Question

Air at 10º C and 80kPa enters the diffuser of a jet engine steadily with a velocity of. 200 m/s. The inlet area of the diffuser is 0.5 m. 2 . The air leaves the diffuser with a velocity that is very small compared with the inlet velocity. Determine a).the mass flow rate of the air b).the temperature of the air leaving the diffuser.

Answer 1

Given data

Pressure P = 80 kPa

Temperature T = 10°C = 283 K

Velocity V = 200 m/s

Area of diffuser = 0.5 m2

Gas constant R =0.287 kPa-m3 /kg-K

Part a

Calculate the specific volume

= R x T/P

= 0.287 kPa-m3 /kg-K x 283 K / 80 kPa

= 1.015 m3/kg

Mass flow rate = velocity x Area / Specific volume

= 200 x 0.5 / 1.015

= 98.497 kg/s

Part b

At T1 = 283 K

Enthalpy, h1 = 283.14 kJ/kg

At steady state

Enthalpy in = enthalpy out

283.14 x 200 x 200 / 2 = h2

h2 = 303.14 kJ/kg

From the air properties

T2 = 303.14 K