Water from height h flows in time t. If height = 4h, time will be:
Correct answer: C. 2t
- A. t
- B. 4t
- C. 2t
- D. t/4
Explanation
For a tank draining through a small hole, Torricelli gives outflow speed v∝√h. Solving the tank-draining differential equation shows the emptying time T∝√h. So if the initial height becomes 4h, the emptying time becomes √4h /h= 2 times the original.
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Fluid flow is described through speed, pressure and density, including steady flow and the equation of continuity for conserving mass. Bernoulli's equation relates pressure, speed and height, while fluid drag and terminal velocity explain why a falling object eventually moves at constant speed when drag balances its weight.
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