Pressure Archives

Understanding Pressure Using Pascal’s Principle

December 18, 2020December 18, 2020 by Veerendra

Understanding Pressure Using Pascal’s Principle

A boy applies pressure on a tube of toothpaste. The pressure applied to the tube is transmitted throughout the toothpaste and forces it out of the opening of the tube.
Figure shows a boy holding a plastic bag with holes. When he squeezes the plastic bag, the water squirts from all the holes in all directions.
Figure shows an apparatus that consists of a glass barrel fitted to a plunger and ending with a bulb with holes of uniform size. This apparatus is fully filled with water. When the plunger is pushed in, water squirts equally from all the holes.
From above Figures, it is shown that
(a) when pressure is applied on a liquid, it is transmitted throughout the liquid.
(b) the pressure acts in all directions.
Pascal’s principle states that pressure applied to an enclosed fluid is transmitted uniformly to every part of the fluid and to the walls of the container of the fluid.
Figure shows a big and a small syringe connected by a rubber tube. The syringes and rubber tube are filled with water.
(a) A force, F₁ acting on the small syringe is balanced by a force, F₂ acting on the large syringe.
(b) According to Pascal’s principle, the pressure Fj, exerted by the small piston, on the water is equal to the pressure, P, exerted by the large piston on the water.
Pascal’s principle can be used as a force multiplier in a hydraulic system. Figure shows a small input force, F₁ on the small piston can result in a big output force, F₂ on the big piston. From the above formula, we get:

Applications of Pascal’s Principle

Figure shows a hydraulic jack lifting the back portion of a car.
(a) When the small piston is pulled up, valve B opens and valve A closes. Hydraulic oil is drawn from the reservoir into the space under the small piston.
(b) When the small piston is pushed down, valve A opens and valve B closes. Hydraulic oil is forced through valve A and raises the large piston.
(c) Continuous up-and-down movements of the small piston will cause the large piston to move up to lift the car.
(d) When the release valve is opened, the weight of the car will force the large piston downward, pushing the hydraulic oil back into the reservoir. The car will be lowered.
An automobile hydraulic brake system consists of a master cylinder attached to the brake pedal and various slaves cylinders near the wheels.
Figure shows the brake system of a car.
(a) When the brake pedal of a car is pressed, pressure is exerted on the brake fluid (oil) and is transmitted uniformly from the master cylinder, through the pipe, to the slave cylinders near the wheels.
(b) This will move the slave pistons forward, forcing the brake pads against the discs or drums attached to the wheels to slow down the car.
(c) However, it is important to note that this system works only because of the fact that the brake fluid is incompressible.
(d) If there is an air bubble in the system, then the pressure applied to the piston in the master cylinder will not be effectively transferred to the slave cylinders as the air bubble is compressible. This will affect the moving of the pistons in the slave cylinders and result in the car not being able to stop or slow down effectively.
A power shovel applies the Pascal’s principle in its operation. Figure shows a power shovel at work. It uses hydraulic cylinders to manipulate its boom and bucket to dig, lift or dump material.

Pascal’s Principle Example Problems with Solutions

Example 1. In the hydraulic system shown in Figure, an input force of 10 N is used to balance an output force, F₂.
Understanding Pressure Using Pascal’s Principle 6
Calculate the value of F₂.
Solution:

Example 2. Figure shows an activity to demonstrate the hydraulic system as a force multiplier. A small boy uses a force of 8 N to press the piston of the small syringe with a cross-sectional area of 1.6 cm². His elder brother presses the piston of the large syringe with a cross-sectional area of 64 cm².
Understanding Pressure Using Pascal’s Principle 8
What is the minimum force that the. elder brother needs to apply so that the piston of the large syringe will not be forced to move backward?
Solution:

Understanding Gas Pressure

December 18, 2020December 18, 2020 by Veerendra

Understanding Gas Pressure

Figure shows a boy pressing the front tyre of his bicycle.
(a) When he presses the tyre with his thumb, he feels an opposing force acting on his thumb.
(b) The force is due to the air pressure in the tyre.
(c) The air pressure is due to the collisions of air molecules in the tyre against the wall of the tyre.
Figure shows air molecules in an enclosed container. Air pressure can be explained by the kinetic theory.
(a) When an air molecule hits the wall of a container, it bounces back.
(b) The change of momentum per second gives the force exerted on the wall by the molecule.
(c) With a large number of molecules hitting the container wall, a large force is exerted on it.
(d) By using the formula for pressure, P = F/A, the force per unit area gives the pressure exerted by the air on the wall.

