Section outline

  • General

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    In this course you will learn about:

    1. What pressure is
    2. Pressure in solids
    3. Pressure in liquids
    4. What Pascal's principle is
    5. Atmospheric pressure

  • Lesson 1: The concept of pressure

    • What is pressure?

      Pressure influences our daily lives without us even knowing it, here are some examples:

      • Sharp knives help us cut through meat or vegetables
      • Hammers are used to insert nails into wood to build a desk or cabinet
      • Backpacks have thick padded shoulder straps to ensure that a loaded pack won't dig into your shoulders and hurt you
      • When you walk on grass in high heels do you  notice how your heels sink into the grass whereas if you wear flat heels they don't?
      • And so the list can go on...


      But what exactly is pressure?


    • Consider the following two scenarios:

      Scenario one

      If you hammer a nail into a piece of wood with the sharp point against the wood, the nail should go into the wood quite easily. However, if you flip the nail so that the head of the nail is against the wood, and then use the same amount of force and try to hammer the nail into the wood, you will not be very successful.


      Scenario two

      If you try and push two pieces of wood, using the same amount of force, into a softer object, you will observe that the piece of wood with the smaller surface area will penetrate the object easier than the wood with the larger surface area.


      So what can we conclude from these two scenarios?

      When force is applied to an object, the results are affected by the size of the surface area on which the force is applied. This is the concept of pressure. An object will experience pressure when force is applied to it. There is a direct relationship between force and the surface area on which it is applied, the smaller the surface area, the larger the amount of pressure exerted.

      \( Pressure = Force \div Area \) 

      or in another format:


    • What unit is pressure measured in?

      Now that you know the formula to measure pressure viz.:


      you need to understand the unit that pressure is measured in.

      • Force is measured in Newtons (N)
      • Area is measured in m2  or cm2
      • Therefore pressure is measured in Newton per square metre: N/m2  
      • N/m2  is also known as the Pascal Pa. 1 Pa = 1 N/m2

    • Activity

      Using the forum tool below, provide some other examples of how pressure manifests itself e.g. a high heel in grass versus a flat heel in the grass.

      Each participant should post at least one comment. Review what other course participants have posted.

    • Forum discussion
      Students must
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      Make forum posts: 1

    • Watch the short YouTube video below which clearly summarises what has been covered so far:


      NinetyEast. (2019). What is pressure? (Standard YouTube licence)

  • Lesson 2: Pressure due to solids

    • You should now be familiar with the concept that pressure in solids depends on the surface area of the contact. If you apply a force to a small surface area the pressure will be greater than if you applied the same force to a larger surface area. Watch the YouTube video below which proves this concept, based on the formula:


      Revision Monkey. (2021). Pressure in solids. (Standard YouTube licence)

    • Let's consolidate what was covered in the video by providing you with another example:


      This object weighs 5 N. Let's calculate the pressure created when this object is placed with its largest base in contact with the table:

       
      Now let's look at if the object which weighs 5N being placed on the table with its smallest surface area in contact:



      Conclusion

      0.208 N/cm2 > 0.125 N/cm2 therefore this proves that the smaller surface area exerts more pressure on an object than the larger surface area. 

      In the above example we have illustrated the effect that the size of a surface area has on pressure. However, if the amount of applied force is increased i.e. F increases, then the amount of pressure exerted on the object will also increase.

    • Applications of pressure due to solids

      To round off this topic, let's look at further practical applications of pressure due to solids:

      • Screws, nails and drawing pins are designed with sharp points to increase their penetration ability
      • Knives have sharp blades in order to enable them to cut through objects
      • Porcupines have sharp quills in order to protect them from predators
      • High heeled shoes can be problematic when walking on sand or grass. Flat shoes will not pose the same problem
      • Railway sleepers are placed under the railway tracks to provide a larger surface area for the weight for the train
      • Buildings are constructed with wide foundations in order to absorb the weight of the construction over a larger area


      What other examples can you think of?


  • Lesson 3: Pressure in liquids

    • Do liquids exert pressure? What do you think? To find out the answer, watch the YouTube video below:


      Revision Monkey. (2020). Pressure in liquids. (Standard YouTube licence)

    • Liquids will exert pressure on an object in the liquid as well as on the walls and base of the container in which it resides. Pressure in a liquid acts in all directions. 

      Activity

      In the video you watched, the presenter explained the experiment on proving that the pressure is higher the deeper the liquid is. Now it's time for you to prove that yourself!

