Lesson Worksheet: Fluid Pressure and Integration Mathematics

In this worksheet, we will practice applying integration to find the force exerted by a fluid on a body submerged in it.

Q1:

A right triangular plate with a base of 20 cm and a height of 30 cm is submerged vertically in water, with the top of the triangle 2 m below the surface. Find the force on one side of the plate to the nearest decimal, given that the density of water is 1,000 kg/m3 and 𝑔=9.8/ms.

Q2:

A circular plate of radius 2 m is submerged vertically in water such that the top of plate is at a depth of 6 m. Given that the density of the water is 1,000 kg/m3 and 𝑔=9.8/ms, find the force exerted by the water on one side of the plate approximated to the nearest decimal place.

Q3:

A pool is filled with water to a depth of 10 m. The density of the water is 1,000 kg/m3. Calculate the fluid force on one side of a 3 m by 4 m rectangular plate if the plate rests vertically at the bottom of the pool on its 4 m edge.

Q4:

A cubical container with side length 20 cm is filled with liquid mercury. Find the fluid force exerted on one side of the cubical container, given that that the density of mercury is 13,534 kg/m3 and 𝑔=9.8/ms. Give your answer to 1 decimal place.

Q5:

Calculate the force on one side of the semicircular plate, shown in the figure. The plate is submerged 1 cm in water, which has a density of 1,000 kg/m3. Note that 𝑔=9.8/ms. Give your answer to the nearest two decimal places.

Q6:

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

Q7:

A horizontal right circular cylindrical tank of diameter 100 cm carries oil. Determine the force that the oil exerts on each end of the tank when the tank is half-full given that the oil density is 950 kg/m3 and 𝑔=9.8/ms. Give your answer approximately to one decimal place.

Q8:

The given figure is of the vertical side of a tank full of water. Given that the water has a density of 1,000 kg/m3 and 𝑔=9.8/ms, find the fluid force on the vertical side of the tank approximately to one decimal place if needed.

Q9:

The following triangular plate is submerged in water, as shown.

Determine the fluid force on the face of the plate approximately to the nearest newton given that the density of the water is 1,000 kg/m3 and 𝑔=9.8/ms.

This lesson includes 63 additional question variations for subscribers.

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