I. Air enters a diffuser at 27⁰C and 1 N / M². The approach velocity is 300m/sec, assume the flow to be isentropic. If the velocity of the air leaving the diffuser is 60m/sec, calculate the entrance and exit Mach numbers, the static pressure at exit and the percent change in cross-sectional area between entrance and exit.

Ans. Ma(entrance) = 0.864, Ma(exit) = 0.1616, p(exit) = 1.6 N/m ² , increase in area=258%

II. Carbon dioxide discharges to the atmosphere through a 10mm diameter hole in the wall of a tank in which the pressure is 8 bars(gauge) and temperature is 20⁰C. What is the velocity of the jet ? Take γ =1.3 and R=188 J/KgK and atmospheric presuure=1 bar.

Ans. 249.54 m/sec

III. Air flows isentropically through a duct. At a given point the area is and the Mach number is 0.4. At another point in the duct, the area is 0.36 m². What is the Mach number at the second point? What would the area be at a point where Ma=1?

Ans. Ma=0.64 or 1.4516, A= 0.3144 m²

IV. The stagnation temperature and stagnation pressure of air in a reservoir supplying a convergent-divergent nozzle are are 450K and 4 N/m² respectively. The nozzle throat area is 1 cm² and the nozzle exit area is 3 cm². A shock is noted at a position in the diverging portion where the area is 2 cm².

(i) What are the exit pressure, temperature and velocity?( The Mach no. just before the shock is 2.1972)

Ans. p(exit)= 2.3386 N/m², T(exit)=441 K, V(exit)=137.2 m/sec

(ii) What value of the back pressure would cause the shock to stand in the exit plane of the nozzle so that the flow through the nozzle is completely supersonic?

Ans. p= 1.505 N/m²

(iii) What value of the back pressure would result in completely isentropic flow interior and exterior to the nozzle?

Ans. p= 0.1892 N/m²(supersonic flow at exit); (subsonic flow at exit)

End of Assignment! To view recap of chapter-12, click on the next button.