Discussion
Consider a steady, isentropic, supersonic flow (Mach number \(M \gt 1\)) entering a Convergent-Divergent (CD) duct as shown in the figure. Which one of the following options correctly describes the flow at the throat?
(The figure shows a duct that narrows to a marked Throat and then widens, with the flow at \(M \gt 1\) entering from the left.)
Answer: C
The flow at the throat can either be sonic or supersonic.
In isentropic flow, \(dA/A = (M^{2} - 1)\,dV/V\). With \(M \gt 1\), a decreasing area slows the flow, so the Mach number falls through the convergent part, but it can only reach 1 where the area is a minimum, at the throat. If the throat area equals the critical (sonic) area for the entering flow, the flow is just sonic there; if the throat is larger, it is still supersonic there and simply speeds up again in the divergent part.
It cannot be subsonic at the throat: in isentropic flow the Mach number cannot pass through 1 inside a converging section, and slowing to subsonic before the throat would need a shock, which is not isentropic. So 'only supersonic', 'only sonic' and 'only subsonic' are all wrong.
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