Pressure and pressure differences in fluids

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Pressure in Fluids

A fluid is either a liquid or a gas.
Pressure is the concentration of a force, or the force per unit area.
Pressure is calculated using p = F / A, where p is in pascals (Pa), F in newtons (N) and A in metres squared (m²).
The area used is always the cross-sectional area — the area where the force acts at right angles.
A fluid exerts pressure evenly across the whole surface of an immersed object and in all directions.
The forces created by fluid pressure act at 90° (normal) to the surface.
Spreading a force over a large area gives a small pressure; concentrating it over a small area gives a large pressure.
Examples: tractor tyres are wide to reduce pressure and stop sinking into mud; nails and high heels have small areas to create large pressures.

Atmospheric Pressure

The atmosphere is a thin layer of air around the Earth, extending more than 100 km into space.
At sea level, atmospheric pressure is about 100–101 kPa.
Atmospheric pressure is caused by air molecules colliding with a surface, creating a force per unit area.
The atmosphere becomes less dense with increasing altitude, so pressure decreases as height increases.
The number of air molecules (and so the weight of air) above a surface decreases as the surface's height above ground increases.
As height increases there is always less air above a surface than at a lower height, so atmospheric pressure decreases with height.
Atmospheric pressure varies slightly from day to day with the weather; fine clear weather is usually linked to high pressure.

Pressure in a Liquid

The greater the depth of the liquid, the greater the pressure.
The greater the density of the liquid, the greater the pressure.
Liquid pressure is caused by the weight of the liquid pushing against objects immersed in it.
As depth increases, the amount (and weight) of liquid above a point increases, so pressure increases.
A more dense liquid has a greater weight, so it exerts a higher pressure.
In a column of water, the highest pressure is at the bottom — a hole there produces a strong jet, while a hole near the top produces a weak jet.
The pressure on the seabed is far higher than at the surface of the ocean.
Liquid pressure does not depend on the shape of the container or the total volume of liquid.

Pressure in a liquid increases with depth and density, and acts equally in all directions.

Calculating Pressure in a Liquid

The pressure due to a column of liquid is calculated using p = h × ρ × g.
p = pressure in pascals (Pa); h = height of the column in metres (m).
ρ = density of the liquid in kg/m³; g = gravitational field strength in N/kg.
The value of g will be given in any calculation.
This equation is given on the Physics equation sheet, but you must be able to rearrange it for h, ρ or g.
The equation gives the difference in pressure at different depths, since pressure changes with depth.
Example: at a depth of 10 m in water, the extra pressure is about 100 kPa; adding the 101 kPa atmospheric pressure gives a total of 201 kPa.

A hydraulic lift: a pump creates pressure in the liquid, transmitted to a piston of known cross-sectional area to raise the platform.

Upthrust

Upthrust is a force that pushes upwards on an object submerged in a fluid.
It always acts in the opposite direction to the object's weight.
Upthrust arises because a submerged object experiences greater pressure on its bottom surface than on its top surface.
This is because pressure is proportional to depth, so the difference in pressure creates a resultant force upwards.
The size of the upthrust depends on the density of the fluid and the volume of fluid displaced (equal to the volume of the object).
The denser the liquid, the greater the upthrust it exerts.
Upthrust equals the weight of fluid displaced.
Upthrust is why objects appear to weigh less when immersed in a liquid.

Floating and Sinking

If the upthrust equals (or is greater than) the object's weight, the object floats.
If the upthrust is smaller than the weight, the object sinks.
An object less dense than the fluid will float; an object more dense than the fluid will sink.
A denser-than-fluid object can never displace enough fluid to create an upthrust that supports its weight.
Polystyrene (0.05 g/cm³) floats in water (1.0 g/cm³); a wooden block (0.9 g/cm³) floats partially submerged; an iron block (7.9 g/cm³) sinks.
Objects float because upthrust balances weight, not simply because they are light.

