Keywords

• aerofoil
• atmosphere
• density .
• floating.
• Fluids pressure
• Principles
• Sinking submerging
• Pressure in Solids and Fluids

By the end of this chapter, you will be able to:

• Understand that pressure is a result of a force applied on an area.
• Understand the effect of depth on the pressure in a fluid and the implication of this.
• Understand the nature of the atmosphere and how atmospheric pressure is measured.
• Know the structure of the atmosphere and the significance of the different layers.
• Understand the use of the Bernoulli Effect in devices like aero foils and Bunsen burner jets.
• Understand the concept of sinking and flotation in terms of forces acting on a body submerged in a fluid
• Understand and apply Archimedes ‘ principle in different situations.

 INTRODUCTION

Have you ever wondered why it is easy to prick with a sharp pointed pin compared to a blunt one? Or why it is better to walk on muddy ground with a flat shoe than high heeled shoe?

To understand these and others, we need the concept of pressure in this chapter, you will be able to explain pressure in solids and fluids, and identify their applications in everyday life.

Pressure in solids

• Pressure of solids occurs only due to the weight of the solid

Activity 3.1 demonstrating the relationship between pressure in solids and area of cross – section

What you need

• High – heeled shoe, flat shoe, a small basin (where one – foot fits) containing sand.

Figure 3.1: A high – heeled shoe and a flat shoe

What to do

 (a) Choose one learner to put on the high – heeled shoe and stand in the basin containing sand.

 (b) Repeat the demonstration with the same learner by having him / her wear a flat shoe and see how deep the shoe goes inside the sand.

1. Compare the two cases, and state what shoe type goes deeper into the sand.
2. Explain why one shoe goes deeper into the sand than the other.
3. Discuss in groups any other situation in daily life with other where a similar thing occurs and thereafter share groups.

Exercise 3. 1.

1. Why does a hippopotamus walk in mud more easily than a goat?
2. Annette applies a force of 26.BN normal to her book using a pen of area 2mm. Calculate the pressure on the book.
3. Bobby has a mass of 69.3kg and while skating, he uses a shoe that has an area of 105.0cm² in contact with the ground. Calculate the average pressure that he exerted on the road while skating.

Assessment 3.1

 The figure below is of a cuboid of dimensions 15cm x 15cm x 10cm

From the cuboid,

(a) Calculate areas of  A₁, A₂ and A₃

(b) Calculate the pressure exerted on each surface assuming that a force of 100N acts on each surface.  

(c)Calculate which surface exerts minimum and maximum pressure?

(d)Make a general comment basing on the values of pressure obtained on each surface depending on the size of the area.

Exercise 3.2

(a) While in groups, discuss and explain using pressure concepts why:

1. Farm tractors have large rear wheels with wide tyres.
2. Dam walls are built so that they are increasingly thick from top to bottom.
3. Rivers flow faster at a narrow section than at a wide section though the volume does not change.

Report your findings and give a presentation using PowerPoint to the whole class.

Pressure in fluids

• Pressure of liquid occurs due to both weight and movement of the liquid molecules.

 Activity 3.2. Demonstrating pressure in fluids using water

Key Question: How can you demonstrate that pressure increases with depth?

What you need

• A tall can
• Nails
• A hammer
• Water
• Apparatus set – up

 Figure 3.3 a car that shows that pressure increases with depth

What to do

(a) Punch three (3) holes along a vertical line on the side of the container at about 10cm intervals as shown in Figure 3.3.

 (b) Fill the container with water (maintain the level).

(c)  Measure the distance from the container that the water squirts out of each hole.

 (d) Plot a graph of depth (distance of hole from top of water level) against distance.

(e) Use the graph to state the relationship between the depth and distance from the base of the can to where the water falls.

 f) How do your observations relate to pressure in reference to whole distance?

 (g) Present your information in groups.

We can thoroughly experience the fluid pressure in the following ways:

• If you dive down to the bottom of a deep swimming pool, you can feel the water pressure pressing on you from all sides. For this reason, deep – sea divers must wear a reinforced diving suit if they are to work safely at great depths.
• Sometimes water from taps at home may come out slowly it the water supply tank is not much higher than the tap?
• Dam walls are thicker at the bottom than they are at the top because there is high pressure at high depth.
• Hydraulic jacks work on the principle of pressure in fluids and can be used to lift cars or crush objects.

Pressure at the same point.

Activity 3.3 Investigating liquid pressure at the same depth

 Key Question: What happens to the pressure at the same depth in a liquid?

 What you need

• A tall can, nails, water, a hammer.

What to do

 (a) Make 4 holes at different points but at the same level on the tall can.

(b) Pour water into the can and maintain the water level.

(c)What do you observe with the water flowing out of the holes?

 (d) What conclusion can you draw?

Note that in Activity 3.3, the same amount of liquid exists above the holes, since the holes are at the same level. Therefore, the weight of the liquid above the holes will be the same. This means that the force that the liquid exerts on all the holes will be the same. Since the holes have the same cross – sectional area (i.e. .; they were made using the same nail) the pressure of the liquid coming out of the holes will be same.

 Activity 3.4 Investigating how pressure varies with density of fluid

 Key Question: How does pressure in fluids vary with the density of the fluid?

What you need

• U – Shaped open tube, two liquids which do not mix

What to do.

1. Hold the U – tube vertically on a horizontal table with the do open – ends upwards
2. Pour one fluid into the tube until it is 1/4 full
3. Pour the other liquid on top of the first liquid through one of the open limbs.
4. What do you observe? Are the liquids in the two limbs of the U – tube at the same level?
5. What conclusion can you draw?

DID YOU KNOW that the pressure , P , in a liquid can be calculated using the expression P = phg , where p is density of liquid , h is depth below liquid surface and g is acceleration due to gravity .

Example 3.1

Transmission of fluid pressure

 Fluid pressure is a measurement of the force per unit area on an object in the fluid. This pressure can be caused by gravity, or by forces outside a closed container.

Since a fluid has no definite shape, its pressure applies in all directions equally. Fluid pressure can also be amplified through hydraulic mechanisms and changes in the velocity of the fluid.

According to Pascal’s law, any force applied to a confined fluid is transmitted uniformly in all directions throughout the fluid regardless of the shape of the container.

3.1 Applications of Pascal’s Principle and Hydraulic Systems

 Hydraulic systems are used to operate automotive brakes, hydraulic jacks, and numerous other mechanical systems.

 How does it work?

A hydraulic system with two fluids – filled cylinders, capped with pistons connected by a tube called a hydraulic line.

A downward force F₁, on the left piston creates a pressure that is transmitted undiminished to all parts of the enclosed fluid.

This results in an upward force F, on the right piston that is larger than F₂, because the right piston has a larger surface area, as shown in Figure 3.4.

Figure 3.4: Hydraulic system

We can derive a relationship between the forces in this simple hydraulic system by applying Pascal’s principle. Note first that the two pistons in the system are at the same height, so there is no difference in pressure due to a difference in depth.

The pressure

According to Pascal’s principle, this pressure is transmitted undiminished throughout the fluid and to all walls of the container. Thus, a pressure P₂ is felt at the other piston of Area A_Z, that is equal to P₁, That is, P₁= P₂

This equation relates the ratios of force to area in any hydraulic system, provided that the pistons are at the same vertical height and that friction in the system is negligible

Hydraulic systems can increase or decrease the force applied to them.

Example

 The piston of a hydraulic device has a cross – sectional area of 30cm², moving an incompressible liquid with a force of 60N. The other end of the hydraulic pipe is attached to a 2^nd piston with a 60cm² cross sectional area. Determine the force on the second piston.