Instruments for Measuring Gas Pressure

Figure shows a U-tube manometer which can be used to measure gas pressure.
(a) The gas whose pressure is to be measured is connected directly to one side of the U-tube.
(b) The pressure of the gas, P is equal to the sum of atmospheric pressure and the pressure due to the difference in the height, h of the liquid in the manometer.
(c) The pressure of the gas P:
Where ρ is the density of the liquid in the manometer.
Figure shows a Bourdon gauge commonly used in school laboratories, air conditioner service shops, hospitals and factories.
(a) When a Bourdon gauge is attached to a gas cylinder, gas flows from the cylinder into the flattened curved tube in the gauge.
(b) The pressure of the gas causes the curved tube to straighten out.
(c) Through a lever and a gear system, the pointer rotates to measure the pressure of the gas. The scale may be calibrated in N m^-2 or Pa.

Example 1. Figure shows a U-tube manometer used to measure the pressure of gas X.
Gas Pressure 6
Determine the pressure of gas X in
(a) cm Hg,
(b) pascal.
[Density of mercury, ρ = 1.36 x 10⁴ kg m^-3; g = 9.8 N kg^-1; P_atm= 76 cm Hg]
Solution:
Gas Pressure 7

How Pressure is Related to Force and Area

December 18, 2020December 18, 2020 by Veerendra

What Do You Mean By Thrust And Pressure

Thrust

The force acting normally on surface is called ‘thrust’.
This is a vector quantity.
It is measured in newton (N).

Pressure

The thrust on an unit area of a surface is called ‘pressure’.
\(\text{Pressure}=\frac{\text{Thrust}}{\text{Area}}\text{ or P}=\frac{F}{A}\)
Unit: The SI unit of pressure is newton per meter square or N/m², other units of pressure are pascal and bar.
One Pascal: One pascal is defined as the pressure exerted on a surface area of 1m² by a thrust of 1 newton.
i.e. 1 Pascal = 1 N/m²

Some very important and useful devices like syringes, dropper, and drinking straw, work on the principle of pressure.

People also ask
Applications of Pressure in Daily Life

Some examples based on pressure

Inserting a pointed nail in a wooden block is an easier task than to insert a rod inside a wooden block with the same force because the nail has a smaller area and thus it will experience more pressure even with the same force.
A sharp knife cuts better than a blunt knife.
While walking, a man exerts more pressure on the ground in comparison to when he is standing.
Figure (a) shows a boy named Tarkan lying on a mattress. When he stands on the mattress as in Figure (b), he notices the mattress sinks deeper. The reason is that the pressure acting on the mattress when he is standing is greater than that when he is lying.

Activity

Aim: To observe the effect of pressure.
Materials needed: A sheaf (bundle) of paper and a sharpened pencil.
Method: Press the papers very hard with the butt end of the pencil. Now turn the pencil around and press very hard on the paper with the sharp end of the pencil.
Observation: You will find that if you press very hard, you may be able to make an impression on the paper with the pencil butt. However, with much less effort you could even make a hole in the paper with the sharp end.
Conclusion: The surface area of the pencil butt is larger than the surface area of the sharp end. Therefore, with a much smaller force a greater pressure is produced with the sharp end of the pencil.

Variation of Pressure with Area
Increasing the area over which a particular force acts decreases the pressure produced. The converse is also true decreasing the area over which a particular force acts increases the pressure produced. For example, the pointed end of a high-heeled shoe exerts a greater pressure than the flat end, as the force is acting over a smaller area at the pointed end.

Thrust and Pressure Example Problems with Solutions

Example 1. A force of 150 N is applied on an area of 1.5 m². Calculate the pressure exerted.
Solution: Force, F = 150 N; area, A = 1.5 m²
\( \text{Pressure}=\frac{\text{Force}\,}{\text{Area}} \)
\( \text{P}=\frac{\text{F}\,}{\text{A}}=\frac{\text{150N}\,}{\text{1}\text{.5}{{\text{m}}^{\text{2}}}}=100\text{ N/}{{\text{m}}^{\text{2}}} \)

Example 2. A force of 500 dynes is applied on an area of 20 cm². Calculate the pressure exerted.
Solution: Force, F = 500 dynes = 500 × 10^-5 newton
Area, A = 20 cm² = 20 × 10^-4 m²
\( \text{Pressure},\text{ P}=\frac{\text{F}\,}{\text{A}}=\frac{\text{500 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-5}}}\text{N}}{\text{20 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}{{\text{m}}^{\text{2}}}}=2.5\text{ N/}{{\text{m}}^{\text{2}}} \)

Example 3. If a force of 2 N is applied over an area of 2 cm², calculate the pressure produced.
Solution: To get the pressure in Pa, we have to make sure that the force is in newton and the area in m². Here, the area is in cm². To convert this into m², we have to divide the given area by 10,000.
How Pressure is Related to Force and Area 1

Example 4. Calculate the pressure if a force of 2 N is applied on an area of 2 mm².
Solution: Here, again the area is not in m². To change it into m², we divide the area by 1,000,000.
How Pressure is Related to Force and Area 2

In these examples, we took the same force and calculated the pressure over two different areas. The same force acting on a smaller area produces a greater pressure.