Calculating Upthrust

To find upthrust, first calculate the volume of the object immersed in the fluid.
Use mass = density × volume (m = ρV) to find the mass of fluid displaced.
Use weight = mass × gravitational field strength (W = mg) to find the weight of displaced fluid.
The upthrust equals this weight of displaced fluid.
Example: a cube 40 cm × 40 cm × 40 cm submerged to 20 cm displaces 32 000 cm³ of water, giving a mass of 32 kg and an upthrust of 320 N (with g = 10 N/kg).

Key Equations and Units

p = F / A — pressure equals force normal to a surface divided by the area of that surface.
p = h ρ g — pressure due to a column of liquid.
Pressure is measured in pascals (Pa); 1 kPa = 1000 Pa.
Force is measured in newtons (N); large forces may be quoted in kN (1 kN = 1000 N).
Density is measured in kg/m³; gravitational field strength in N/kg.
Always convert areas from cm² to m² before substituting into equations.

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1.What is the correct definition of pressure?
Easy
- AThe force per unit area
- BThe total force acting on a surface
- CThe weight of an object
- DThe volume of a fluid
2.Which of the following is the correct unit for pressure?
Easy
- ANewton (N)
- BPascal (Pa)
- CJoule (J)
- DKilogram (kg)
3.The pressure in a fluid acts at right angles to any surface it contacts.
Easy
True or false?
4.Which of the following statements about atmospheric pressure are correct? (Select all that apply)
Medium
- AAtmospheric pressure decreases as altitude increases.
- BAtmospheric pressure is caused by air molecules colliding with a surface.
- CAtmospheric pressure increases as the density of air decreases.
- DAtmospheric pressure at sea level is about 101 kPa.
- EAtmospheric pressure is greater at the top of a mountain than at sea level.
5.How does the pressure beneath the surface of a liquid change with depth and density?
Easy
- AIt increases with depth and increases with density.
- BIt increases with depth and decreases with density.
- CIt decreases with depth and increases with density.
- DIt decreases with depth and decreases with density.
6.A diver swims deeper into a lake. What happens to the pressure of the water on the diver?
Medium
- AIt increases.
- BIt decreases.
- CIt stays the same.
- DIt first increases then decreases.
7.Why is the total pressure on a diver greater than just the pressure due to the water above the diver?
Medium
- ABecause the atmosphere also exerts pressure on the diver.
- BBecause the diver's body creates additional pressure.
- CBecause water pressure acts in all directions.
- DBecause the diver is moving.
8.An aeroplane gains height after take-off. Which two factors affect the atmospheric pressure on the aeroplane as it rises?
Medium
- AThe density of the air and the height above the surface
- BThe speed of the aeroplane and the temperature of the air
- CThe weight of the aeroplane and the volume of air displaced
- DThe gravitational field strength and the density of the aeroplane

