ANS:A - increases in the downstream direction.

When we discuss "increases in the downstream direction" in the context of flow velocity in a pipeline, we are referring to a specific scenario that applies to supersonic flow conditions. Here’s a more detailed explanation:

1. Supersonic Flow: Supersonic flow occurs when the flow velocity (v) within the pipeline exceeds the speed of sound (Mach 1). In such cases, the behavior of the flow differs significantly from subsonic flow (where v < Mach 1).
2. Expansion Waves: In supersonic flow, when there is an increase in the cross-sectional area of the pipeline (such as from a nozzle exit or a sudden expansion), expansion waves are generated. These expansion waves travel downstream at the speed of sound relative to the flow velocity.
3. Effect on Velocity: As the expansion waves propagate downstream faster than the flow velocity itself, they effectively increase the flow area and allow the flow velocity to increase in the downstream direction. This is a fundamental aspect of supersonic flow behavior.
4. Nozzle Example: For instance, consider a converging-diverging nozzle used in supersonic flow applications (like in rocket engines or supersonic wind tunnels). As the flow exits the converging section into the diverging section, the flow expands and the area increases. This expansion causes the flow velocity to increase downstream in the diverging section beyond the sonic throat (where the flow velocity reaches Mach 1).
5. Characteristics: Unlike subsonic flow, where velocity typically decreases due to frictional losses and conservation of mass principles, supersonic flow experiences increasing velocity due to the expansion waves moving faster than the flow itself.

In summary, "increases in the downstream direction" specifically describes the behavior of flow velocity in supersonic flow conditions, where expansion waves generated by increases in cross-sectional area cause the flow velocity to rise as it moves downstream in the pipeline or nozzle.