All About Pressure in Fluids

1. All About Pressure in Fluids A Mr. Liu Production

2. Pressure Changes with Depth • You experience pressure exerted by fluids every day. Wind is moving air that can lift your hair or push against you. Water running out of a faucet can rince away bits of food from a plate. This type of pressure is called flow pressure, or pressure that causes motion because the fluid is moving. Fluid pressure can also exert a force on an object even if the fluid is not moving. This is known as static pressure.

3. Pressure Changes with Depth • The plumbing system in your home uses both types of pressure. When a faucet is turned off, the water under pressure in the pipes is an example of static pressure. As soon as you turn the faucet on, water flows out of the tap. This is an example of flow pressure.

4. All About Pressure in Fluids • Every time you lean against a wall, you are exerting pressure on the wall. Pressure is a measure of the force acting perpendicular to a unit. When you press your hand against a wall, you are applying pressure on that area of the wall. If the wall were made of whipped cream, your hand would push right through that whipped cream, leaving a hand shape that is the outline of the area over which the force was applied. If the force is increased, the pressure will increase.

5. A Formula for Pressure Force (F) F Pressure (P) = ----------- or P = ---- Area (A) A • Force is measured in newtons (N) and area is often measured in square metres (m2). The unit for pressure, therefore, is newtons per square metre (N/m2). This unit is also called a pascal (Pa), named after the French scientist Blaise Pascal (1623-1662) in honour of his pioneering work with pressure. A kilopascal (kPa) is equal to 1000 Pa).

6. A Formula for Pressure • Imagine a cubic aquarium that is 1 m X 1 m X 1 m. Suppose it is full of water and a pressure gauge (an instrument for measuring pressure) is attached to the bottom to the bottom of the aquarium. What pressure reading would the gauge show? The answer to this question would depend on two factors: the weight of the water, and the area of the base of the aquarium.

7. A Formula for Pressure • The density of water is 1 g/cm3, or 1000 kg/m3 (that is, a 1000 kg mass of water occupies a 1 m3 volume of water). If 1 m3 of gravity is approximately 10 N for every kilogram (9.8 N/kg), then one cubic metre of water would exert a force of approximately 1000 kg x 10 N/kg. This equals a weight of 10 000 N.

8. A Formula for Pressure • When the 10 000 N “cube” of water in the aquarium rests on a surface, its weight pushes down over a certain area. Determine the area of the base of the cubic aquarium: • Area = length x width • = l x w • = 1 m x 1 m • = 1 m2

9. A Formula for Pressure • If F = 10 000 N and A = 1 m2, then P = F A If F = 10 000 N and A = 1 m2, then P = 10 000 N 1 m 2 = 10 000 N/m2 = 10 000 PA = 10 kPa (kilopascals)

10. Pressure and the Particle Theory • The particle theory states that particles in solids, liquids, and gases are constantly moving. Particles move quickly if they have a great deal of energy. They move more slowly if they have less energy. When particles move, there is always a chance that they will bump into each other, like bumper cars. When a collision occurs, the particles move apart, leaving only empty space between them.

11. Pressure and the Particle Theory • Why do fluids, such as juice in a cup or air in a tire, appear to be at rest if all their particles are moving? Moving particles exert a force in the direction of their motion. Fluid particles are moving in all directions at all times. Thus, most of the forces cancel each other out, but some are not cancelled. These forces are exerted against the walls of the container, causing pressure. What happens if there is a crack in a cup or a hole in a tire? In which direction does the fluid flow?

12. A Formula for Pressure • Regardless of where the crack or hole is, the result is always the same: the fluid flows out. This indicates that the pressure of a fluid is exerted equally in all directions. As the particles in the inner walls of the container apply pressure on the fluid to stay inside the container, the particles of the fluid press against the container with an equal force.

13. Compressibility • The particles in a fluid push against each other until something more rigid, for example, the walls of their container, exerts a force in the opposite direction. What would happen if a fluid were completely enclosed and pressure were exerted on the walls of a flexible container?

14. Compressibility • According to the particle theory, the amount of empty space between particles depends on two factors: • 1. the physical state of the substance (whether the substance is a solid, liquid, or gas) • 2. the amount of energy that the particles have

15. Compressibility • In general, the amount of empty space between solid particles and between liquid particles is small, but the amount of empty between gas particles is huge.

16. Compressibility • An interesting property of gases, then is compressibility, the ability to be squeezed into a smaller volume. Gases are compressible because gas particles are extremely far apart. However, the particles remain far enough apart to behave like a gas, even if the gas is compressed.

17. Compressibility • Although there is empty space between the particles of solids and liquids, the spaces are already almost as small as possible. Thus, when a force is applied to a solid or liquid, the particles cannot move much closer together. Because solids and liquids cannot be squeezed into a smaller volume, they are said to be almost incompressible.

18. Compressibility • Instead of changing the volume of either the solid or the liquid, the applied force is transmitted (passed along), from one particle to the next, throughout the substance, somewhat like falling dominoes.

19. Under Pressure • Gases under pressure are ready to expand because the particles have so much energy. If gases under pressure find a way to escape from a container – for example, through a nozzle or a hole – they exit the container with a great deal of force. That force can be used in many applications to push or move objects. The compressibility of gases is useful for storing gases in a small volume (for example, in oxygen tanks).

20. Pressure Changes with Depth You experience pressure exerted by fluids every day. Wind is moving air that can lift your hair or push against you. Water running out of a faucet can rinse away bits of food from a plate. This type of pressure is called flow pressure, or pressure that causes motion because the fluid is moving. This is known as static pressure.

21. Pressure Changes with Depth The plumbing system in your home uses both types of pressure. When a water faucet is turned off, the water under pressure in the pipes is an example of static pressure. As soon as you turn the faucet on, water flows out of the tap. This is an example of flow pressure.

22. Pressure Changes with Depth • You can feel the effects of static pressure in a swimming pool. You may have noticed your ears begin to hurt if you swim deep underwater. This discomfort is caused by water pressure on your eardrums. The weight of all the water – and the air – above you pushes down on you and the water below.

23. Pressure Changes with Depth • Since gravity pulls everything toward the centre of the Earth, all particles have weight. As suggested by the particle theory, fluid particles exert their weight on the particles beneath them. Therefore, water pressure is greater the deeper you go underwater. The same is true for gases, such as air. Air pressure is greater at sea level than at higher altitudes, and it decreases as you rise in the atmosphere.

24. Pressure and Temperature • The particle theory suggests that particles move faster when they are heated because they gain more energy. • The particles of air inside a chilled balloon are moving slowly and are colliding infrequently with the particles that make up the inner walls of the balloon. • The particles of air inside this balloon are moving faster and are colliding frequently with the particles that make up the inner walls of the balloon.

25. Homework Questions 1. Define pressure. (2 marks) 2. What unit is used to measure pressure? (1 mark) 3. What is another way to express this unit? (1 mark) 4. Explain why fluid pressure varies with depth in a) liquids, and b) gases. (4 marks) 5. Why do you think airplane cabins are “pressurized”? If an airplane door were to open at a high altitude, in which direction would the air move – into or out of the plane? Why? (3 marks) 6. The atmosphere is a layer of gases that surrounds Earth and is approximately 1000 km high. Normal atmospheric pressure at sea level, at 25 degrees Celsius, is about 101 300 Pa. As you rise through the air, atmospheric pressure decreases steadily. Imagine that you are in a hot-air balloon, and you need to measure the air pressure regularly, from the time the balloon starts to rise off the ground. Without doing any calculations, what would you predict the reading to be when you reach the outermost limit of Earth’s atmosphere? Explain your reasoning. (4 marks)