A diffuser has air entering at 100 kPa and 300 K with a velocity of 200 m/s. The

Question

A diffuser has air entering at 100 kPa and 300 K with a velocity of 200 m/s. The inlet cross sectional area of the diffuser is 100 mm2. At the exit the cross sectional area is 860 mm2 and the velocity is 20 m/s.

a- State the assumptions.

b- Find the exit temperature of the air.

c- Calculate the pressure of the air leaving the diffuser.

d- Compare the exit T and P with the inlet ones and discuss the differences.

e- If the exit kinetic energy in a real diffuser is 80% of that in an ideal diffuser (adiabatic), find the exit T and P in the real diffuser and compare the results with those obtained from the ideal diffuser.

Explanation / Answer

mi=Aivi=me=Aeve/ve

hi+(1/2)vi^2=he+(1/2)Ve^2

he-hi=(1/2)Vi^2-(1/2)Ve^2

=(200^2/2 x 1000)-2062/2 X 100

Te=Ti+(he-hi)^2/Cp

=300+19.8/1.005=319.72k

according to equation of continuity

Ve=Vi(AeVe/AiVi)=RTi/Pi x AeVe/AiVi =RTe/Pe

Pe=Pi(Te/Ti)(AiVi/AeVe)

=100(319.72/300)(100 x 200/800 x20)=123.92kpa

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