An Introduction to Pressure in CSEC Physics.pdf
- 2. Pressure Pressure is defined as the force acting perpendicular per unit area.Pressure is measured in pascal (Pa) as well as Newton Meter squared (Nm-2).
- 3. Pressure Formula: P = F / A P = Pressure (Pa) F = Force (N) A = Area (m²) 1 Pascal (Pa) = 1 Newton per square meter (N/m²)
- 4. Scenario It has been mathematically proven that an average sized lady in high-heeled shoes is more likely to dent a wooden floor than a six (6) ton elephant. In essence, her heels exert a greater pressure than the elephant’s feet, even though her force is significantly less. The force (or the weight) of the lady may be small when compared to the elephant’s, but it is concentrated at the heels over a small surface area. The elephant’s feet on the other hand are large, which basically means that even though its force (or weight) is quite significant, it is distributed over a large surface area resulting in less pressure than that of the lady’s heels.
- 5. ● Why is it more painful to stand barefoot on small pebbles or gravel than on a smooth surface? ● In snowy regions, why do people wear cumbersome shoes? ● Why do footballers have studs on their boots? (Homework) ● If a boy falls through ice on a pond, why is it better for a rescuer to crawl across the ice? ● Why is it easier to cut a loaf of bread with a sharper knife? Pressure
- 7. Sample A block of mass 72 g exerts a pressure over an area of 0.6 m2. Calculate the pressure exerted by this block. (g = 10 N/kg). An object resting on a surface area of 5 m2 exerts a pressure of 2 kPa. Calculate the mass of this object. (g = 10 N/kg)
- 8. Sample A block of mass 4 Mg sits on a surface of area 8 m2. What is the pressure being exerted on the surface by this block? (g = 10 N/kg) An object exerts a pressure of 15 kPa over an area on the ground of 0.3 m2. Calculate the mass of this object if gravity is taken to be 10 N/kg.
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- 11. Pressure in Fluids Fluids are the states of matter that possesses the ability to flow, for example liquids and gases, and they also exert pressure on anything they come into contact with. When considering pressure in fluids one must understand that: 1. Pressure in fluids increases with depth. Which basically means that the deeper down into the fluid you go the greater the pressure becomes. The reason for this is that the deeper down into the fluid one goes the greater the weight of the fluid above becomes, and a greater weight of fluid above basically means that there is more force acting down at the point in the fluid being considered. And since pressure is directly proportional to force, a greater force automatically results in a greater pressure. 2. The pressure at the same depth is EQUAL, no matter the direction in which it is being exerted. 3. The greater the density of a fluid the greater is its pressure.
- 12. Pressure in Fluids P =𝝆𝒈𝒉 Where: P = Pressure ρ = Density h = Depth (the opposite of height)
- 14. Application of Pressure When building Dams, Engineers have to make sure that the walls at the bottom are thicker than the walls at the top. This is because pressure increases with depth, which basically means that the pressure being experienced by the walls of the dam at the bottom of the lake, is far greater than that being experienced by the walls at the top. And in order to withstand the enormous pressure that is generated at the bottom, the walls have to be made as thick as possible.
- 15. A diver experiences a pressure of 1.2 MPa at the bottom of a tank. If the tank is sealed from atmospheric pressure, the density of the water is 1000 kg/m3, and gravity is taken to be 10 N/kg, calculate the depth of the water in this tank. The maximum pressure of the salt water at the bottom of a desalination tank of depth 80 m is 900 kPa. Calculate the density of this water if gravity is taken to be 10 N/kg Pressure
- 16. Fluid Pressure ● The atmosphere is a fluid of gaseous particles, and as a result of this will also exert a pressure on anything it interacts with. Like all fluids Atmospheric pressure increases with depth, which means that the closer you are to sea level the greater the pressure becomes. ● Sea level is a standard point of reference that is used when specifying Atmospheric pressure, and the Atmospheric pressure experienced by all bodies at sea level has been experimentally found to be approximately 101.1 kPa. ● Atmospheric pressure at sea level has also been found to support a column of 760 mm of mercury (Hg). Which basically means that a column of 760 mm mercury is equal to 101100 Pa of Atmospheric pressure. One should also make note of the fact that: ● Atmospheric pressure exerts pressure on the surfaces of liquids that are open to the atmosphere. And this is something that must be taken into account when performing calculations.
