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A cylindrical vessel is open at the top, 20 cm high and 10 cm in diameter. A hole of cross-sectional area 1 cm² is cut at the center of the bottom. Water is poured into the vessel from above at a rate of 100 cm³/s. Find the steady-state height (in cm) of water in the vessel.
- 20.0
- 19.6
- 5.1
- 2.5
Correct answer: 20.0
Solution
At steady state: inflow = outflow. Outflow = 1 * sqrt(2*980*h) = 100. So sqrt(1960*h) = 100 => 1960*h = 10000 => h = 5.1 cm. Since 5.1 < 20, the vessel does not overflow and steady state height is approximately 5.1 cm.
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