Supersonic velocities are readily a

Supersonic velocities are readily attained in the diverging section of a properly designed
convergingldiverging nozzle (Fig. 7.1). With sonic velocity reached at the throat, a further
decrease in pressure requires an increase in cross-sectional area, a diverging section in which
the velocity continues to increase. The transition occurs at the throat, where dA/dx = 0.
The relationships between velocity, area, and pressure in a convergingldiverging nozzle are
illustrated numerically in Ex. 7.2.
The speed of sound is attained at the throat of a convergingldiverging nozzle only when
the pressure at the throat is low enough that the critical value of P2/ PI is reached. If insufficient
pressure drop is available in the nozzle for the velocity to become sonic, the diverging section
of the nozzle acts as a diffuser. That is, after the throat is reached the pressure rises and the
velocity decreases; this is the conventional behavior for subsonic flow in diverging sections.
The relation of velocity to pressure in an isentropic nozzle can be expressed analytically
if the fluid behaves as an ideal gas. Combination of Eqs. (6.8) and (7.3) for isentropic flow
gives: