Pressure Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Pressure.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Pressure is the amount of force acting on each unit of area.

Pressure is how concentrated a force is. The same force on a smaller area creates more pressure.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Pressure asks how mass, volume, pressure, and displacement determine the fluid interaction.

Common stuck point: Students often know a formula related to pressure but skip the recognition step: Am I reasoning about a fluid or object in a fluid, with volume, area, depth, density, or displaced fluid identified? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I reasoning about a fluid or object in a fluid, with volume, area, depth, density, or displaced fluid identified?

Worked Examples

Example 1

medium

A hydraulic lift has input piston area

0.02 \text{ m}^2

and output piston area

0.4 \text{ m}^2

. To lift a car of weight

8000 \text{ N}

, what input force is required?

Answer

F_{1} = 400 N

First step

Pressure is transmitted equally (Pascal's principle):

F_1/A_1 = F_2/A_2

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Example 2

medium

A U-tube contains water and a less dense oil (

\rho_o = 800

). The oil column is

0.10 \text{ m}

tall. Find the height of the water column on the other side so the bottom pressures match. (

\rho_w = 1000

)

Example 3

medium

A scuba diver descends from

5 \text{ m}

25 \text{ m}

in fresh water. By how much does the gauge pressure increase? (

\rho = 1000

g = 10

)

Example 4

medium

A mercury barometer reads

0.74 \text{ m}

. What is the atmospheric pressure? Use

\rho_{Hg} = 13600 \text{ kg/m}^3

g = 9.8 \text{ m/s}^2

Example 5

hard

A cubic block of side

0.2 \text{ m}

is fully submerged with its top face

0.5 \text{ m}

below the water surface (

\rho = 1000

g = 10

). Compute the downward pressure force on its top face and the upward force on its bottom face. Verify the difference equals the buoyant force.

Example 6

hard

An open container of water sits in an elevator that accelerates upward at

a = 2 \text{ m/s}^2

. Find the pressure at depth

h = 0.5 \text{ m}

. Use

\rho = 1000

g = 10

Example 7

hard

A sealed container of fluid has gauge pressure

40 \text{ kPa}

at its top. Find the absolute pressure at depth

2 \text{ m}

in water below this gas layer. (

P_{atm}=100 \text{ kPa}

\rho=1000

g=10

)

Example 8

hard

In a U-tube manometer one side connects to a gas at pressure

P_g

and the other side is open. The mercury column on the open side is

0.05 \text{ m}

higher than on the gas side. Atmospheric pressure is

100 \text{ kPa}

. Find

P_g

. (

\rho_{Hg}=13600

g=9.8

)

Example 9

challenge

A cylinder of cross-section

A = 0.01 \text{ m}^2

contains air at

P_0 = 100 \text{ kPa}

trapped by a massless frictionless piston open above. Water is poured on top until

0.5 \text{ m}

of water sits on the piston. Treating air as isothermal, find the new air pressure. (

\rho=1000

g=10

)

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A force of

200 \text{ N}

acts on an area of

0.5 \text{ m}^2

. Find the pressure.

Example 2

easy

Find the pressure

2 \text{ m}

deep in water (

\rho = 1000 \text{ kg/m}^3

g = 10 \text{ m/s}^2

Example 3

easy

A pressure of

5000 \text{ Pa}

acts over

0.2 \text{ m}^2

. Find the force.

Example 4

easy

A box weighing

300 \text{ N}

sits on a base of

0.6 \text{ m}^2

. Find the pressure on the floor.

Example 5

easy

Why do snowshoes stop you sinking into snow? Answer in one principle.

Example 6

easy

Pressure increases by

\rho g h

. At what depth in water is

\Delta P = 50000 \text{ Pa}

? (

\rho=1000

g=10

)

Example 7

easy

Atmospheric pressure is about

100000 \text{ Pa}

. What force does it exert on a window of

2 \text{ m}^2

Example 8

easy

Mercury has density

13600 \text{ kg/m}^3

. Find pressure

0.76 \text{ m}

deep (

g=9.8

Example 9

medium

A hydraulic press has a small piston of area

0.01 \text{ m}^2

and large piston

0.5 \text{ m}^2

. A

20 \text{ N}

force pushes the small piston. Find the output force.

Example 10

medium

Find the total (absolute) pressure

3 \text{ m}

deep in water if atmospheric pressure is

100000 \text{ Pa}

. (

\rho=1000

g=10

)

Example 11

medium

A dam wall is

10 \text{ m}

tall and water fills to the top. Find the pressure at the base. (

\rho=1000

g=10

)

Example 12

medium

A nail tip has area

1 \times 10^{-6} \text{ m}^2

. A hammer delivers

50 \text{ N}

. Find the pressure at the tip.

