m³/kg K (Table A-1). The enthalpies are (Table A-17)

T₁ = 27°C = 300 K → h₁ = 300.19 kJ/kg

T₂ = 42°C = 315 K → h₂ = 315.27 kJ/kg

Analysis:

(a) There is only one inlet and one exit, and thus \(\overset •m_1 = \overset •m_2 = \overset •m\). We take diffuser as the system, which is a control volume since mass crosses the boundary. The energy balance for this steady-flow system can be expressed in the rate form as

(b) The exit pressure of air is determined from the conservation of mass and the ideal gas relations