      • Source an empty plastic bottle
      • Fill it up with water
      • Starting at the top of the bottle and working your way down, insert holes at regular intervals
      • Note how the water travels out of the bottle


      Water coming out of the hole at the lowest part of the bottle will travel further than water coming out of the top hole - this is due to the fact that there is a higher pressure in the liquid at the bottom of the bottle, as well as more weight on the liquid at the bottom.

      As the depth of the liquid increases, so too does the weight of the liquid and therefore the pressure increases with depth.

    • Let's look at this in a little more depth. Think of a liquid containing lots of water balloons on top of each other, as illustrated below.


      The weight of a balloon on the top pushes downward force onto the balloons below. The balloons below need to counter this downward force by pushing a stronger upward force. The balloons at the bottom are required to support the weight of all the balloons above them and experience increased pressure. Should the water balloons be in a container, the balloons at the bottom will exert sideways force against the walls of the container, since they are being squashed by the weight of the balloons on top of them. 


      You should now clearly understand why, when you insert holes in a full water bottle, the water travels further through the bottom hole as opposed to the top hole. It's all down to pressure!


      Imagine now how much pressure a submarine must endure when it deep dives. The amount of pressure and weight exerted on its structure is astronomical. Imagine too the effect of this increased pressure on the human body when a person deep dives, especially with no oxygen tank support. 

    • How to calculate pressure in a liquid

      The formula to calculate pressure in a liquid is:
      \[P=hg\rho \]
      ...but how did we get to this? Review the steps below to find out:

      • P = F ÷ A
      • We know that force = mass x gravitational pull i.e.
      • \[F=mg\]
      • Mass = volume x density i.e.
      • \[M=lwh\rho \]
      • therefore:
      • \[F=lwhg\rho \]
      • We know that A = length x width therefore
      • \(P=lwhg\rho \div \)lw
      • Cancel out the two sets of lw and you get the result:
      • \[P=hg\rho \]

      To put this in words:

      Pressure in liquids = height of the liquid column x density of liquid x acceleration due to gravity.

      It's important to understand that pressure in a liquid isn't dependent on the area or shape of the container, but rather on the depth and density of the liquid.

    • Watch the YouTube video below (start at 4:30) in which the presenter thoroughly explains how to calculate the pressure in a liquid.

      The Organic Chemistry Tutor. (2018). Introduction to pressure and fluids (Standard YouTube licence)

    • Let's summarise the characteristics of pressure in liquids:

      • The greater the depth the greater the pressure
      • Pressure in a liquid acts in all directions
      • The higher the density of a liquid the higher the pressure


      A further interesting example of pressure in liquids is the following:


      When water, or any liquid, is poured into a communicating vessel like the one above, the liquid will be at the same level in all the tubes, irrespective of their shape. This is due to the fact that the pressure is the same at all points of similar depths. The pressure at A = the pressure at B = C = D = E.

    • Pressure in liquids and upthrust

      Going back to our illustration of water balloons, but this concept will be relevant for any object placed in a liquid:


      You now know that the liquid at the bottom will experience greater pressure than the liquid at the top. The difference in this pressure will result in an upward force known as an upthrust. 

      The horizontal forces increase with depth but these horizontal forces balance each other out with zero net effect.

    • Example 1

      Let's look at this concept by way of an example:

      A cube sized 2 cm on each side is submerged in water. The bottom of the cube is at a depth of 10 cm. Assume the following:

      • Ρ (the density of water) = 1027 kg/m3 
      • g = 10 N/kg
      • Remember the formula for pressure = hΡg


      What is the difference in the pressure between the top and bottom of the cube?

      Pressure at the bottom
      Pressure = hΡg
      = 0.1 m x 1027 kg/m3 x 10 m/s2
      = 1027 N/m2

      Pressure at the top
      The depth at the top = 0.1 m - 0.02 m (since the sides are 2 cm)
      = 0.08 m x 1027 kg/m3 x 10 m/s2 
      = 821.6 N/m2 

      The difference in pressure between the bottom and top:
      = 1027 N/m2 - 821.6 N/m2 
      = 205.4 N/m2 

    • Example 2

      Using the same assumptions and cube size detailed above, let's work out what the difference in force will be between the top and bottom of the cube. 

      Pressure = Force ÷ Area
      => Difference in pressure = Difference in force ÷ Area
      => Difference in force = Difference in pressure x Area
      Area of a cube = length2 
      = (0.02 m)2 
      = 0.0004 m2 

      Difference in force = Difference in pressure x Area
      = 205.4 N/m2 x 0.0004 m2 
      = 0.0822 N

      The above number therefore represents the upthrust of force.

    • Watch the YouTube video below which clearly explains pressure in liquids and upthrust. This video will also help you understand why some objects float and others sink in a liquid.

