Question

What is the ratio of throat area of diffuser to nozzle in supersonic wind tunnel with flow at Mach 2.7?

(a) 0.4236

(b) 0.8338

(c) 2.36

(d) 1.199

I have been asked this question in class test.

My question is taken from Supersonic Wind Tunnels topic in chapter Compressible Flow through Nozzles, Diffusers and Wind Tunnels of Aerodynamics

Answer 1

Right choice is (c) 2.36

To explain: Given M = 2.7

If we assume that there’s a normal shock present at the entrance of the diffuser, then using the gas table we can find the ratio of total pressures \(\frac {p_{01}}{p_{02}}\).

For M = 2.7, \(\frac {p_{02}}{p_{01}}\) = 0.4236

Using the relation beween the throat areas and total pressure we get

\(\frac {A_{t2}}{A_{t1}} = \frac {p_{01}}{p_{02}} = \frac {1}{0.4236}\) = 2.36