Explanation:

A converging-diverging nozzle is a device that converts the energy of a fluid into kinetic energy by accelerating it to high velocities. This device consists of two sections, a converging section where the cross-sectional area decreases and a diverging section where the cross-sectional area increases.

The velocity of the fluid increases in the converging section due to the reduction in the cross-sectional area. As the fluid reaches the throat, the cross-sectional area is at its minimum and the velocity is at its maximum, according to the principle of continuity. The fluid then expands in the diverging section, which causes a decrease in velocity and an increase in pressure.

The maximum discharge through a converging-diverging nozzle occurs when the flow is sonic at the throat. This means that the velocity of the fluid at the throat is equal to the speed of sound in the fluid. When the flow is sonic at the throat, the pressure at the exit is equal to the ambient pressure, which is the pressure outside the nozzle.

The reason for this is that the pressure at the exit is determined by the velocity of the fluid, which in turn is determined by the pressure and temperature at the throat. If the pressure at the exit is higher than the ambient pressure, the fluid will be slowed down and compressed, which reduces the mass flow rate. If the pressure at the exit is lower than the ambient pressure, the fluid will expand and create a shock wave, which also reduces the mass flow rate. Therefore, the maximum discharge occurs when the pressure at the exit is equal to the ambient pressure.

In conclusion, the maximum discharge through a converging-diverging nozzle occurs when the flow is sonic at the throat because it ensures that the pressure at the exit is equal to the ambient pressure.