In the figure shown, water flows into the open vessel through pipe A at a constant rate. The water can flow out of the vessel by pipe B. The maximum flow-rate fo the water in pipe B is slightly more than that in pipe A. Final height of the water level in the vessel would be

Options

A. `h_(0)`
B. `h_(f)`
C. somewhere in-between `h_(0)` and `h_(f)`
D. The water level will keep oscillating in the vessel

Answer

C

Explanation

At first, the level of water will gradually rise to height `h_(0)`. After reaching height `h_(0)`, some of the water will get drained through the siphon. As soon as the entire cross section of the top of the siphon pipe is filled with water, the water level will begain to drop since, from given conditions, the flow-rate of the water flowing from pipe B is greater than from pipe A. As the water level drops, the pressure that drives the siphon decreases and as a result the velocity of water in pipe B decreases. Level will continue to sink until the flow rate of water through pipe B becomes equal to that through pipe A.