HYDRAULIC JACK

A hydraulic jack is used to lift heavy loads, such as the ones used by auto mechanics to raise an automobile. It consists of an incompressible fluid in a U – tube fitted with a movable piston on each side. One side of the U – tube is narrower than the other. A small force applied over a small area can balance a much larger force on the other side over a larger area, as shown in Figure 3.5.

Figure 3.5: Hydraulic jack

 In the figures presented above:

(a) A hydraulic jack operates by applying forces ( F₁,  F₂. ) to an incompressible fluid in a U – tube , using a movable piston ( A₁ , A₂ ) on each side of t tube .

(b) Hydraulic jacks are commonly used by car mechanics to lift vehicles so that repairs and maintenance can be performed.

From Pascal’s principle, it can be shown that the force needed to lift the car is less than the weight of the car:

3.2 Atmospheric Pressure

The air around you has weight, and it presses against everything it touches. That pressure is called atmospheric pressure, or air pressure.

Research 3.1

 In groups, using the internet and other textbooks, explain:

 (a) How the atmosphere is experienced and varies in regard to altitude.

(b) The standard atmospheric pressure at normal sea level.

 (c) Why mountain climbers use bottled oxygen while climbing?

(d) The instrument used to measure atmosphere.

Activity 3.5 Comparing densities of different liquids using Hare’s method

What you need

 Hare’s apparatus (consisting of 2 beakers, limbs of tube, and liquids of different densities) and a metre rule.

 What to do

In groups:

1. Using the materials mentioned, construct a simple Hare’s apparatus, as shown in Figure 3.6.
2. Dip the two limbs / tubes of your apparatus in different liquids (like oil and water), as shown in Figure 3.6.
3. By use of either your mouth or syringe, suck air out of the limbs at point P until liquids have risen to suitable heights.
4. When you are done sucking, close the clip at point P and measure the heights reached by each of the liquid.
5. In each case, determine the resultant pressure and then compare the two and come up with an expression that relates the two heights reached by the two liquids.
6. Use the expression obtained in (e) above to compare the densities of the two liquids.
7. Basing on your deductions, which of the liquid investigated (g) is denser?
8. Using the same concept, explain why the pressure at a depth of about 10m in the sea is higher than at the surface.

Figure 3.6: Hare’s apparatus

Activity 3.6 Explaining particles theory using hot water

What you need

• Hot water, an empty plastic bottle having a cap.

 What to do

 In groups,

(a) Pour hot water in an empty bottle and cover it.

(b) While observing, use particle theory to explain what happens when a small amount of hot water is poured into an empty plastic bottle and the cap placed tightly.

 (c) Report your findings on posters (using Manila paper and markers) and finally discuss your findings with the whole class or with your group members.

Exercise 3.3

1. Convert 760mmHg to pascals.
2. “The base of the dam walls must be more strongly reinforced than the top “. Justify the validity of this statement.
3. When you swim under water, the pressure of the water gets greater on your body the deeper you get. Explain: “Why you are not crushed by all this weight?”

 Assessment 3.2

 In groups, carry out research and compare the value of atmospheric pressure at the top of Mount Rwenzori and that at the bottom. Discuss in class and give reasons why there is a big difference in the two values.

Activity 3.7 Investigating how to measure pressure

What you need

• Straws, syringes, siphons and plastic bottles.

What to do

 While in groups.

(a) Carry out investigations using the items provided and find out how these materials can be used to measure pressure.

(b) Explain how atmospheric pressure is measured using a barometer and explain why atmospheric pressure varies daily.

(c)Explain how atmospheric pressure is applied when using drinking straws, a syringe, a siphon and pumps

(d) Basing on the knowledge and skills you have attained from this chapter, explain why a space is left when bottling liquids and why you think soda bottles do not have flat bottoms.

(e) Discuss how altitude affects atmospheric pressure and impact on our breathing, the weather and the climate,

 LAYERS OF THE ATMOSPHERE.