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9.The Dead Sea has a density of about 1250 kg/m³. What is the relationship between the pressure of a liquid, gravitational field strength, density of the liquid and depth?
Medium
- APressure = density × gravitational field strength × depth
- BPressure = density × gravitational field strength ÷ depth
- CPressure = depth × gravitational field strength ÷ density
- DPressure = density ÷ (gravitational field strength × depth)
10.A glass container has sections of different shapes. Water is poured into one section. What happens to the water levels in the other sections?
Medium
- AThey all reach the same level as the first section.
- BThey are lower in narrower sections.
- CThey are higher in wider sections.
- DThey depend on the shape of each section.
11.A metal cylinder floats in seawater with 1.2 m of its 1.8 m length submerged. What is the relationship between the weight of the cylinder and the upthrust?
Medium
- AThey are equal.
- BThe weight is greater than the upthrust.
- CThe upthrust is greater than the weight.
- DThere is no upthrust because the cylinder is partly out of the water.
12.Which statement about upthrust is correct?
Medium
- AUpthrust acts in the opposite direction to the object's weight.
- BUpthrust acts in the same direction as the object's weight.
- CUpthrust only acts on objects that are completely submerged.
- DUpthrust is caused by the object's density.
13.An object will float if its density is greater than the density of the fluid it is in.
Easy
True or false?
14.Which of the following affect the size of the upthrust on an object submerged in a fluid? (Select all that apply)
Medium
- AThe density of the fluid
- BThe volume of fluid displaced
- CThe mass of the object
- DThe depth of the fluid
- EThe shape of the object
15.Match each term with its correct definition.
Medium
- Pressure
- Upthrust
- Atmospheric pressure
- Force per unit area
- Upward force on a submerged object
- Pressure exerted by air molecules
16.Place the following steps in order to calculate the pressure at a depth in a liquid.
Medium
- Identify the depth of the liquid
- Identify the density of the liquid
- Multiply depth by density by gravitational field strength
- State the pressure with the correct unit
17.Why does atmospheric pressure decrease as altitude increases?
Medium
- AThere are fewer air molecules above the surface.
- BThe air molecules move faster.
- CThe gravitational field strength increases.
- DThe temperature of the air increases.
18.A diver experiences a total pressure of 201 kPa at a depth of 10 m in water. What is the pressure due to the water alone? (Atmospheric pressure = 101 kPa)
Medium
- A100 kPa
- B201 kPa
- C101 kPa
- D302 kPa
19.Which of the following statements about pressure in a fluid are correct? (Select all that apply)
Medium
- AA fluid can be either a liquid or a gas
- BThe force from fluid pressure acts at right angles to a surface
- CPressure in a fluid is measured in newtons
- DA fluid exerts pressure evenly across the whole surface of an immersed object
- EFluid pressure only acts downwards
20.A diver is 10 m below the surface of the sea. The atmospheric pressure at the surface is 101 kPa and the pressure due to the water alone at this depth is 100 kPa. What is the total pressure on the diver?
Medium
- A201 kPa
- B101 kPa
- C100 kPa
- D1 kPa
21.Which of the following factors affect the pressure at a point in a liquid? (Select all that apply)
Medium
- AThe depth of the liquid above the point
- BThe density of the liquid
- CThe shape of the container
- DThe gravitational field strength
- EThe total volume of liquid in the container
22.An object floats in water. Which statement is correct?
Medium
- AThe upthrust on the object is equal to its weight
- BThe upthrust on the object is greater than its weight
- CThe upthrust on the object is less than its weight
- DThe object has no weight
23.A student measures the pressure at different depths in a beaker of water and plots pressure against depth. What is the shape of the graph?
Medium
- AA straight line through the origin
- BA curve that gets steeper as depth increases
- CA horizontal line
- DA curve that gets less steep as depth increases
24.Which of the following statements about upthrust are correct? (Select all that apply)
Hard
- AUpthrust acts in the opposite direction to the weight of the object.
- BUpthrust is equal to the weight of the fluid displaced by the object.
- CUpthrust increases as the density of the fluid increases.
- DUpthrust depends on the shape of the object.
- EUpthrust is caused by the pressure difference between the top and bottom of the object.
25.Atmospheric pressure is caused by air molecules colliding with a surface.
Easy
True or false?
26.A student measures the pressure at the base of a container of water, then repeats the measurement after pouring in more water so the depth doubles. The liquid density stays the same. What happens to the pressure at the base?
Medium
- AIt stays the same because the container is the same
- BIt doubles because pressure is proportional to depth
- CIt halves because the water is spread out more
- DIt quadruples because pressure depends on depth squared
27.A pressure gauge is lowered into a tank of liquid. The reading increases by 8000 Pa when the gauge is moved 0.5 m deeper. The gravitational field strength is 10 N/kg. What is the density of the liquid?
Medium
- A1600 kg/m³
- B400 kg/m³
- C16 000 kg/m³
- D160 kg/m³
28.A student investigates how the pressure at the base of a tall measuring cylinder of water changes as water is added. Which of the following statements about this practical are correct? (Select all that apply)
Medium
- AThe pressure at the base should increase as more water is added
- BThe reading on a pressure sensor at the base depends on the total volume of water only
- CThe depth of water should be measured from the base to the water surface
- DThe pressure at the base would be the same if the cylinder were replaced by a wider one of the same water depth
- EThe density of the water must be found by weighing the cylinder
29.In a liquid, the pressure at a point increases with the height of the column of liquid above that point.
Easy
True or false?
30.A diver is 15 m below the surface of the sea. The pressure due to the water alone at this depth is 150 kPa and the atmospheric pressure at the surface is 101 kPa. What is the total pressure on the diver?
Hard
- A49 kPa
- B150 kPa
- C251 kPa
- D101 kPa
31.A student sets up a tall glass tube open at the top and filled with water. She makes three identical small holes at different heights up the side. Which statement best describes what she observes?
Medium
- AThe jet from the lowest hole travels furthest because the pressure there is greatest
- BAll three jets travel the same distance because the holes are the same size
- CThe jet from the highest hole travels furthest because it is nearest the surface
- DThe jets travel furthest from the hole nearest the middle of the tube
32.Place the following steps in the correct order to find the upthrust on an object fully submerged in water, using the weight of fluid displaced.
Medium
- Measure the volume of the object that is submerged
- Multiply the volume by the density of the water to find the mass of water displaced
- Multiply the mass of water displaced by the gravitational field strength to find its weight
- State that the upthrust equals the weight of water displaced
33.An object is fully submerged in a beaker of water and hangs from a newton meter. Which of the following statements about this experiment are correct? (Select all that apply)
Hard
- AThe newton meter reading is less than the object's weight in air
- BThe upthrust equals the difference between the weight in air and the reading in water
- CThe upthrust acts downwards on the object
- DThe upthrust equals the weight of water displaced by the object
- EThe reading on the newton meter equals the upthrust
34.Which of the following best describes what a fluid is?
Easy
- AA liquid or a gas
- BA solid or a liquid
- COnly a liquid
- DOnly a gas
35.In which direction does the pressure in a fluid act on a surface?
Easy
- AAt right angles to the surface
- BParallel to the surface
- CAt 45° to the surface
- DIt acts in all directions equally, including parallel to the surface
36.What is the approximate value of atmospheric pressure at sea level?
Easy
- A101 kPa
- B10 kPa
- C1000 kPa
- D1 kPa
37.Which of the following statements about atmospheric pressure is correct?
Easy
- AAtmospheric pressure decreases as altitude increases.
- BAtmospheric pressure increases as altitude increases.
- CAtmospheric pressure remains constant with altitude.
- DAtmospheric pressure first increases then decreases with altitude.
38.A student measures the pressure at the base of a container of water, then repeats the measurement after pouring in more water so the depth doubles. The liquid density and gravitational field strength remain constant. What happens to the pressure at the base?
Medium
- AIt doubles.
- BIt halves.
- CIt stays the same.
- DIt quadruples.
39.A student sets up a tall glass tube open at the top and filled with water. She makes three identical small holes at different heights up the side. Which statement about the jets of water from the holes is correct?
Hard
- AThe jet from the lowest hole travels furthest because the pressure is greatest there.
- BThe jet from the highest hole travels furthest because the pressure is greatest there.
- CAll three jets travel the same distance because they are in the same tube.
- DThe jet from the middle hole travels furthest because the pressure is intermediate.
40.The pressure in a liquid depends on the shape of the container.
Easy
True or false?
41.What name is given to the upward force exerted by a fluid on a submerged object?
Easy
42.Complete the word equation defining pressure in liquids.
Easy
Pressure in a liquid is the ____ of the liquid × gravitational field strength × change in ____.
