This lesson explains how pressure works in liquids (hydrostatics) and gases, and how these principles are used in everyday life, from drinking with a straw to lifting a car.

1. Short Notes: Core Concepts

A. Pressure Basics

• Definition: Pressure is the force acting perpendicularly on a unit area.

• Formula: Pressure (P) = Force (F) / Area (A)

• Unit: The SI unit is the Pascal (Pa). 1 Pa = 1 N/m².

B. Pressure in Liquids (Hydrostatic Pressure)

• Key Principles:

  • Pressure increases with depth. This is why dam walls are thicker at the bottom.

  • At any given depth, pressure acts equally in all directions.

  • Pressure at the same horizontal level in a continuous liquid is the same.

• Formula: The pressure exerted by a liquid column is given by: P = hρg

  • h = height (depth) of the liquid column (in meters, m)

  • ρ (rho) = density of the liquid (in kg/m³)

  • g = acceleration due to gravity (approx. 10 m/s²)

C. Transmission of Pressure (Pascal's Principle)

• Principle: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.

• Application - The Hydraulic Press/Jack: This principle is used to multiply force. A small force applied to a small piston creates pressure in a fluid (like oil), which then exerts a large force on a larger piston.

  • Examples: Hydraulic car lifts, vehicle brake systems, hydraulic jacks.

D. Atmospheric Pressure

• Definition: The pressure exerted by the weight of the air in the atmosphere.

• Measurement: Measured with a barometer. Standard atmospheric pressure at sea level can support a column of mercury 76 cm high (76 cm Hg).

• Applications: Drinking with a straw, using a rubber sucker, the siphon method.

E. Sinking and Floating

• Upthrust: When an object is immersed in a fluid, the fluid exerts an upward force on it. This force is called upthrust.

• Archimedes' Principle: The upthrust on an object is equal to the weight of the fluid displaced by the object.

• The Law of Floatation:

  • An object sinks if its Weight > Maximum Upthrust.

  • An object floats fully submerged if its Weight = Maximum Upthrust.

  • An object floats partially submerged if its Weight < Maximum Upthrust. (It sinks just enough to displace a weight of fluid equal to its own weight).

• Hydrometer: An instrument used to measure the density of liquids. It floats higher in denser liquids and lower in less dense liquids, based on Archimedes' principle.

2. Tips & Tricks for the Exam

• Formula Triangle: Use a formula triangle to easily rearrange P = hρg and P = F/A.

• Units Matter: Always check that you are using SI units in your calculations: force in Newtons (N), area in square meters (m²), height/depth in meters (m), and density in kg/m³.

• Upthrust = Apparent Loss in Weight: A quick way to find the upthrust is to subtract the object's weight in the fluid from its weight in air. Upthrust = Weight in air - Weight in fluid.

• Hydraulics Logic: Small force on small piston → Big force on big piston. The pressure is the same on both sides.

3. Important Points & Common Exam Questions

• Pressure Calculation: "A water tank is 5m deep. Calculate the pressure at the bottom. (Density of water = 1000 kg/m³, g = 10 m/s²)."

  • Answer: P = hρg = 5 1000 10 = 50,000 Pa.

• Dam Wall Question: "Why is the wall of a dam built to be much thicker at its base than at the top?"

  • Answer: Liquid pressure increases with depth. A thicker base is needed to withstand the greater force exerted by the water at the bottom.

• Hydraulic System Explanation: "Explain briefly how a small force on a car's brake pedal can produce a large force to stop the wheels."

  • Answer: The force on the pedal creates pressure in the brake fluid. According to Pascal's principle, this pressure is transmitted to the larger pistons at the wheels, producing a much larger force.

• Floating/Sinking Problems: "An object weighs 20 N in air. When fully submerged in water, it displaces 15 N of water. Will the object float or sink? Explain."

  • Answer: The maximum upthrust is the weight of the displaced water, which is 15 N. Since the object's weight (20 N) is greater than the maximum upthrust (15 N), the object will sink.