We can now have a brief description of each of these layers.

 Troposphere

• This is the lowest layer of our atmosphere. Starting at ground level, it extends upwards to about 10km above sea level.
• We humans live in the troposphere, and nearly all weather occurs in this lowest layer. Most clouds appear here, mainly because 99 % of the water vapor in the atmosphere is found in the troposphere.
• Air pressure drops, and temperatures get colder, as you climb higher in the troposphere.

Stratosphere

• The stratosphere extends from the top of the troposphere to about 50km above the ground.
• The infamous ozone layer is found within the stratosphere. Ozone molecules in this layer absorb high – energy ultraviolet (UV) light from the sun, converting the UV energy into heat.
• Unlike the troposphere, the stratosphere gets warmer the higher you go! That trend of rising temperatures with altitude means that air in the stratosphere lacks the turbulence and updrafts of the troposphere beneath.
• Commercial passenger jets fly in the lower stratosphere, partly because this less – turbulent layer provides a smoother ride. The jet stream flows near the border between the troposphere and the stratosphere.

Mesosphere

• Above the stratosphere is the mesosphere. It extends upwards to a height of about 85km (53 miles) above our planet.
• Most meteors burn up in the mesosphere. Unlike the stratosphere, temperatures once again grow colder as you rise through the mesosphere.
• The coldest temperatures in the earth’s atmosphere, about -90 C, are found near the top of this layer.
• The air in the mesosphere is far too thin to breathe. Air pressure at the bottom of the layer is well below 1 % of the pressure at sea level and continues dropping as you go higher.

Thermosphere  

• The layer of very rare air above the mesosphere is called the thermosphere.
• High – energy X – rays and UV radiation from the sun are absorbed in the thermosphere, raising its temperature to hundreds or at times thousands of degrees
• However, the air in this layer is so thin that it would feel freezing cold to us! In many ways, the thermosphere is more like outer space than a part of the atmosphere. Many satellites orbit the earth within the thermosphere!
• Variations in the amount of energy coming from the sun exert a powerful influence on both the height of the top of this layer and the temperature within it.

Exosphere.

• Although some experts consider the thermosphere to be the uppermost layer of our atmosphere, others consider the exosphere to be the actual “final frontier “of the earth – s gaseous envelope.
• As you might imagine, the “air ” in the exosphere is very , very , very thin , making this layer even more space – like than the thermosphere . In fact, air in the exosphere is constantly though very gradually, “leaking out of the earth’s atmosphere into outer space.
• There is no clear – cut upper boundary where the exosphere finally fades away into space.

Ionosphere

• This is not a distinct layer like the others mentioned above. Instead , the ionosphere is a series of regions in parts of the mesosphere and thermosphere where high – energy radiation from the sun has knocked electrons loose from their parent atoms and molecules .
• The electrically charged atoms and molecules that are formed in this way are called ions , giving the ionosphere its name and endowing this region with some special properties .

EFFECT OF LAYERS OF ATMOSPHERE ON WEATHER AND CLIMATE

Weather can also be affected by the very height differences within the troposphere and other levels of the atmosphere as well . As you move up the troposphere, temperature decreases which also results in changing air pressure and wind currents

 As a result, the weather and climate of that particular place is affected.

BERNOULLI’S EFFECT.

 Figure 3.8 An aeroplane flying

• Bernoull’s effect is the decrease in pressure of a fluid as its velocity increases. And Bernoull’s principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure.
• This principle is applied to lift aeroplanes as illustrated below. The velocity of the air above the aeroplane is higher than that below it because of the shape of the aeroplane. Thus, the pressure above the aeroplane is lower than that below it. A resultant upward force therefore exists, which lifts the aeroplane, as illustrated below

Research 3.2

In groups,

1. State Bernoulli’s effect and explain how it is applied also in Bunsen burner jets.
2. Why do you think it feels very comfortable when airplanes fly in regions where air flows in streamline?
3. Explain why cars feel light when moving at high speed.

