Worksheet: Pressure Produced by Fluids

In this worksheet, we will practice using the formula p = ρgh to calculate the pressure produced at different depths by different fluids that gravity acts on.

Q1:

The difference in pressures at a depth of 3.75 m for sea water and fresh water is 735 Pa. What is the difference in their densities?

Q2:

A scuba diver dives to a depth of 1.25 m below the surface of the sea. The sea water has a density of 1,025 kg/m3. What pressure does the water exert on the diver, to the nearest pascal?

Q3:

A pool containing a liquid with a density of 1,000 kg/m3 at the surface of an unknown planet produces a pressure of 8,400 Pa at a depth of 2.4 m. What is the acceleration due to gravity at the surface of this planet?

Q4:

The pressure from water at a depth 𝑑 is 21,560 Pa. Find the depth 𝑑 using a value of 1,000 kg/m3 for the density of water.

Q5:

A hollow container with a cross-sectional area of 25 m2 is suspended from a cable in a sealed room. Air is pumped into the room until the air pressure is 5.7 atmospheres. The air inside the container is at a pressure of 1.2 atmospheres. Find the net force on the outer surface of the container, using a value of 101 kPa for one atmosphere.

Q6:

Two identical steel ball bearings are dropped into two different liquids 𝐴 and 𝐡. Liquid 𝐴 has a density of 1,200 kg/m3 and liquid 𝐡 has a density of 1,500 kg/m3. How many times deeper does the ball bearing have to fall into liquid 𝐴 to be subject to the same pressure as the ball bearing in liquid 𝐡?

Q7:

Which of the following formulas correctly shows the relationship between the pressure exerted by a fluid, the height β„Ž of the fluid above the point at which pressure is measured, the density 𝜌 of the fluid, and the gravitational acceleration rate 𝑔?

  • A𝑃=π‘”πœŒβ„Ž
  • B𝑃=β„ŽπœŒπ‘”
  • C𝑃=πœŒπ‘”β„Ž
  • D𝑃=π‘”β„ŽπœŒ
  • E𝑃=πœŒπ‘”β„Ž

Q8:

The hull of a sunken boat, laying on the seabed, is 12 m below the surface of the sea, where the sea water has an average density of 1,025 kg/m3. The hull’s surface area is 15 m2. What is the total force exerted by seawater on the hull?

Q9:

In a well, a 0.35 m high bucket full to the brim with water of density 1,000 kg/m3 is supported by a rope. The bucket is dropped into the well and its fall is slowed by the tension in the rope. During the bucket’s fall, the pressure on its base is 2 310 Pa. At what rate does the bucket accelerate down the well?

Q10:

The pressure exerted by an oil at a depth of 2.5 m is 36β€Žβ€‰β€Ž750 Pa. What is the density of the oil, to the nearest kg/m3?

Q11:

What is the pressure exerted by water at a depth of 2.5 m? Use a value of 1,000 kg/m3 for the density of water.

Q12:

Two different gases, gas A and gas B, form bubbles in a container of water where chemical reactions are occurring. Many bubbles are released upward at different speeds for different gases. The pressure on the bubbles of both types of gas is equal when the bubbles are of the same size. The bubbles of gas A and gas B have the same size when the bubbles of gas A are 2.5 cm below the surface of the water and the bubbles of gas B are 7.5 cm below the surface of the water. The water in the container has different average densities at different depths as the amount of gas dissolved in the water is different at different depths. The density of the water 2.5 cm below the surface is 900 kg/m3. What is the density of the water 7.5 cm below the surface?

Q13:

The difference in pressure a liquid exerts at different depths is shown in the graph. To the nearest kilogram per cubic meter, find the density of the liquid. Estimate the line of best fit for the graph to do this.

Q14:

The pressure of a gas on the opposite sides of a horizontal section of the wall of a container is shown in the diagram. The greater pressure is exerted on the inside of the container.

What is the net outward pressure exerted on that section?

What is the net force exerted on that section?

Q15:

A submarine in the sea can dive to a depth where the pressure exerted by the water on the submarine is ten atmospheres. The sea water has a density of 1,025 kg/m3. Find the maximum safe depth to which the submarine can dive, rounded to one decimal place, using a value of 101 kPa as the pressure of one atmosphere.

Q16:

The magnitude of the atmospheric pressure at different heights above sea level is shown in the diagram. The atmospheric pressure is shown at sea level and at a height β„Ž at which the atmospheric pressure is 0.5 times the atmospheric pressure at sea level. One atmosphere of pressure is equivalent to 101 kPa of pressure.

How does the atmospheric pressure change as the height above sea level increases?

  • AThe atmospheric pressure increases.
  • BThe atmospheric pressure is constant.
  • CThe atmospheric pressure decreases.

How does the rate of change of the atmospheric pressure change as the height above sea level increases?

  • AThe rate of change of atmospheric pressure is constant.
  • BThe rate of change of atmospheric pressure decreases.
  • CThe rate of change of atmospheric pressure increases.

What is the atmospheric pressure at the sea level, to the nearest kilopascal?

