Summary of Fluid Mechanics | Module 1 | Numericals on Properties of Fluid | Part 1 (Lecture 6)

Summary of Video: Fluid Mechanics | Module 1 | Numericals on Properties of Fluid | Part 1 (Lecture 6)

This lecture by Gopal Sharma focuses on solving numerical problems related to fundamental properties of fluids in Fluid Mechanics. The video covers various concepts such as Relative Density, Viscosity, Surface Tension, shear stress, velocity distribution, Newton’s law of Viscosity, and Terminal Velocity, with detailed step-by-step solutions and explanations.

Relative Density (RD) or specific gravity is the ratio of the density of a liquid to the density of water.
Given Relative Density and temperature, density of the liquid can be calculated using:
ρ_liquid = RD × ρ_water
Unit weight (γ) is calculated as:
γ = ρ × g
Example numerical: Liquid at 10°C with RD = 0.8 and kinematic Viscosity given; find density, unit weight, and dynamic Viscosity.

Kinematic Viscosity (ν) and dynamic Viscosity (μ) are related by:
μ = ρ × ν
Units conversion between centistokes (cSt), m²/s, and Pascal-second (Pa·s) is emphasized.
Dynamic Viscosity is often required in Pascal-second for calculations.

Work done in forming a soap bubble is related to Surface Tension (σ) and change in surface area (ΔA):
W = σ × ΔA
For a soap bubble, two surfaces exist, so total surface area is twice the surface area of a sphere.
Important to distinguish between soap bubbles (two surfaces) and droplets (one surface).

When two plates are separated with a liquid film between them, Surface Tension creates an excess pressure.
Force required to pull the plates apart is derived from balancing pressure force and Surface Tension force.
Key formula derived for force:
F = (π d² h σ) / 2
where d is diameter, h is height, and σ is Surface Tension.

Velocity distribution in fluid flow and shear stress on walls are calculated using Newton’s law:
τ = μ (du/dy)
Velocity profiles can be nonlinear (parabolic) or approximated as linear in very thin fluid films (order of millimeters).
Shear stress is calculated by differentiating velocity distribution with respect to distance from the wall.

In narrow passages or thin films, velocity profile can be approximated as linear.
The velocity of fluid at the boundary matches the velocity of the solid surface (no-slip condition).
This linear approximation simplifies calculations in lubrication and thin film flow problems.

Terminal Velocity is the velocity at which net force on a sliding block is zero (forces balance).
Forces considered: component of weight down the incline, frictional resistance due to viscous lubrication (skin drag).
Skin drag force is calculated using shear stress and contact area.
Equations of motion balance weight component and viscous resistance to find Terminal Velocity.

When a plate is placed between two parallel plates separated by fluid layers with different viscosities, the position of the plate affects resistance to motion.
The goal is to find the position where the total viscous resistance (sum of shear forces from both fluids) is minimized.
Using linear velocity profiles and Newton’s law of Viscosity, a formula is derived for the position y of the intermediate plate:
y / (x - y) = √(μ₁ / μ₂)
where x is total gap, μ₁ and μ₂ are viscosities of upper and lower fluid layers respectively.

Calculating Density and Unit Weight from Relative Density
- Identify given Relative Density and temperature.
- Use standard water density at that temperature.
- Multiply Relative Density by water density to get fluid density.
- Calculate unit weight by multiplying density by gravitational acceleration.
Converting Kinematic Viscosity to Dynamic Viscosity
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