Air is decelerated in a diffuser from 220 m/s. The exit velocity and the exit pressure of air are to be determined.
Assumptions:
- This is a steady-flow process since there is no change with time.
- Air is an ideal gas with variable specific heats.
- Potential energy changes are negligible.
- 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