A partially open sluice gate is suddenly raised to its full opening. The resulting surge waves at the gate area) a positive wave travels towards the gate from the upstream side while a negative wave travels downstream from the gateb) a positive wave travels from the gate onto the upstream side while a positive wave travels downstream from the gatec) a negative wave travels from the gate onto the upstream side while a positive wave travels downstream from the gated) a negative wave travels towards the gate from the upstream side whereas a positive wave travels downstream from the gateCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

C. a negative wave travels from the gate onto the upstream side while a positive wave travels downstream from the gate

When a partially open sluice gate is suddenly raised to its full opening, it causes a surge of water known as surge waves. These surge waves propagate in both upstream and downstream directions from the gate. The behavior of these waves can be explained as follows:

1. Initial conditions:
- Before the gate is raised, there is a steady flow of water in the upstream direction towards the gate.
- The partially open sluice gate creates a flow restriction, causing an increase in water level upstream of the gate.
- Downstream of the gate, the water level is relatively lower due to the gate's partial closure.

2. Raising the sluice gate:
- When the sluice gate is suddenly raised to its full opening, the flow restriction is removed, allowing a large amount of water to pass through the gate.
- This sudden increase in flow rate creates a surge of water that propagates in both upstream and downstream directions.

3. Negative wave on the upstream side:
- As the high-velocity water passes through the gate, it creates a negative wave that travels upstream.
- This negative wave is caused by the sudden decrease in flow velocity and corresponds to a decrease in water level.
- The negative wave travels towards the upstream side because the gate is open, allowing water to flow freely in that direction.

4. Positive wave on the downstream side:
- Simultaneously, the surge of water passing through the gate creates a positive wave that travels downstream.
- This positive wave is caused by the sudden increase in flow velocity and corresponds to an increase in water level.
- The positive wave travels downstream because the gate is open, allowing water to flow freely in that direction.

In summary, when a partially open sluice gate is suddenly raised to its full opening, a negative wave travels from the gate onto the upstream side, while a positive wave travels downstream from the gate. This behavior is due to the sudden changes in flow velocity and water level caused by the opening of the gate.

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