Definitions [11]
Define Poisson’s ratio.
Poisson’s ratio, which is defined as the ratio of relative contraction (lateral strain) to relative expansion (longitudinal strain).
It is denoted by the symbol μ.
Poisson’s ratio, μ = `"Lateral strain"/"Longitudinal strain"`
Define strain.
Strain is defined as the ratio of change in size to the original size of an object. It measures the degree of deformation.
Strain, ε = `"Change in size"/"Original size" = (Δ"L")/"L"`
Define stress.
The force per unit area is called as stress.
Stress, σ = `"Force"/"Area" = "F"/"A"`
Define velocity gradient.
The rate of change of velocity (dv) with distance (dx) measured from a stationary layer is called velocity gradient.
∴ Velocity gradient = `(dv)/dx`
The property of a fluid by virtue of which it opposes the relative motion between its different layers, with the force that comes into play, is called viscosity; and that force is called the viscous force.
where η is the coefficient of viscosity.
Define the coefficient of viscosity of a liquid.
The coefficient of viscosity of a liquid is defined as the viscous force acting tangentially per unit area of a liquid layer having a unit velocity gradient in a direction perpendicular to the direction of flow of the liquid.
Define terminal velocity.
The maximum constant velocity acquired by a body while falling freely through a viscous medium is called the terminal velocity VT.
Define the surface tension of a liquid.
Surface tension is defined as the force acting on a unit length of an imaginary line drawn on the free surface of the liquid, the direction of the force being perpendicular to the line so drawn and acting parallel to the surface.
Define angle of contact.
When a liquid is in contact with a solid, the angle between the tangent drawn to the free surface of the liquid and the surface of solid at the point of contact measured inside the liquid is called the angle of contact.
Define surface tension.
Surface tension is defined as the force per unit length acting at right angles to an imaginary line drawn on the free surface of the liquid.
Define the angle of contact for a given pair of solid and liquid.
The angle between tangents drawn at the point of contact to the liquid surface and the solid surface inside the liquid is called the angle of contact for a pair of solid and liquid. It is denoted by θ.
Theorems and Laws [1]
Statement:
"According to this theorem, the total energy (pressure energy, potential energy and kinetic energy) per unit volume or mass of an incompressible and non-viscous fluid in steady flow through a pipe remains constant throughout the flow, provided there is no source or sink of the fluid along the length of the pipe."
Mathematical Form:
For unit volume of liquid flowing through a pipe:
\[P+\rho gh+\frac{1}{2}\rho v^2\] = constant
where:
- P = pressure energy per unit volume
- ρ = density of the fluid
- g = acceleration due to gravity
- h = height of the fluid (potential energy term)
- v = velocity of the fluid (kinetic energy term)
Applications of Bernoulli's Theorem:
- Speed of efflux
- Venturi tube
- Lifting up of aeroplane
- Working of an atomizer
- Blowing off of roofs by stormy wind
Key Points
Types of Properties
-
Physical Properties — can be observed or measured without altering the chemical nature of the substance. Examples: colour, odour, melting point, boiling point, density.
-
Chemical Properties — involve a chemical change in the substance; the original substance is converted into something new. Example: burning coal produces CO₂.
SI Fundamental Units
The International System of Units (SI) defines seven base units that serve as building blocks for all scientific measurement:
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Mass | Kilogram | kg |
| Temperature | Kelvin | K |
| Length | Metre | m |
| Time | Second | s |
| Electric Current | Ampere | A |
| Amount of Substance | Mole | mol |
| Luminous Intensity | Candela | cd |
Key Notes to Remember:
- Mass measures the quantity of matter and is independent of location. Weight depends on gravity — the same object has different weight on Earth vs. the Moon, but identical mass.
- Temperature and heat are not the same. Heat is energy being transferred; temperature tells us the direction of that transfer.
- 0°C = 32°F; 100°C = 212°F. A rise of 1°C corresponds to a rise of 9/5°F on the Fahrenheit scale.
- Units can be written in two equivalent ways: g/cm³ or g cm⁻³ — both are acceptable.
- A highly soluble impurity increases surface tension, while a partially soluble impurity (e.g., detergent) decreases it; a waterproofing agent increases it.
- Surface tension decreases with increase in temperature, given by T = T0(1 − αθ), where T0 is surface tension at 0°C and α is the temperature coefficient.
- When a soap bubble is charged (positively or negatively), force acts outward on the surface, increasing its radius — thus electrification always decreases surface tension.
