Final Answer:
When the back pressure in a convergent-divergent nozzle is increased such that a shock appears in the divergent portion, the exit Mach number decreases.
Step-by-step explanation:
In a convergent-divergent nozzle, when operating isentropically, an exit Mach number of 1.8 signifies supersonic flow. When the back pressure increases to the point where a shock forms in the divergent section, it causes the flow to be restricted and decelerated, resulting in a reduction of the exit Mach number. This decrease occurs because the shock wave slows down the airflow, causing it to transition from supersonic to subsonic speeds. Consequently, the exit Mach number decreases from the initially observed value of 1.8.
Increasing the back pressure beyond the nozzle's design limits causes a disruption in the flow pattern within the divergent section. The shock wave that forms acts as a flow constriction, increasing pressure and decreasing velocity. Consequently, the exit flow, initially supersonic at Mach 1.8, transitions to a lower Mach number due to the shock-induced deceleration.
This phenomenon demonstrates the sensitivity of supersonic flow systems to changes in back pressure. As the pressure increases beyond the nozzle's capacity, shock waves disrupt the flow, leading to a reduction in exit Mach number.