What is the atmospheric pressure at the top of Earth’s atmosphere, to the nearest kilopascal?

Is the height β„Ž at which the atmospheric pressure is 0.5 times the atmospheric pressure at sea level more than, less than, or exactly half way from sea level to the top of the atmosphere?

  • AMore than halfway
  • BLess than halfway
  • CExactly halfway

Q17:

The magnitude of the atmospheric pressure at different heights above sea level is shown in the diagram. The atmospheric pressure is shown at two heights β„ŽοŠ§ and β„ŽοŠ¨, where β„Ž=2β„ŽοŠ¨οŠ§. The change in the pressure between the top of Earth’s atmosphere and β„ŽοŠ¨ is equal to Ξ”π‘ƒοŒ . The change in the pressure between β„ŽοŠ¨ and β„ŽοŠ§ is equal to Ξ”π‘ƒοŒ‘.

How does the atmospheric pressure change as the height above sea level decreases?

  • AThe atmospheric pressure decreases.
  • BThe atmospheric pressure is constant.
  • CThe atmospheric pressure increases.

How does the rate of change of the atmospheric pressure change as the height above sea level decreases?

  • AThe rate of change of atmospheric pressure increases.
  • BThe rate of change of atmospheric pressure decreases.
  • CThe rate of change of atmospheric pressure is constant.

Is β„Žβ„ŽοŠ§οŠ¨ greater than, less than, or the same as Ξ”π‘ƒΞ”π‘ƒοŒ οŒ‘?

  • Aβ„Žβ„Ž=Ξ”π‘ƒΞ”π‘ƒοŠ§οŠ¨οŒ οŒ‘
  • Bβ„Žβ„Ž>Ξ”π‘ƒΞ”π‘ƒοŠ§οŠ¨οŒ οŒ‘
  • Cβ„Žβ„Ž<Ξ”π‘ƒΞ”π‘ƒοŠ§οŠ¨οŒ οŒ‘

Q18:

A diver swims in water of density 1,015 kg/m3, as shown in the diagram. What is the difference between the water pressure at the diver’s head and at his feet? Answer to the nearest pascal.

Q19:

An air column is defined as all the air within a cuboid that has a cross-sectional area of 1 square meter that stretches from the ground to the top of Earth’s atmosphere, as shown in the diagram. The top of the atmosphere can be taken as 15 km above the surface of Earth. The pressure from the air at the base of an air column is 101 kPa.

Find the weight of the air in an air column.

Find the mass of the air in an air column. Round your answer to the nearest kilogram.

Find the average density of the air in the air column. Round your answer to two decimal places.

Assume that the density of the air in the air column varies uniformly from the bottom to the top. What is the air’s density at the top of the air column if the density at the base of the column is 1.23 kg/m3? Round your answer to two decimal places.

Q20:

An oil leak left a 0.4 m thick layer of oil floating on top of the seawater. Calculate the pressure due to the water and the oil 2.1 m below water surface. Take 𝜌=850/oilkgm, 𝜌=1,000/wkgm, and 𝑔=9.8/ms.

  • A45,325 N/m2
  • B33,248 N/m2
  • C23,912 N/m2
  • D21,413 N/m2

Q21:

The given figure shows three vessels of different shapes. They are filled with water to the same level, and they have the same base area. Which of the following statements about the pressure of the water on the vessels’ bases is correct?

  • A𝑃=𝑃>π‘ƒοŠ§οŠ©οŠ¨
  • B𝑃>𝑃>π‘ƒοŠ¨οŠ©οŠ§
  • C𝑃>𝑃>π‘ƒοŠ§οŠ©οŠ¨
  • D𝑃=𝑃=π‘ƒοŠ§οŠ¨οŠ©

Q22:

In the following figure, if the density of the seawater is higher than that of the swimming pool water, which swimmer is exposed to higher pressure?

  • A(C)
  • B(B)
  • C(A)
  • D(D)

Q23:

A glass container open to air has a layer of water above a layer of liquid mercury. Which of the following graphs represents the relation between the total pressure 𝑃 and the depth β„Ž from the surface of the whole fluid?

  • A
  • B
  • C
  • D

Q24:

These three containers are filled with oil to the same level. They all have the same base area but differ in shape, as shown in the figure. Which of the following statements is correct?

  • AThe pressure at A is less than the pressure at B but equal to the pressure at C.
  • BThe pressure at B and C is equal and greater than the pressure at A.
  • CThe pressure at C is less than the pressure at B which is less than the pressure at A.
  • DThe pressure at A, B, and C is the same.

Q25:

The pressure on a point at a depth of 6 cm in a beaker which contains oil is 0.5Γ—10 Pa. Find the density of the oil in terms of the acceleration due to gravity, 𝑔.

  • A1.2Γ—10𝑔οŠͺ kg/m3
  • B1Γ—10𝑔οŠͺ kg/m3
  • C5Γ—10π‘”οŠ¨ kg/m3
  • D8.3Γ—10π‘”οŠ© kg/m3

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