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Practice: Fluid Pressure and Integration

The following figure shows a plate that has an uneven length 𝑥 submerged vertically inside a tank full of a liquid of density 𝜌.

Which of the following is the liquid force 𝐹 on the plate?

  • A𝐹=𝜌𝑥(𝑦)𝑦𝑦d
  • B𝐹=𝑥(𝑦)𝑦𝑦d
  • C𝐹=𝜌𝑔𝑥𝑦(𝑥)𝑥d
  • D𝐹=𝑥𝑦(𝑥)𝑥d
  • E𝐹=𝜌𝑔𝑥(𝑦)𝑦𝑦d

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