A supersonic nozzle possessing an area ratio of 25 is suppli

A supersonic nozzle possessing an area ratio of 2.5 is supplied from a large reservoir and is allowed to exhaust to atmospheric pressure (101.3 kPa). Determine the range of reservoir pressures over which a normal shock will appear in the nozzle. For what value of reservoir pressure will the nozzle be perfectly expanded with supersonic flow at the exit plane? Find the minimum reservoir pressure to produce sonic flow at the nozzle throat. Assume isentropic flow except for shocks with y = 1.4 Repeat Problem 2 with Helium (Table 3.1).

Solution

Answer:

From isentropic gas flow tables for A/A^* = 2.5 and k=1.4

(p/p_o)_C = 0.9607 and

(p/p₀)_D = 0.5062

where C and D correspond to upper and lower limit of normal shock pressure

Hence range of pressure is

101.3 x 0.9607 = 97.31 kPa to

101.3 x 0.5062 = 51.3 kPa

The same procedure can be repeated for Heliun if Isnentropic flow table for Helium is provided.