      GCSE Physics. Cognito. (2020). Liquid pressure and upthrust (Standard YouTube licence) 

    • Pascal's Principle

      Pascal's principle of pressure transmission in fluids states that a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. (Wikipedia)

      Put differently: if a pressure is applied to a liquid in a closed contained space, the pressure is transmitted equally in all directions to all parts of the liquid and container walls.

      Watch the short YouTube video below which illustrates Pascal's principle:

      myhometuition. (2017). Pascal's Principle (Standard YouTube licence)


    • The image below illustrates Pascal's Principle:


      Remember that if holes are inserted into this container, the liquid will be dispersed the same distance, no matter the direction. The more pressure that is applied to the liquid in the contained space, the further the liquid will travel.

      Examples of where Pascal's principle is applied include hydraulic car jacks, car brakes and many mechanical bulldozers. 

      If you're interested, watch the YouTube video below which illustrates how hydraulic brakes function in a vehicle.

      Simon. (2020). How do hydraulic brakes in cars and light vehicles work. (Standard YouTube licence)

  • Lesson 4: Atmospheric pressure

    • What is atmospheric pressure?

      The earth's surface is surrounded by a layer of air (which contains a mixture of gases) called the atmosphere. The weight of this layer of air is known as atmospheric pressure. 

      At sea level, the pressure exerted by the weight of the atmosphere has a mean value of 101,325 pascals i.e. 101,325 Pa or 101 kPa. 

      A barometer is the instrument used to measure atmospheric pressure. Under normal circumstances and at sea level, we don't feel atmospheric pressure since the fluids in our bodies exert a pressure which is greater than that of atmospheric pressure.

      The higher the altitude the lower the atmospheric pressure i.e. atmospheric pressure decreases the higher the altitude. Let's look at an example: Mount Kilimanjaro in Tanzania.

      The summit of Mount Kilimanjaro is 5895 m above sea level. The atmospheric pressure at the summit is measured at 50 kPa. When compared to the 101.3 kPa at sea level, the atmospheric pressure at the summit is only 49% of that at sea level. Only 49% of oxygen is available at the summit compared to 100% at sea level. This is due to the fact that the density of air is greater at sea level. The higher the altitude the lower the density of air and the lower the atmospheric pressure. 

      An interesting application of this fact is the training of athletes at high altitudes. For example, East African middle distance and endurance runners have dominated races across the world. One of the reasons attributed to this dominance is that they train at high altitudes. Their bodies are having to function and create energy with less oxygen available. This is achieved by their bodies creating more red blood cells which results in their blood being able to carry more oxygen.

    • Review the table below which illustrates the point that atmospheric pressure does indeed increase the lower the altitude.


      An interesting observation is the Dead Sea. The Dead Sea is actually a landlocked lake that is situated between Jordan and Israel. The Dead Sea is approximately 430 m BELOW sea level. This lake has an extremely high salt content making it very dense. Therefore humans are able to float in the Dead Sea since the human body is less dense than the lake.


    • We can safely say then, that atmospheric pressure (P)at any given point of constant g is dependent on the following two factors:

      • the density of the air (p)
      • the height of the air column (h)

      Therefore:

      P = hpg

    • Let's now look at some examples which proves that atmospheric pressure does indeed exist!

      Magdeburg hemisphere


      The Magdeburg hemisphere consists of two half spheres which are joined together forming an airtight sphere. The air is merely trapped inside the hemisphere and not compressed. Therefore the pressure outside the sphere is the same as the pressure inside the sphere, as indicated by the red arrows in the image. The spheres can therefore be pulled apart easily and without any real resistance.




      Now, what happens if the air inside the sphere is removed, thereby creating a partial vacuum inside? The pressure outside the sphere will therefore be greater than the pressure inside the sphere resulting in the spheres being pressed tightly together (as indicated by the arrows in the image to the right). It will be difficult to pull the spheres apart. 

    • Watch the short YouTube video below which provides a great example of the workings of atmospheric pressure.

      The Sci Guys. (2014). The air pressure can test (Standard YouTube licence)

    • Measuring atmospheric pressure

      As mentioned earlier, atmospheric pressure is measured using a barometer. In this section, we will explore three types of barometers viz, the mercury barometer, the aneroid barometer and the digital barometer.

      Mercury barometer


      This is the oldest barometer in existence, having been invented by Evangelista Torricelli in 1643.

      It consists of a glass tube which is closed at the top and open at the bottom. It sits in a pool of mercury. As the atmospheric pressures rises, the mercury is forced by this increasing atmospheric pressure to rise and vice versa. 