 Activity 3.8: Demonstrating Bernoulli’s effect

Key Question: Explain how you can demonstrate Bernoulli’s effect.

What you need

• Two pieces of paper.

What to do

1. Hold the two papers hanging downwards as seen in the diagram below.
2. Blow air between the papers as seen in the figure.

Questions

1. In groups, write down what you have observed.

2. Explain the impact of blowing air between the papers and that outside the papers.

3. Share with other groups and discuss the reasons for the observation.

4. Make research on the internet and find out the machines that operate upon this principal.

Why is it necessary to measure the rate of flow?

• In various industrial processes, it is crucial to measure the rate of fluid flow accurately within a system as a whole or in part. This applies equally to gases and liquids which are an integral part of the process, or to compressed air, water or steam, which is essential to plant operation.
• Flow describes a wide range of fluid movement, such as blowing through the air, flowing through a pipe, or running along a surface. The flow of a fluid is classified in a variety of different ways, based upon the various properties of the flow.
• A flowmeter is used to measure the rate of fluid or energy flow to allow the process to be controlled and so ensure that the product is of the appropriate quality.

Research 3.3

 In groups,

(a) Basing on the knowledge and skills attained from previous concepts studied so far, carry out a research about the applications of pressure in irrigation, water supply and other fields

(b) Communicate your findings to the rest of class members.

 SINKING AND FLOATING

Why do you think it is easier to lift a jerrycan of water from a pond than on the surface?

Activity 3.9 Experimenting forces on a floating object

What you need

• A basin filled with water, a feather .

What to do

1. Put a feather on top of water. What do you observe?

 2. Explain your observation in (1) above

3. Also, explain what would happen if the mass of the feather is increased.

 4. Basing on your observations, explain why objects weigh less water than in air and relate your findings to the density of the body.

An object floats when the weight of the object is balanced by the upward push of the water on the object. The upward push of the water increases with the volume of the object that is under water, it is not affected by the depth of the water or the amount of water.

 If the weight of the object is greater than the upward push of the water on the object, then the object will sink. If the reverse is true, then the object will float.

Different objects float at different levels in the water because as most regular objects are lowered into the surface of water, the upward push of the water steadily increases until it is in balance with the weight of the object, and the object then continues floating at this level with the two forces in balance.

 Many objects that are hollow (and so generally contain air) float because the hollow sections increase the volume of the object (and so the upward push) for very little increase in weight force down. However, it is not necessary for an object to contain air in order to float.

No object can float without some part of it being below the surface of water.

Activity 3.10 Demonstrating sinking and floating

Key Question: Explain how you can demonstrate sinking and floating using locally available materials.

What you need

• Two oranges (one peeled), transparent glass, water.

What to do

 In pairs:

1. Fill the glass to about three quarters with water.
2. Drop the peeled orange in the glass.
3. Drop also the unpeeled orange and observe

 Question

 Why do you think the unpeeled orange floats and the peeled one sinks?

 Note: Two glasses should be used for peeled and unpeeled oranges respectively, and then a comparison is made.

Figure 3.9: An orange floating on water

Activity 3.11 demonstrating more other floating materials

 Key Question: Describe how you can demonstrate sinking and floating using locally available materials.

What you need

Basin, water, pumped balls, metallic bearings, feather.

What to do

In pairs,

(a) Fill the basin with water.

(b) Drop the balloon, bearings, feather and ball in the basin.

Questions

1. Basing on the observations, does floating depend on the size of the material?
2. What do you think are the factors upon which floating and sinking depend?
3. Carry out research using the internet in groups and find out machines that are designed upon the principle of floating of sinking.

Assignment 3.3:

 In groups, using the above activities, the internet and other text books

(a) Explain comprehensively the forces that act on a floating body.

b) Explain what happens if the mass of the floating body

1. Increased
2. decreased

c) Explain the operation of a submarine.

