Fluids at Rest | Waec Physics

Waec Lesson note on volume, density and relative density and related

Fluids at Rest

1. Fluids are substances that flow and include both liquids and gases.
2. A fluid at rest is in a state of equilibrium with no net movement of particles.
3. The study of fluids at rest is called hydrostatics.
4. The pressure at any point in a fluid at rest is the same in all directions.
5. Surface tension occurs at the interface between a liquid and air in a fluid at rest.
6. Buoyancy is a property of fluids at rest that enables objects to float.
7. Fluids transmit pressure uniformly in all directions.
8. Incompressibility is a characteristic of most liquids in a state of rest.
9. The weight of a fluid creates pressure within the fluid.
10. Fluids at rest are studied to understand phenomena like flotation and buoyancy.
    
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Volume, Density, and Relative Density

11. Volume is the amount of three-dimensional space occupied by an object.
12. The SI unit of volume is the cubic meter (m³).
13. Density is the mass per unit volume, given by $\rho = m/V$.
14. The SI unit of density is kilograms per cubic meter (kg/m³).
15. Relative density is the ratio of a substance's density to that of water.
16. Relative density has no unit because it is a ratio.
17. Substances with relative density less than 1 float in water.
18. Substances with relative density greater than 1 sink in water.
19. Volume is measured for liquids using graduated cylinders or beakers.
20. Solid volumes can be determined using the water displacement method.
    
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Experimental Determination for Solids and Liquids

21. The mass of solids is measured using balances.
22. The volume of irregular solids can be found using displacement in water.
23. The relative density of solids is determined using the principle of flotation.
24. Liquids' densities are calculated by dividing their mass by their measured volume.
25. A U-tube is used to measure the relative density of immiscible liquids.
26. The density of a liquid can also be determined using a hydrometer.
27. A spring balance helps determine the weight of a solid submerged in water.
28. Hare’s apparatus measures the relative density of two liquids.
29. Proper calibration of measuring tools ensures accurate results.
30. The immersion method involves submerging a solid in water to find its volume.
    
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Pressure in Fluids

31. Pressure is the force exerted per unit area, # P = F/A $.
32. The SI unit of pressure is the pascal (Pa).
33. Pressure in a fluid at rest depends on its depth, density, and gravitational force.
34. The formula $P = \rho g h$ calculates pressure at a given depth.
35. Incompressible fluids exhibit constant density and pressure transmission.
36. The pressure at the same depth in a fluid is uniform.
37. Pressure increases linearly with depth in a fluid.
38. Fluids transmit pressure equally in all directions.
39. Fluids in a container exert pressure on the container walls.
40. The pressure in a liquid supports buoyancy and flotation.
    
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Pascal’s Principle

41. Pascal’s principle states that pressure applied to a fluid is transmitted equally throughout the fluid.
42. Hydraulic presses amplify small forces over large areas using this principle.
43. Hydraulic car brakes operate based on Pascal’s principle.
44. Hydraulic lifts enable heavy loads to be lifted with minimal effort.
45. Pascal’s principle applies only to incompressible fluids.
46. The force multiplication in hydraulic systems depends on the ratio of areas.
47. This principle is crucial in designing industrial and automotive machinery.
48. Pascal’s principle illustrates the efficiency of fluid power systems.
49. Hydraulic systems minimize human effort through force amplification.
50. Accurate pressure transmission requires the absence of air bubbles in hydraulic systems.
    
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Dependence of Pressure on Depth Below a Liquid Surface

51. Pressure in a liquid increases with depth due to the weight of the overlying fluid.
52. The formula $P = \rho g h$ explains the dependence on depth.
53. Greater depths mean more fluid weight above, leading to higher pressure.
54. This principle is used in designing dams to withstand water pressure.
55. Submarine hulls are reinforced to endure high underwater pressure.
56. Divers experience increasing pressure as they descend underwater.
57. Buoyant force calculations depend on pressure differences at varying depths.
58. The uniformity of pressure at a depth is a key principle of hydrostatics.
59. Depth-related pressure changes are crucial for fluid mechanics applications.
60. Oceanographers study depth pressure to understand underwater environments.
    
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Atmospheric Pressure

61. Atmospheric pressure is the weight of air per unit area.
62. Standard atmospheric pressure at sea level is $101,325Pa$ or $1atm$.
63. Atmospheric pressure decreases with altitude.
64. Weather patterns are influenced by atmospheric pressure variations.
65. Atmospheric pressure supports the siphon principle.
66. Barometers measure atmospheric pressure.
67. Low atmospheric pressure can cause altitude sickness.
68. High atmospheric pressure is used in scuba diving to maintain air supply.
69. Atmospheric pressure ensures water boils at a specific temperature at sea level.
70. Variations in atmospheric pressure are used in weather forecasting.
    
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Simple Barometer

71. A barometer measures atmospheric pressure using mercury or water.
72. A simple barometer consists of an inverted tube in a mercury-filled container.
73. Atmospheric pressure supports a mercury column in the tube.
74. At standard pressure, the mercury column is about 76 cm high.
75. Variations in mercury height indicate atmospheric pressure changes.
76. Barometers help predict storms based on pressure drops.
77. Modern barometers use digital sensors for accuracy.
78. Mercury barometers are being replaced due to mercury's toxicity.
79. The barometer's accuracy depends on calibration.
80. Barometers demonstrate the physical effects of atmospheric pressure.
    
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Manometer

81. A manometer measures the pressure of gases or liquids.
82. It consists of a U-tube filled with liquid, typically mercury or water.
83. The height difference of the liquid columns indicates pressure differences.
84. Manometers are used in gas pipelines for pressure monitoring.
85. The pressure reading is accurate if the fluid is incompressible.
86. Manometers are used in laboratories for fluid experiments.
87. Proper alignment ensures accurate pressure readings.
88. Inclined manometers provide greater sensitivity for small pressure differences.
89. Manometers can measure absolute or gauge pressure.
90. They are fundamental tools in fluid dynamics and engineering.
    
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Siphon

91. A siphon transfers liquid from one container to another using a tube.
92. The liquid flows due to gravity and atmospheric pressure.
93. The siphon's intake must be higher than the discharge point.
94. The flow stops if air enters the siphon tube.
95. Siphons are used to drain water from tanks.
96. Atmospheric pressure maintains the continuous flow of liquid in a siphon.
97. The siphon principle demonstrates the interplay of pressure and gravity.
98. Siphons are used in agriculture for irrigation systems.
99. A siphon must maintain a sealed path to function effectively.
100. The efficiency of a siphon depends on the tube's diameter and length.
     
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Syringes and Pumps

101. Syringes use suction and pressure to draw and expel fluids.
102. The plunger creates low pressure to draw fluid into the barrel.
103. Pumps transfer liquids by creating pressure differences.
104. Hand pumps operate by manually displacing air or water.
105. Mechanical pumps use pistons or rotors to move fluids.
106. Syringes are used in medical procedures to administer medications.
107. Pumps are used in industries for water and oil transfer.
108. Both devices demonstrate the practical applications of fluid dynamics.
109. Pumps must be primed to remove air for efficient operation.
110. Syringes illustrate Pascal’s principle in fluid movement.
     
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Determination of Relative Density of Liquids with U-Tube

111. A U-tube compares the relative densities of two liquids.
112. Equal volumes of liquids are poured into the U-tube's arms.
113. The relative density is calculated using the height of the columns.
114. The U-tube must be clean and air-free for accurate results.
115. The liquid with higher density occupies a shorter column.
116. U-tube manometers provide quick relative density measurements.
117. The method is simple and reliable for comparative density studies.
118. U-tubes are commonly used in physics and fluid mechanics experiments.
119. Proper calibration ensures consistent and accurate results.
120. U-tube experiments illustrate the importance of pressure equilibrium in fluids.
     
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Waec Lesson notes on Equilibrium of bodies

Equilibrium of Bodies

1. Equilibrium occurs when the net force and net torque on a body are zero.
2. A body in equilibrium remains at rest or moves with constant velocity.
3. Equilibrium can be static (no movement) or dynamic (constant movement).
4. The conditions for equilibrium are: $\sum F = 0$ (no net force) and $\sum \tau = 0$ (no net torque).
5. Stable equilibrium occurs when a displaced body returns to its original position.
6. Unstable equilibrium occurs when a displaced body moves further away from its original position.
7. Neutral equilibrium occurs when a displaced body remains in its new position.
8. Examples of equilibrium include a balanced seesaw and a stationary book on a table.
9. The center of gravity plays a key role in maintaining stability.
10. A lower center of gravity increases the stability of a body in equilibrium.
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Identification of Forces Acting on a Body Partially or Completely Immersed in a Fluid

11. The forces acting on an immersed body include weight, buoyant force, and tension or support force.
12. The weight of the body acts downward due to gravity.
13. The buoyant force acts upward, opposing the weight of the fluid displaced.
14. The magnitude of the buoyant force equals the weight of the displaced fluid.
15. For a partially immersed body, the buoyant force depends on the submerged volume.
16. For a completely immersed body, the buoyant force depends on the entire volume of the body.
17. If the buoyant force equals the weight of the body, the body floats.
18. If the weight exceeds the buoyant force, the body sinks.
19. Tension in a string or force from a support balances the forces in equilibrium.
20. A diagram showing all forces (free-body diagram) helps in analyzing equilibrium.
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Archimedes’ Principle

21. Archimedes’ principle states that a body submerged in a fluid experiences an upward force equal to the weight of the displaced fluid.
22. This principle explains why objects float or sink in fluids.
23. The buoyant force acts through the center of buoyancy, located at the centroid of the displaced fluid.
24. Archimedes’ principle applies to solids, liquids, and gases.
25. The principle is fundamental in understanding flotation and buoyancy.
26. A heavier-than-water object sinks unless it displaces an amount of water equal to its weight.
27. An object with density less than the fluid floats.
28. The principle also explains why hot air balloons rise in air.
29. Archimedes’ principle is used in the design of ships and submarines.
30. The apparent weight of an object submerged in a fluid decreases due to buoyant force.
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Use of Archimedes’ Principle to Determine Relative Densities of Solids and Liquids

31. The relative density of a solid is determined by measuring its weight in air and when submerged in water.
32. Relative density is the ratio of the weight of the solid to the weight of the displaced fluid.
33. For liquids, a U-tube or Hare’s apparatus is used with Archimedes’ principle.
34. The weight of the displaced fluid provides the necessary information for calculations.
35. Relative density = (Weight of object in air) / (Apparent loss in weight when submerged).
36. The principle is applied in hydrometer design for measuring liquid densities.
37. Careful calibration ensures accurate determination of relative density.
38. Experimental errors can arise from improper measurements or fluid contamination.
39. The principle allows quick comparison of the densities of immiscible liquids.
40. This method is widely used in laboratory experiments and industrial applications.
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Law of Flotation

41. The law of flotation states that a floating body displaces its own weight of fluid.
42. A body floats if its density is less than or equal to the fluid's density.
43. The buoyant force balances the weight of the floating body.
44. For a fully submerged floating body, the weight equals the buoyant force.
45. For a partially submerged body, only the displaced volume contributes to buoyancy.
46. The law of flotation applies to boats, ships, and rafts.
47. Stability in floating objects depends on the distribution of weight and buoyant force.
48. Flotation efficiency improves with careful design and material selection.
49. The center of buoyancy must align with the center of gravity for stability.
50. Changes in fluid density, such as salinity in water, affect flotation.
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Establishing the Conditions for a Body to Float in a Fluid

51. A body floats if the weight of the displaced fluid equals the weight of the body.
52. The body’s average density must be less than the fluid’s density.
53. Stability in floating occurs when the center of buoyancy is directly below the center of gravity.
54. The shape of the body affects its ability to displace sufficient fluid.
55. Large, flat shapes displace more water and improve flotation.
56. Submarines adjust buoyancy by controlling water in ballast tanks.
57. Floating objects must have material strength to prevent deformation under fluid pressure.
58. Air pockets in hollow bodies reduce overall density, aiding flotation.
59. Proper weight distribution ensures floating stability.
60. The depth of immersion depends on the body’s density relative to the fluid.
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Applications in Hydrometer, Balloons, Boats, Ships, Submarines, etc.

61. Hydrometer: Measures liquid density using Archimedes’ principle.
62. A hydrometer sinks deeper in low-density liquids and less in high-density ones.
63. Hot Air Balloons: Float because hot air is less dense than cooler air around it.
64. The buoyant force lifts the balloon as it displaces heavier air.
65. Boats: Float because their shape ensures they displace enough water to balance their weight.
66. Buoyancy chambers in boats provide additional stability and flotation.
67. Ships: Use displacement and ballast tanks to maintain buoyancy and stability.
68. Ships are designed to distribute weight evenly for safe flotation.
69. Large cargo ships carry immense loads while floating due to careful design.
70. Submarines: Adjust their buoyancy by filling or emptying ballast tanks with water or air.
71. Submarines sink when ballast tanks are filled with water, increasing their density.
72. They rise by expelling water and filling tanks with air, reducing their density.
73. Life Jackets: Contain buoyant materials that ensure a person floats in water.
74. Floating Docks: Use hollow structures to stay above water level.
75. Oil Rigs: Float on water using buoyant supports to drill undersea.
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Additional Practical Applications

76. Pontoons: Provide buoyancy for bridges and temporary platforms.
77. Rafts: Float due to lightweight materials and large displacement areas.
78. Fishing Floats: Indicate fish activity using buoyancy principles.
79. Buoys: Remain afloat to mark navigation routes or hazards.
80. Floatation Tanks: Provide therapeutic relaxation by keeping users afloat in saline water.
81. Rescue Boats: Use lightweight and buoyant materials for emergencies.
82. Icebergs: Float because the density of ice is less than seawater.
83. Scuba Gear: Includes weight adjustments to manage buoyancy underwater.
84. Water Wings: Help swimmers stay afloat by displacing water.
85. Hovercraft: Use air cushions for flotation over water surfaces.
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Summary of Key Principles

86. Buoyant force depends on the volume of displaced fluid.
87. Archimedes’ principle governs all applications of flotation.
88. A floating body maintains equilibrium between weight and buoyancy.
89. The density of the fluid affects the extent of flotation.
90. Stability in floating objects depends on the alignment of forces and centers of gravity.
91. Objects with irregular shapes experience complex buoyancy effects.
92. Saltwater increases buoyancy compared to freshwater due to higher density.
93. Air pressure affects the buoyancy of balloons and airships.
94. The law of flotation simplifies the design of waterborne vessels.
95. Practical applications span industries, including transport, rescue, and recreation.
    
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Experimental Demonstrations

96. Using a hydrometer to measure sugar concentration in liquids.
97. Determining the relative density of solids using Archimedes’ principle.
98. Demonstrating flotation with hollow objects like metal cans.
99. Measuring buoyant force with submerged weights in water.
100. Comparing floating behaviors of different materials and shapes in fluids.

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