Work, energy, pressure and fluids: Pascal…

Core facts

Work = force x displacement in the direction of force. Unit: joule (J). No displacement means no work.
Kinetic energy = ½mv². Potential energy (gravitational) = mgh.
Power = work / time. Unit: watt (W) = 1 J/s. 1 horsepower = 746 W.
1 kilowatt-hour (kWh) = 3.6 x 10⁶ J; it is the "unit" on an electricity bill.
Law of conservation of energy: energy can be changed from one form to another but neither created nor destroyed.
Pressure = force / area. Unit: pascal (Pa) = N/m². Same force on a smaller area gives more pressure (needle, knife).
Atmospheric pressure at sea level: about 1.013 x 10⁵ Pa = 760 mm of mercury = 1 atm. Measured by a barometer (invented by Torricelli, 1643).
Pascal's law: pressure applied to an enclosed fluid is transmitted equally in all directions. Used in the hydraulic lift and hydraulic brakes.
Archimedes' principle: a body in a fluid feels an upward buoyant force equal to the weight of fluid displaced.
Bernoulli's principle: where the speed of a fluid is higher, its pressure is lower.
Density = mass / volume. Water: 1000 kg/m³ (1 g/cm³) at 4 °C.

Explained

Energy forms and transformation

Device	Conversion
Electric generator	mechanical to electrical
Electric motor	electrical to mechanical
Microphone	sound to electrical
Solar cell	light to electrical
Battery (discharging)	chemical to electrical

Efficiency = useful output energy / input energy. No machine is 100% efficient.
Levers and other simple machines trade force for distance; they do not give extra energy.

Atmospheric pressure in daily life

Pressure falls with altitude, so water boils at a lower temperature on mountains; a pressure cooker raises the pressure so water boils above 100 °C and cooks faster.
Drinking through a straw and a dropper work because of pressure difference with the atmosphere.
A manometer measures gas pressure; a sphygmomanometer measures blood pressure.

Floating and sinking

A body floats if its average density is less than the fluid's; it sinks if more.
Ice floats on water because its density (about 917 kg/m³) is lower than water's.
A steel ship floats because its hollow shape displaces a large weight of water.
A submarine dives by filling ballast tanks with water and rises by expelling it.
The Plimsoll line on a ship's hull shows the safe loading limit for different waters.
Swimming is easier in sea water than in a river, and easiest in the Dead Sea, because denser water gives a larger buoyant force.
Hydrometer measures the density of liquids; lactometer checks the purity of milk.

Bernoulli in practice: aircraft wing lift (air faster over the curved top, lower pressure above), spray bottle and atomiser, and the pull of a passing train on a person standing too close.

Common traps

✗ "Kilowatt-hour is a unit of power." ✓ It is a unit of energy (3.6 x 10⁶ J); kilowatt is power.
✗ "Carrying a heavy load while standing still is work in physics." ✓ No displacement means zero work.
✗ "Pascal's law is about buoyancy." ✓ Buoyancy is Archimedes; Pascal is about transmission of pressure.
✗ "Barometer was invented by Pascal." ✓ Torricelli (1643).
✗ "Ice floats because it is lighter in mass." ✓ It floats because its density is lower.
✗ "Bernoulli says faster fluid has higher pressure." ✓ Faster fluid has lower pressure.

Quick revision

Work in joule; power in watt; 1 hp = 746 W.
1 kWh = 3.6 x 10⁶ J (energy).
KE = ½mv²; PE = mgh.
Pressure in pascal; 1 atm = 760 mm Hg = 1.013 x 10⁵ Pa.
Barometer: Torricelli.
Pascal: hydraulic lift and brakes.
Archimedes: buoyancy = weight of fluid displaced.
Bernoulli: faster flow, lower pressure; aircraft lift.
Lactometer: milk; hydrometer: liquid density.

Go deeper: Deeper, Mains writing (beyond what APPSC Paper I usually asks)

Deeper Advanced

Work-energy theorem: net work done on a body equals its change in kinetic energy.
Power as force x velocity. This links engine power and speed.
Hydraulic machines multiply force by the ratio of piston areas, but the smaller piston moves proportionally further, so work is conserved.
Surface tension causes drops to be spherical and lets insects walk on water; soap lowers surface tension. Capillary rise lifts water in thin tubes and plant stems. Viscosity is the internal friction of fluids; it falls as liquids are heated and rises as gases are heated.
Terminal velocity: a falling body in a fluid stops accelerating when drag plus buoyancy equals weight. Parachutes lower terminal velocity by increasing drag.
Magnus effect explains the swing of a spinning cricket or football; Bernoulli's principle alone is a simplified account.

Mains writing Mains writing

Frame: energy conservation and fluid laws underlie both everyday technology and national energy debates.
Analysis:
- Efficiency losses (heat in power stations, transmission) are why efficiency programmes save as much as new supply.
- Hydraulic systems are the basis of heavy equipment and aircraft controls.
- Understanding pressure explains why high-altitude operations need pressurised cabins.
Way forward: promote high-efficiency appliances and star-rating labels to cut wasted energy.
Example: hydroelectric dams convert gravitational potential energy of stored water to electricity; thick, curved dam walls resist pressure that increases with depth.

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2.1.2 Work, energy, pressure and fluids: Pascal, Archimedes and Bernoulli

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