      Aneroid barometer

      The aneroid barometer was invented in 1844 by Lucien Vidi. This barometer measures atmospheric pressure without the use of any liquid. Instead, a sealed metal chamber expands and contracts based on the level of atmospheric pressure around it. A lever which is connected to the chamber moves a pointer which displays the measurement of the atmospheric pressure.


      Digital barometer

      The digital barometer is the most commonly used barometer these days, particularly since it displays the data quickly and more accurately. This information can then be downloaded and used in data analysis.

      For further background on the history of the mercury barometer, watch the short YouTube video below.

      TedEd. (2014). The history of the barometer (Standard YouTube licence)

    • Examples of devices which use atmospheric pressure

      The following examples below are just some of the common devices which make use of atmospheric pressure:

      • Drinking straws
      • Cupping therapy
      • Bicycle pumps
      • Vacuum cleaners
      • Siphons
      • Syringes


      Let's look at a few of these in further detail.

    • Siphon 



      A siphon is a continuous tube which enables liquid to drain from a higher point to a lower point due to the difference in pressure. No pumps are required.

      The liquid rises in the tube due to the atmospheric pressure which is pushing down on the liquid. The long arm of the tube carries more liquid and is therefore heavier. The force of gravity draws the liquid through the long side of the tube. 

      This liquid will continue to flow until the level of liquid is lower than the intake point.



    • Watch the short YouTube video below which clearly explains the siphon process.

      ScienceOnline. (2010). The Siphon (Standard YouTube licence)

      Did you know that the toilet flushing cisterns (ball and chain cistern) make use of this siphon process? Can you think of any other examples where this siphon process is used?


    • Vacuum cleaners

      The vacuum cleaner works in a similar way to when you suck juice from a straw. The rotating fan within the vacuum cleaner creates a vacuum and will then begin to suck in air (and dust / dirt) through the nozzle due to the higher pressure being 'outside' the vacuum cleaner.





      Syringe


      Have you ever wondered how the syringe is able to draw blood or any other liquid?
      When the plunger is pulled back this creates a lower pressure inside the syringe than the outside pressure, causing the fluid to move into the syringe. When the plunger is pushed into the tube, the pressure inside is less than the pressure outside the tube, therefore the liquid squirts out.  

    • Summary

      The following topics were covered in this course:

      • What is pressure?
      • Pressure due to solids
      • Pressure in a liquid
      • Atmospheric pressure


      You will now know that pressure is the amount of force which is exerted over a specified area. 


      Using the above formula you are now able to determine that:

      P = hgp

      Pressure is measured in Pascal's where 1 Pa = 1 N/m2    

      You now understand that pressure in a solid will be higher the smaller the area e.g. walking in high heels on grass will cause the heels to sink into the grass (due to the force over a small area) as opposed to walking in flat shoes on grass (the downward force is spread over a larger area).

      You also determined that pressure in a liquid is determined by the density and depth of the liquid. Pascal's principle was introduced: any pressure change on the surface of an enclosed fluid will be transmitted equally throughout the fluid.

      Atmospheric pressure at sea level is 101 kPa. The higher the altitude the lower the atmospheric pressure i.e. atmospheric pressure is dependent on the density of the air and the height of the air column. At sea level, the air is more dense, there are more oxygen particles in the air. The higher the altitude, the less dense the air is.

      We encourage you to reflect on everyday examples where the use of pressure is demonstrated.

      Finally, to test your understanding of this topic, answer the questions in the short quiz below. A pass mark of 50% is deemed to be successful - good luck!

    • Final quiz
      Students must
      Receive a grade
      Receive a passing grade

    • Attribution

      The following resources were consulted in the compilation of this training module:

      • Tanzania Institute of Education. (2021). Physics for Secondary Schools Form One. (©)
      • NinetyEast. (2019). What is pressure? (Standard YouTube licence)
      • Revision Monkey. (2021). Pressure in solids. (Standard YouTube licence)
      • Revision Monkey. (2020). Pressure in liquids. (Standard YouTube licence)
      • The Organic Chemistry Tutor. (2018). Introduction to pressure and fluids (Standard YouTube licence)
      • GCSE Physics. Cognito. (2020). Liquid pressure and upthrust (Standard YouTube licence) 
      • myhometuition. (2017). Pascal's Principle (Standard YouTube licence)
      • Simon. (2020). How do hydraulic brakes in cars and light vehicles work. (Standard YouTube licence)
      • The Sci Guys. (2014). The air pressure can test (Standard YouTube licence)
      • TedEd. (2014). The history of the barometer (Standard YouTube licence)
      • ScienceOnline. (2010). The Siphon (Standard YouTube licence)