ARCHIMEDES ‘ PRINCIPLE AND LAW OF FLOATATION

 Activity 3.12 Demonstrating Archimedes ‘ principle

Key Question: Describe a laboratory experiment you can perform to demonstrate Archimedes ‘ principle

 What you need

• Measuring cylinder, stone tied on the string, spring balance.

Figure 3.1 Demonstrating Archimedes principle

What to do

 Procedure

1. in pairs,

1. Fill the measuring cylinder with water more than half way.
2. Measure and record the initial volume, V₀. , of the water .
3. Measure and record the weight of the stone in air using a spring balance.
4. Gently insert the stone inside the measuring cylinder.
5. Read and record the new volume, V₁, of the water.

 Questions

1. Explain why volume V₀ is less than V₁
2. What is the significance of the value obtained from (V₁ – V₀? If the density of water is 1000kgm “, calculate the weight of the water displaced by the stone.
3. What is the relationship between the volume of the displaced water and that of the stone?
4. Explain your major conclusion from this activity in relation to upthrust force, weight of displaced water, and weight of the stone.

When a body is submerged into a liquid, it either sinks or floats on that liquid depending on the density of that liquid. However, there is always a force (normally upward force) that acts on that body. This force is explained by Archimedes ‘ principle.

Archimedes ‘ principal states that “when a body is totally or partially immersed in a fluid, it experiences an upthrust equal to the weight of the fluid displaced.

FLOATATION

Ships, canoes and ferries move on the upper part of the water bodies. We say they float, as shown in Figure 3.11.

A balloon filled with lighter gas such as hydrogen will keep rising when released from the hand. A hot air balloon will keep rising as well with the people in the carriage once the air in the balloon has been heated and expanded.

Therefore, floatation can be defined as the tendency of an object to rise up to the upper levels of the fluid or to stay an on the surface of the fluid

 The opposite of floatation is sinking and this can be defined as the tendency of an object to go to the lower levels of the fluid.

Figure 3.11: A boat floating on water

The law of floatation

The law of floatation states that a floating body displaces its own weight of the fluid in which it floats.

This means that, if a log of 200kg (2,000N) floating in water displaces 200kg (2,000N) of water, if the same log is placed in other liquid and is able to float, it will displace the same 200kg of fluid in which it floats.

 Conditions for objects to float

1. The average density of the object should be less than the density of the fluid in which the object has to float. For example, a ship is very heavy but it floats because its hollow inside contains air. This causes its average density to be less than that of water.
2. The upthrust force of the fluid on the object must be equal to the weight of the object (law of flotation). For example, a coin will sink to the bottom when placed on the surface of water. This is because the up thrust of water on coin is less than its weight
3. The volume of the object submerged must be large so as to displace a large amount of fluid.

 Uses of Archimedes ‘ principle

 Archimedes ‘ principle is a very useful and versatile tool. It can be useful in measuring the volume of irregular objects, such as gold crowns, as well as explaining the behavior of any object placed in any fluid.

Archimedes ‘ principle describes how ships float, submarines dive, hot air balloons fly, and many other occurrences.

 Archimedes ‘ principle is also used in a large variety of scientific research subjects, including medicine, engineering, entomology and geology.

Assessment 3.4

 In a swimming pool or at a beach, there is a deep and a shallow end, and the amateurs in swimming are always advised to use only the shallow end. Discuss in groups and come up with several reasons why, and thereafter, share as a class.

Chapter Summary

 In this chapter, you have learnt that:

• Pressure is the force acting normally per unit area and can be calculated from the formula H =F/A then measured in N / M³.
• The atmosphere is made up of the following layers: troposphere, stratosphere, mesosphere, thermosphere and exosphere.
• An object floats when the weight force on the object is balanced by the upward push of the water on the object, but when the weight is more, the object sinks.
• Bernoulli’s principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure