Air enters a diffuser with a pressure of 200 kPa, a temperature of 50oC, and a velocity of 250 m/s. The inlet of the diffuser is circular, with a diameter of 2.5 cm. The exit velocity is 20 m/s. Plot the exit temperature for heat transfer rates ranging from -20.0 kW to 20.0 kW. Repeat the calculations for an outlet velocity of 100 m/s.

Question

Given: Air, P1 = 200 kPa; T1 = 50oC = 323 K; V1 = 250 m/s; D1 = 2.5 cm = 0.025 m; V2 = 20 m/s; and V2 = 100 m/s

What will be an ideal response?

Answer 1

For a diffuser, assume steady –state, steady-flow single-inlet, single-outlet flow, and assume that W?=?pe=0

These assumptions result in the first law being (State 1 is inlet, State 2 is outlet)

As the temperature change is likely small, we will consider air to be an ideal gas with constant specific heats: h2 – h1 = cp (T2 – T1)

A1 = ?D12/4 = 0.0004908 m2

m?=?1V1A1=P1RT1V1A1 = 0.2648 kg/s

where R = 0.287 kJ/kg-K. For air, take cp = 1.005 kJ/kg-K

Substituting into the First Law:



Notice, with the specified conditions, there is no outlet pressure dependency

The plot below compares the results for the two outlet velocities.