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In this lesson, we will learn how to use the formula p = Οgh 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 1β025 kg/m^{3}. What pressure does the water exert on the diver, to the nearest pascal?

Q3:

A pool containing a liquid with a density of 1 0 0 0 kg/m^{3} at the surface of an unknown planet produces a pressure of 8 4 0 0 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 π is 2 1 5 6 0 Pa. Find the depth π using a value of 1 0 0 0 kg/m^{3} for the density of water.

Q5:

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?

Q6:

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 0 2 5 kg/m^{3}. The hullβs surface area is 15 m^{2}. What is the total force exerted by seawater on the hull?

Q7:

In a well, a 0.35 m high bucket full to the brim with water of density 1 0 0 0 kg/m^{3} 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 bucketβs fall, the pressure on its base is 2β310 Pa. At what rate does the bucket accelerate down the well?

Q8:

Two identical steel ball bearings are dropped into two different liquids π΄ and π΅ . Liquid π΄ has a density of 1 2 0 0 kg/m^{3} and liquid π΅ has a density of 1 5 0 0 kg/m^{3}. How many times deeper does the ball bearing have to fall into liquid π΄ to be subject to the same pressure as the ball bearing in liquid π΅ ?

Q9:

What is the pressure exerted by water at a depth of 2.5 m? Use a value of 1 0 0 0 kg/m^{3} for the density of water.

Q10:

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 0 2 5 kg/m^{3}. 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.

Q11:

A hollow container with a cross-sectional area of 25 m^{2} 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.

Q12:

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

Q13:

The pressure exerted by an oil at a depth of 2.5 m is 3 6 7 5 0 Pa. What is the density of the oil?

Q14:

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/m^{3}. What is the density of the water 7.5 cm below the surface?

Q15:

The difference in pressure a liquid exerts at different depths is shown in the graph. To the nearest kilogram per cubic meter, what is the density of the liquid?

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