Example 13

medium

Two connected tubes hold water. The left tube has a

40 \text{ N}

load on a

0.02 \text{ m}^2

piston. What pressure must the right tube provide to balance it?

Example 14

medium

A diver descends from

5 \text{ m}

25 \text{ m}

in water. By how much does the gauge pressure increase? (

\rho=1000

g=10

)

Example 15

medium

A flat roof of area

30 \text{ m}^2

has air pushing up at

99000 \text{ Pa}

below and

100000 \text{ Pa}

above. Find the net downward force.

Example 16

medium

Convert atmospheric pressure

101325 \text{ Pa}

into an equivalent water-column height. (

\rho=1000

g=9.8

)

Example 17

medium

A water tank is

4 \text{ m}

deep. Find the pressure halfway down (at

2 \text{ m}

) versus at the bottom. (

\rho=1000

g=10

)

Example 18

challenge

A U-tube holds water on one side and oil (

\rho=800

) on the other. The oil column is

0.10 \text{ m}

tall above the interface. Find the height of water on the other side that balances it. (

\rho_w=1000

)

Example 19

challenge

A cube of side

0.2 \text{ m}

is submerged with its top at depth

1 \text{ m}

in water. Find the difference between the force on its bottom face and top face. (

\rho=1000

g=10

)

Example 20

challenge

A sealed tank of gas at

150000 \text{ Pa}

has a circular safety valve of radius

0.05 \text{ m}

held by a spring. Outside pressure is

100000 \text{ Pa}

. Find the net outward force on the valve.

Example 21

easy

A force of

150 \text{ N}

acts uniformly on an area of

0.3 \text{ m}^2

. Find the pressure.

Example 22

easy

A pressure of

2000 \text{ Pa}

acts over an area of

0.15 \text{ m}^2

. Find the force.

Example 23

easy

What is the pressure at a depth of

4 \text{ m}

in fresh water? Use

\rho = 1000 \text{ kg/m}^3

and

g = 10 \text{ m/s}^2

Example 24

easy

A flat brick of weight

24 \text{ N}

rests on its

0.08 \text{ m}^2

face. Find the pressure on the floor.

Example 25

easy

A swimmer is at depth

5 \text{ m}

in seawater (

\rho = 1025 \text{ kg/m}^3

g = 10

). Find the gauge pressure.

Example 26

easy

At what depth in fresh water is the gauge pressure

25 \text{ kPa}

? (

\rho=1000

g=10

)

Example 27

medium

A column of oil (

\rho = 850 \text{ kg/m}^3

) is

3 \text{ m}

tall. Find the gauge pressure at its base (

g = 10

Example 28

medium

80 \text{ kg}

person stands on one foot of contact area

0.015 \text{ m}^2

. Find the pressure on the floor (

g = 10

Example 29

medium

A submarine porthole has area

0.2 \text{ m}^2

at depth

100 \text{ m}

in seawater (

\rho = 1025

g = 10

). Find the net inward force from gauge pressure.

Example 30

medium

A vertical rectangular tank wall is

2 \text{ m}

wide and

3 \text{ m}

tall, fully filled with water. Find the average pressure on the wall and the total force on it. (

\rho = 1000

g = 10

)

Example 31

medium

At sea level a tire is inflated to

200 \text{ kPa}

gauge pressure. Find its absolute pressure (use

P_{atm}=100 \text{ kPa}

Example 32

hard

A vertical

4 \text{ m}

tall,

1.5 \text{ m}

wide dam wall holds back water to the top. Find the total hydrostatic force on it. (

\rho = 1000

g = 10

)

Example 33

hard

A hydraulic press has small-piston area

A_1 = 0.005 \text{ m}^2

and large-piston area

A_2 = 0.25 \text{ m}^2

. The small piston is pushed down

0.20 \text{ m}

. By how much does the large piston rise?

Example 34

hard

A vertical pipe of cross-section

0.001 \text{ m}^2

is open at the top and connected at the bottom to a sealed tank. The water in the pipe stands

12 \text{ m}

above the tank fluid surface. What is the gauge pressure of the gas in the tank? (

\rho = 1000

g = 10

)

Example 35

hard

A flat

0.5 \text{ m}^2

window is at the side of a tank, with its top edge

1 \text{ m}

below the water surface and its bottom edge

1.5 \text{ m}

below. Find the hydrostatic force on it. (

\rho=1000

g=10

)

Example 36

challenge

A vertical tube of cross-section

A = 5 \times 10^{-5} \text{ m}^2

holds a column of water

h

tall, supported only by atmospheric pressure from below (closed top, vacuum above water). Find the maximum

h

before water column breaks at standard conditions. (

P_{atm}=100 \text{ kPa}

\rho=1000

g=10

)

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Related Concepts

Force Density Buoyancy Archimedes' Principle

Background Knowledge

These ideas may be useful before you work through the harder examples.

forcemass density