Example 5. Refer to Figure. The weight of Tarkan is 360 N. Calculate the pressure exerted by Tarkan on the mattress when
(a) he is lying down as in Figure (a) and the area of contact between Tarkan and the mattress is 0.24 m².
(b) he is standing as in Figure (b) and the area of contact between his soles and the mattress is 0.024 m².
Solution:

Example 6. Figure shows a fireman standing on a piece of plywood placed on the surface of a muddy ground. The muddy ground can withstand a maximum pressure of 1050 Pa without sinking.
pressure 3
If the fireman has a mass of 78 kg and by considering the mass of the plywood as negligible, calculate the minimum area of the plywood that can be used. [g = 9.8 N kg^-1]
Solution:

Example 7. Tarkan is digging a hole with a spade.
pressure 5
Explain why it is important that the edge of the spade must be sharp.
Solution:
When the edge of the spade is Figure. sharp, its surface area of contact with the ground is small. When a force is applied, a big pressure is resulted. This makes the digging easier.

Example 8. Tarkan’s sister, Daryah weighs 436 N. She has three pairs of shoes X, Y and Z.
pressure 6
(a) By referring to Figure, calculate the pressure, P exerted on the floor by Daryah for each pair of the shoes.
(b) Which pair of shoes is most suitable to be worn by Daryah if she intends to go to the beach? Explain your answer.
Solution:
pressure 7

Example 9. Figure shows the webbed feet of a duck.
pressure 8
Explain why besides helping in the paddling of water, the webbed feet of a duck also allow it to move around more easily on the muddy ground.
Solution:
The webbed feet provide a big surface area of contact between the feet of the duck and the ground. This reduces the pressure exerted on the ground. The legs will not sink too deeply into the muddy ground.

Applications of Pressure in Daily Life

December 18, 2020December 18, 2020 by Veerendra

Applications of Pressure in Daily Life

Some of the applications of pressure are given below.

The area of the edge of a knife’s blade is extremely small. This creates a pressure high enough for the blade to cut through a material.
Syringes are used to take blood for blood tests. The pressure of the liquid (blood) forces the liquid to move into the syringe when its plunger is withdrawn.
When air is sucked out of a drinking straw, the air pressure inside if decreases and the atmospheric pressure outside forces the liquid to go inside the straw.
Skis have a large area to reduce the pressure on the snow. This ensures that the skis do not sink into the snow too far.
The pressure under the studs on the soles of football shoes is high enough for them to sink into the ground, which gives extra grip.
A vacuum cleaner has a fan inside that creates a low pressure inside the device. Consequently, air and dirt particles are sucked into the device.

Applications of Pressure in Daily Life 1

What is Atmospheric Pressure

December 23, 2020December 18, 2020 by Veerendra

What is Atmospheric Pressure

Scientists discovered atmospheric pressure in the seventeenth century. This discovery uncovered an interesting fact that air actually has weight! The weight of the atmosphere presses down on the Earth’s surface and creates a pressure on it. The pressure at any point exerted by the weight of the air above it is called atmospheric pressure.

Atmospheric Pressure

The pressure due to the Earths atmosphere can be considered as the result of the weight of the air acting on per unit area of the Earth’s surface.
The atmospheric pressure is the pressure exerted by the atmosphere on the surface of the Earth as well as all objects on the Earth.
At sea level, the atmospheric pressure is about 1.013 x 10⁵ N m^-2. This value is usually referred to as 1 atmosphere.
Meteorologists express pressure in millibars. One millibar is 100 N m^-2 or 100 Pa. Hence, 1 atmosphere is about 1013 millibars.
The atmospheric pressure decreases slowly with altitude because the atmosphere becomes thinner at higher altitude. Figure illustrates the decreasing atmospheric pressure with altitude.

Variation of Atmospheric Pressure With Altitude

The altitude of a place is its height above sea level. The atmospheric pressure at a place depends on its altitude and decreases as we go up. We know that atmospheric pressure at a place is the force exerted by the weight of the air column above that place. As we go up, the length of the air column above us decreases. This means its weight decreases, and, therefore, the atmospheric pressure is smaller at higher places (than at sea level).

