Surface Tension and Liquid Behavior Quiz

Chapter 2: Force & Motion in Fluids (7%)

• Fluids adapt to container boundaries, unlike solids. They flow when external force is applied.
• Examples include water, honey, water vapor, and oxygen.
• Acceleration due to gravity (g) is calculated using Newton's law of gravitation.
• The acceleration 'g' is independent of the body's mass.
• Acceleration 'g' also remains relatively constant near the earth's surface.
• Acceleration due to gravity varies with altitude. It decreases as the distance from the Earth's surface increases.
• At sea level, 'g' is approximately 9.81m/s².
• For Earth, G ≈ 6.67 x 10⁻¹¹ Nm²/kg², R ≈ 6.38 x 10⁶ m, Me ≈ 5.98 x 10²⁴ kg.
• For Moon, G ≈ 6.67 x 10⁻¹¹ Nm²/kg², R ≈ 1.74 x 10⁶ m, Mm ≈ 7.35 x 10²² kg.
• The body's mass remains the same regardless of location, but weight differs due to 'g' variations.
• On the Moon, a 1kg object weighs about 1.67 N compared to 9.8N on Earth.

Motion of a Body Falling in Uniform Gravitational Field with Fluid (Air) Resistance

• A falling body experiences gravitational and resisting forces in opposite directions.
• Terminal velocity is the maximum constant velocity reached when resisting force equals the weight.
• Terminal velocity (vt) is calculated using the equation vt = mg/k, where k is a constant.
• Velocity increases exponentially initially and approaches a constant value (terminal velocity).
• Acceleration decreases exponentially with time. As the body reaches terminal velocity, acceleration becomes zero.

Surface Tension

• Surface tension (s) is a property of a liquid's free surface. It tends to minimize surface area.
• The surface acts like a stretched membrane due to cohesive forces within the liquid.
• Spheres have the least surface area for a given volume.
• Surface tension is force per unit length perpendicular to an imaginary line on the liquid's surface (SI unit: N/m).
• Surface tension decreases with increasing temperature.
• Highly soluble substances increase surface tension, while sparingly soluble ones decrease it.
  • Examples of surface tension applications include: droplet formation, soap bubbles, insects walking on water.
• Molecular theory of surface tension: Surface molecules are pulled inward by cohesive forces.
• Surface molecules have higher potential energy than molecules inside the liquid.

Molecular Theory for Surface Tension

• Molecules at the surface experience a net downward force to the interior.
• Moving a molecule from the interior to the surface requires work (increase in potential energy).
• Liquid surfaces tend to have minimum surface area.

Surface Film

• Surface film is a thin layer of liquid near the surface, with a thickness equal to the molecular range of the liquid.
• Molecules in this film experience an inward cohesive force.

Factors Affecting Surface Tension

• Surface tension is inversely proportional to temperature.
• Highly soluble substances increase surface tension, while sparingly-soluble substances decrease it.
• Examples include detergent effects, which reduce surface tension, thereby improving cloth cleaning efficiency.

Applications of Surface Tension

• Washing cloths with soap
• Adding flux in soldering
• Spreading of antiseptics
• Floating of objects like ducks on water.

Relation between Surface Tension and Surface Energy

• Surface energy is potential energy per unit area of a liquid's surface.
• The work required to increase a liquid's surface area is stored as surface energy.
• Surface energy is equal to surface tension: T = W/ΔA

Rotation Between Liquid Tension and Surface Energy

• Liquid films have two free surfaces, so work done is double the surface tension times the change in area (2TΔA).
• Surface energy and surface tension relate as T = W/ΔA.

Types of Fluid Flow

• Streamline flow: All particles follow the same path and have same velocity at a given point.
• Tube of flow: Streamlines enclosed by a tube through which a fluid moves.

Laminar Flow

• A continuous flow in parallel layers. Adjacent layers do not mix. Ideal condition for a uniform flow pattern. Velocity is constant.

Turbulent Flow

• Disordered flow with mixing of layers. High speeds and irregularities. Velocity is not constant.

Critical Velocity

• Velocity beyond which fluid flow becomes turbulent.

Viscosity of Fluids

• Resistance to flow due to friction between adjacent layers.
• Affected by temperature and fluid nature (liquids are more viscous than gases).
• Laminar flow is ideal for low velocities and high viscosity.
• Turbulent flow results from high speeds and low viscosity. (Low viscosity means more mixing.)

Reynolds Number

• A dimensionless quantity that predicts the flow pattern (laminar or turbulent).

Bernoulli's Principle

• In a steady streamline flow of an ideal fluid, the total energy (pressure + kinetic + potential) per unit mass remains constant throughout the liquid.
• Relationship: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

Capillarity

• The rise or fall of a liquid in a narrow tube (capillary).
• Depends on the liquid's surface tension, contact angle, and the tube's radius.

Equation of Continuity

• For incompressible fluids: A₁v₁ = A₂v₂ (A= area, v = velocity)
• Volume flow rate is constant.