Two cylindrical tanks are full of water, where one is oriented horizontally and another vertically. If a hole is drilled in the bottom of the tank, which one empties first?

Mechanical Engineering General ME Questions
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Can we look at this as potential energy being converted into kinetic energy? Vertical tank will have more potential energy than horizontal tank, and it would push water out faster.

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The horizontal tank will generally empty first compared to the vertical tank, assuming identical dimensions (diameter and length) and that the hole size and placement are the same. Here’s why:

1. Water Pressure and Flow Rate (Torricelli’s Law):

  • The rate of water flow through the hole depends on the water pressure, which is proportional to the height of water above the hole.
  • In a vertical tank, the height of the water column decreases linearly as the tank empties, meaning the pressure driving the flow also decreases steadily.
  • In a horizontal tank, the height of the water column decreases much more rapidly as the tank empties because the water level drops over a smaller vertical range.

2. Geometry of the Tanks:

  • For the horizontal tank, as water drains, the exposed cross-sectional area of the water decreases quickly, leading to a faster reduction in water volume.

  • For the vertical tank, the cross-sectional area remains constant, so the decrease in water volume is more gradual.

Conclusion:
The horizontal tank will empty faster because its water column height diminishes more quickly, reducing the flow-driving pressure sooner than the vertical tank.