Air (m=28.97kg/kmol) is uniformly heated at steady state as it flows through a c

Question

Air (m=28.97kg/kmol) is uniformly heated at steady state as it flows through a cylindrical constant area duct. It enters the channel uniformly at 2.5atm, 300K and 80m/s and exits at 1.5atm. What is the necessary heat transfer per unit mass in kJ/kg to achieve the exit conditions under the following flows? (You can assume that the air behaves as ideal gas at constant ?=1.4.)

a) Air exits uniformly at 300m/s.

b) Air flow is laminar with a maximum speed of 300m/s at the exit.

c) Air flow is turbulent (n=7) with a maximum speed of 150m/s at the exit.

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Explanation / Answer

(A) entering condition P1=2.5 atm T1=300K v1=80 m/sec V1=80*Area

Cp/Cv=1.4 or Cp=1.4Cv........(1)

Cp-Cv=R.........(2)

from both equation Cv=2.5R and Cp=3.5R

exit condition: P2=1.5 atm v2=300 m/sec

at steady state : mole of gas in per sec= mole of gas out per second

or (P1V1/RT1)=(P2V2/RT2)

or T2=T1*(P2V2/P1V1)

or T2=300*(1.5*300/2.5*80)

or T2=675 K

therefore heat transfer Q=(1/M)Cp(T2-T1)

=(1/28.97)*(3.5R)(675-300)

=376.67 KJ/Kg

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