Question

Fluid Mechanics

a)Define the Mach number and outline its importance in distinguishing between incompressible and compressible flows, with examples of its typical ranges for the different flows.

b)Diagram 1 shows the flow of air from a reservoir with reservoir conditions pi, Pi to the exit with an exit pressure P2. The fluid flow conditions are both isentropic and adiabatic.

With the aid of a diagram, describe the various states of the system as the exit pressure P2 reduces from an initial value of Pi to a very low value. Assume the flow upstream the throat is subsonic.(8 marks)

c)The reservoir stagnation conditions for air in diagram 1 are: (i) temperature To= 400Kand (ii) pressure Po = 300 kPa; the throat area is A7=0.05m²; the exit area is A2=0.2m. Note: for air: R= 287 J kg' K'; and y=1.4.

(i)What is the maximum mass flow rate through the throat?(3 marks)

(ii)What is the exit pressure under choking conditions when the flowconditions downstream the throat aresupersonic?(6 marks)

(iii)State as to whether the flow would be choked or not if the exit pressureP2 was 250 kPa.


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