Air is supplied to a convergent–divergent nozzle from a
reservoir where the pressure is 100 kPa. The air is then discharged
through a short pipe into another reservoir where the pressure
can be varied. The cross-sectional area of the pipe is twice the
area of the throat of the nozzle. Friction and heat transfer may be
neglected throughout the flow. If the discharge pipe has constant
cross-sectional area, determine the range of static pressure in the
pipe for which a normal shock will stand in the divergent section
of the nozzle. If the discharge pipe tapers so that its cross-sectional
area is reduced by 25%, show that a normal shock cannot be drawn
to the end of the divergent section of the nozzle. Find the maximum
strength of shock (as expressed by the upstream Mach number) that
can be formed.