- 17. Sample If a scuba diver experiences a pressure of 310 kPa at the bottom of a lake, calculate its depth if the density of the water is 1000 kg/m3, gravity is taken to be 10 N/kg, and atmospheric pressure is 101.1 kPa. How deep under the sea would one have to be to experience a pressure of 500 kPa. The density of sea water is 1100 kg/m3.
- 18. Hydraulics: Pressure Transmission in Liquids This law states that whenever pressure is applied to an enclosed static fluid, it is transferred with equal magnitude throughout the entirety of the fluid. The fact that the pressure is translated through the fluid as stated by Pascal’s Law, Engineers have realized that they could use hydraulics to multiply a small force and make it become a larger one of more significance. This is the technology that is used in Hydraulic Jacks, Tractors, Cranes, Dumping Trucks, and any other machine that uses hydraulics.
- 20. Hydraulics: Pressure Transmission in Liquids The Pressure (PB), which is exerted on Piston B is exerted over a larger surface area than that of Pressure (PA), and as a result of this the Force (FB) will become significantly greater than that of the Force (FA). This can be mathematically proven:
- 21. Practice For the diagram that is illustrated previously, the Force (FA) is 40 N, and the Area of the small piston AA is 0.0036 m2. Calculate: 1. The Force (FB) that will be exerted by the large piston AB if its area is 2 m2.
- 22. Practice 1. The Area that the large piston AB should have in order for it to exert a Force of 500 KN
- 23. Manometers Manometers are instruments used to measure the pressure of Fluids, and the simplest form of these devices is the U-tube Manometer. As its name suggest, the U-tube Manometer is a uniformly bored glass tube that is bent in the shape of a U, and this is partly filled with either water, alcohol, or mercury when it is being used.
- 24. Manometer The U-tube Manometer shown in the diagram above, is partly filled with water and its left column (Column G) is connected to a particular gas while its right column (Column A) is left open to the atmosphere. The fact that the Gas pressure (PG) pushes back the atmosphere by pushing on the water indicates that it is stronger than Atmospheric pressure (PA). Which basically means that the level of the liquid is always less in the column which has the greater pressure, and if both columns were experiencing the same pressure, then the level of the water within them would have been the same. .
- 25. Calculating Pressure using Manometer .
- 26. Archimedes Principle Archimedes’ Principle states that the upthrust experienced by an object immersed in a fluid is equal to the weight of the fluid displaced. Objects that are immersed in fluids is exerted upon by an upward force called Upthrust (U), which depends on the upward pressure that is being exerted at that particular point within the fluid.
- 27. Archimedes Principle If you take a keen look at the Spring Balance that is illustrated above, you will see that when the 10 kg mass was not immersed the scale displayed 10 kg, but after being submerged into the water it displayed only 6 kg. The reason for this is because the Upthrust force is acting in the opposite direction to the Weight of the object. The Weight (W) is acting downwards, while the Upthrust (U) is acting upwards.
- 28. Archimedes From the diagram we also see that the weight of water displaced is 40 N, which in accordance to Archimedes’ Principle means that the Upthrust force acting on the object is also 40 N since: Upthrust Force (U) = Weight of Fluid Displaced by Object ● If the weight of the object (W) is equal to the weight of fluid displaced (U), it will float ● If the weight of the object (W) is greater than the weight of fluid displaced (U), it will sink ● If the weight of the object (W) is lesser than the weight of the fluid displaced (U), it will rise
- 29. Practice If an object of mass 70 g floats on water, calculate the Upthrust Force that is being exerted on this object. (g = 10 N/kg) A body experiences an Upthrust of 250 N, which causes it to float on the surface of the water in which it was placed. Calculate the mass of this body if gravity is taken as 10 N/kg.