If the pressure of atmosphere is changed suddenly, the blood vessels in our body will burst due to the pressure of the blood and other fluids inside. This is why astronauts have to wear special pressurized suits—there is no air and, therefore, no air pressure in space.

Variation of Atmospheric Pressure With Altitude 1

Applications of Atmospheric Pressure

Figure shows a person drinking with the help of a straw.
(a) He sucks the air in the straw and creates a partial vacuum in it.
(b) The surrounding atmospheric pressure forces the drink into the straw and enters the mouth of the person.
Figure shows a worker carrying a piece of glass using a pair of rubber suction cups.
(a) When he presses the suction cups against the glass, air is forced out of the cups creating a partial vacuum in it.
(b) The surrounding atmospheric pressure forces the rubber cups tightly against the smooth surface of the glass.
Figure shows a vacuum cleaner in use.
(a) The rotating fan expels air, creating a partial vacuum in the space in front of it.
(b) The surrounding atmospheric pressure forces the air into the tube, carrying dust particles along with it.
(c) When the air passes through the filter, the dust particles are trapped by the filter so that the air expelled out of the vacuum cleaner is clean.

Instruments for Measuring Atmospheric Pressure

Figure shows a simple mercury barometer made by inverting a long glass tube filled with mercury.
(a) Due to the inversion, a vacuum is created at the base of the tube and a column of mercury is supported by the atmospheric pressure.
(b) The units for the measurement of atmospheric pressure can be in terms of centimetres of mercury (cm Hg) or pascal (Pa). Another unit of pressure is torr, where 1 torr is equal to 1 mm Hg.
(c) At sea level, the atmospheric pressure can support a column of mercury with a vertical height, h of 76 cm. Hence the atmospheric pressure, P_atmcan be calculated as:
where, ρ is the density of mercury.
Figure shows a Fortin barometer which is essentially modified from a simple mercury barometer.
(a) The Fortin barometer has a metal scale with a vernier attached and a mirror behind the top of the mercury column to avoid parallax error when taking readings.
(b) With these features, the Fortin barometer measures the atmospheric pressure more accurately than the simple mercury barometer.
Figure shows an aneroid barometer. An aneroid barometer is a more convenient form of barometer because it does not use liquid and can be as small as a wristwatch.
(a) Inside an aneroid barometer there is a partially evacuated metal case made of thin and flexible alloy.
(b) A change of atmospheric pressure will cause the centre of the metal case to move in or out. This movement is magnified by a system of levers.
(c) A chain attached to the last lever rotates the pointer to show the atmospheric pressure measured.

Example 1. A mercury barometer in a physics laboratory shows a 732 mm vertical column of mercury.
What is Atmospheric Pressure 8
Based on this reading, calculate the atmospheric pressure in the laboratory in pascal.
[Density of mercury, ρ = 1.36 x 10⁴ kg m^-3; g = 9.8 N kg^-1]
Solution:
What is Atmospheric Pressure 9

Activity 1

Aim: To show the presence of atmospheric pressure.
Materials needed: A glass tumbler (with a smooth edge at the mouth, and without a rim), a piece of stiff cardboard (a little bigger than the mouth of the tumbler), and water. (It would be convenient to perform this activity over a wash basin or the kitchen sink.).
Method:

What is Atmospheric Pressure 1

Fill the tumbler with water to the brim.
Cover the tumbler with the cardboard piece (figure A).
Place the palm of your hand over the piece of cardboard, and quickly invert the tumbler (figure B).
Slowly remove your hand supporting the piece of cardboard (Figure C).

Observation: You will observe that the cardboard piece will not fall.
Conclusion: Atmospheric pressure provides enough force to support a full glass of water.

Activity 2

Aim: To study atmospheric pressure using rubber suckers.
Materials needed: Rubber suckers.
Method: Take a rubber sucker and press it firmly to a smooth surface like a kitchen tile or a plain glass window. Try to pull it out.

Observation: You will see that it is really difficult to pull the rubber sucker off the smooth surface.
Conclusion: By pushing the rubber sucker against the smooth surface, you have created a partial vacuum, and the pressure of the air pressing on the outer surface of the sucker holds it in place.

Extension: Take a smooth stainless steel or ceramic plate and stick the rubber sucker on it. You can now hold the plate at any angle (horizontal, vertical, upside down, etc.) and try to pull the rubber sucker off the plate. You will find that the rubber sucker remains stuck to the plate regardless of the angle at which you hold the plate. This shows that air exerts pressure in all directions.