43.A skier of weight 750 N stands on skis with a total area of 0.4 m² in contact with the snow. Calculate the total pressure exerted by the skier on the snow.
Medium
44.A swimmer dives to the bottom of a swimming pool which is 2 m deep. The density of the water is 1000 kg/m³ and gravitational field strength is 10 N/kg. Calculate the pressure on the swimmer due to the water.
Medium
45.Complete the following sentences about atmospheric pressure using the words from the box: increases, height, decreases, less, more, colliding.
Medium
Atmospheric pressure varies with ____ above a surface. This is due to air molecules ____ with a surface creating atmospheric pressure. The number of air molecules above a surface ____ as the height of the surface above ground level increases. Therefore, as height increases, there is always ____ air above a surface than there is at a lower height.
46.Calculate the pressure exerted by water at a depth of 20 m in the Dead Sea. The density of the water is 1250 kg/m³ and gravitational field strength is 10 N/kg.
Medium
47.A pressure gauge at the bottom of the Dead Sea reads 5 000 000 Pa. Using a density of 1250 kg/m³ and gravitational field strength of 10 N/kg, estimate the depth of the Dead Sea.
Hard
48.Two containers of water are joined by a pipe at the bottom. The water level in container T is 0.5 m above the base. Calculate the pressure the water causes at the base of container T. Density of water = 1000 kg/m³, g = 10 N/kg.
Hard
49.A cylindrical container has a base of diameter 0.15 m and is filled with water to a depth of 0.35 m. The mass of the water is 6.2 kg. Calculate the weight of the water. Gravitational field strength = 10 N/kg.
Medium
50.Using the same cylinder (base diameter 0.15 m, water depth 0.35 m, water mass 6.2 kg), calculate the pressure due to the liquid on the base of the container. Assume g = 10 N/kg and density of water = 1000 kg/m³.
Hard
51.A bead of hollow glass floats 12 cm above the base of a cylinder filled with water to a depth of 35 cm. Calculate the total pressure on the bead. Atmospheric pressure = 1.01 × 10⁵ Pa, density of water = 1000 kg/m³, g = 10 N/kg.
Hard
52.Complete the sentence about floating and sinking.
Easy
An object will ____ if the upthrust on it is equal to its weight, and will ____ if the upthrust is less than its weight.
53.Explain how switching to narrower skis will affect the pressure which the skier exerts on the snow.
Hard
54.A student makes a small hole near the bottom of a plastic bottle filled with water. As the volume of water decreases, the jet of water travels a shorter distance. Explain this observation.
Hard
55.The actual depth of the Dead Sea is less than the value calculated from the pressure reading. What does this imply about the average density of the water compared to the surface density given?
Medium
56.Explain, in terms of pressure, why the water exerts upthrust on a submerged balloon.
Hard
57.When the taps are opened, water flows in the pipe for some time and then stops. Explain why the water starts to flow and then stops.
Hard
58.A skier of weight 750 N stands on skis with a total area of 0.4 m² in contact with the snow. Calculate the total pressure exerted by the skier on the snow.
Medium
- A1687 Pa
- B1875 Pa
- C2251 Pa
- D2063 Pa
59.A swimmer dives to the bottom of a swimming pool which is 2 m deep. The density of the water is 1000 kg/m³ and gravitational field strength is 10 N/kg. Calculate the pressure on the swimmer due to the water.
Medium
- A18000 Pa
- B24000 Pa
- C20000 Pa
- D22000 Pa
60.Calculate the pressure exerted by water at a depth of 20 m in the Dead Sea. The density of the water is 1250 kg/m³ and gravitational field strength is 10 N/kg.
Medium
- A300000 Pa
- B250000 Pa
- C275000 Pa
- D225000 Pa
61.A pressure gauge at the bottom of the Dead Sea reads 5 000 000 Pa. Using a density of 1250 kg/m³ and gravitational field strength of 10 N/kg, estimate the depth of the Dead Sea.
Hard
- A440 m
- B360 m
- C400 m
- D480 m
62.Two containers of water are joined by a pipe at the bottom. The water level in container T is 0.5 m above the base. Calculate the pressure the water causes at the base of container T. Density of water = 1000 kg/m³, g = 10 N/kg.
Hard
- A4500 Pa
- B6000 Pa
- C5000 Pa
- D5500 Pa
63.A cylindrical container has a base of diameter 0.15 m and is filled with water to a depth of 0.35 m. The mass of the water is 6.2 kg. Calculate the weight of the water. Gravitational field strength = 10 N/kg.
Medium
- A62 N
- B56 N
- C68 N
- D74 N
64.Using the same cylinder (base diameter 0.15 m, water depth 0.35 m, water mass 6.2 kg), calculate the pressure due to the liquid on the base of the container. Assume g = 10 N/kg and density of water = 1000 kg/m³.
Hard
- A3500 Pa
- B3150 Pa
- C3850 Pa
- D4200 Pa
65.A bead of hollow glass floats 12 cm above the base of a cylinder filled with water to a depth of 35 cm. Calculate the total pressure on the bead. Atmospheric pressure = 1.01 × 10⁵ Pa, density of water = 1000 kg/m³, g = 10 N/kg.
Hard
- A103300 Pa
- B92970 Pa
- C123960 Pa
- D113630 Pa

