Air at 80 kPa and 127 °C enters an adiabatic diffuser steadily at a rate of 6000 kg/h and leaves at 100 kPa. The velocity of the air stream is decreased from 250 m/s to 40 m/s as it passes through the diffuser. Determine

(a) the exit temperature of the air, and
(b) the inlet and exit areas of the diffuser.

a) The exit temperature is 430 K

b) The inlet and exit areas are 0.0096 m² and 0.051 m²

Explanation:

a) Given:

T₁ = 127°C = 400 K

At 400 K, h₁ = 400.98 kJ/kg (ideal gas properties table)

The energy equation is:

For a diffuser, w = Δp = 0

The diffuser is adiabatic, q = 0

Replacing:

Where

V₁ = 250 m/s

V₂ = 40 m/s

Replacing:

Using tables, at 431.43 kJ/kg the temperature is 430 K

b) The inlet area is:

The exit area is:

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