Thẻ ghi nhớ

What is a fluid?

A fluid is either a liquid or a gas.

Define pressure.

Pressure is the force per unit area, or the concentration of a force.

What is the equation for pressure at the surface of a fluid?

pressure = force normal to a surface / area of that surface (p = F / A).

What are the units of pressure?

Pascals (Pa).

In what direction does the force from fluid pressure act on a surface?

At 90° (at right angles) to the surface.

How does the pressure beneath the surface of a liquid change with depth?

The greater the depth, the greater the pressure.

How does the pressure beneath the surface of a liquid change with the density of the liquid?

The greater the density of the liquid, the greater the pressure.

What is the equation for the pressure due to a column of liquid?

p = h × ρ × g, where p is pressure, h is height of the column, ρ is density of the liquid, and g is gravitational field strength.

What is atmospheric pressure at sea level?

About 101 kPa (or 100 kPa).

Why does atmospheric pressure decrease as height above a surface increases?

Because the number of air molecules (and so the weight of air) above the surface decreases, so there is less air above the surface.

What causes atmospheric pressure?

Air molecules colliding with a surface, creating a force per unit area.

What is upthrust?

Upthrust is a force that pushes upwards on an object submerged in a fluid, opposite to the object's weight.

Why does upthrust occur?

Because the pressure on the bottom surface of a submerged object is greater than on the top surface, creating a resultant upward force.

What determines whether an object floats or sinks?

If the upthrust is equal to or greater than the object's weight, it floats; if upthrust is less than weight, it sinks. Also, if the object's density is less than the fluid's density, it floats; if greater, it sinks.

How does the pressure on an object immersed in a liquid compare with atmospheric pressure?

The object experiences pressure due to the liquid in addition to atmospheric pressure, so the total pressure is the sum of both.

Why does a drawing pin go into the surface rather than your finger?

The sharp point has a small area, creating a larger pressure that pushes it into the surface.

Why do tractors have large tyres?

To spread the weight over a large area, reducing the pressure and preventing them from sinking into mud.

Why are nails made with sharp points?

The small area concentrates the force, creating a large pressure that allows the nail to be hammered into a wall.

What is the relationship between pressure, force, and area?

Pressure is force per unit area. For a given force, a smaller area gives a larger pressure, and a larger area gives a smaller pressure.

How does the pressure in a liquid change with the height of the column of liquid above a point?

The pressure increases with the height of the column of liquid above that point.

Why does water pour out with more force from a hole at the bottom of a container than from a hole near the top?

Because pressure increases with depth, so the water at the bottom is under greater pressure.

What is the upthrust on an object equal to?

The weight of the fluid displaced by the object.

Why does an object appear to weigh less when immersed in a liquid?

Because the upthrust acts upwards, opposing the weight, so the apparent weight is reduced.

How does the density of a fluid affect the upthrust on a submerged object?

The denser the fluid, the greater the upthrust it exerts on the object.

What happens to atmospheric pressure as altitude increases?

Atmospheric pressure decreases as altitude increases.

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