Fluid Mechanics Study Notes

Common Phases of Matter: Solid, Liquid, Gas
- Solid: Maintains fixed size and shape, requires large force to change volume or shape.
- Liquid: Takes shape of its container, flows, not readily compressible, volume changes only with large force.
- Gas: Neither fixed shape nor volume, expands to fill container.
Plasma: Fourth phase at high temperatures, consists of ionized atoms.
Colloids/Liquid Crystals: Some argue for separate classifications.

Density (ρ): Defined as mass per unit volume: $ ho = rac{m}{V}$ (where m is mass and V is volume).
- *SI Unit: kg/m³
- *Common Units: g/cm³; to convert g/cm³ to kg/m³ multiply by 1000.
Specific Gravity (SG): Ratio of density of substance to density of water at 4°C: $ext{SG} = rac{ ho}{ ho_{ ext{water}}}$ (dimensionless number).
- For example, lead (11.3) and alcohol (0.79).
Density Table (Table 10–1): Lists densities of various substances at specific conditions.
Example of Density Calculation: For a solid iron wrecking ball with radius 18 cm:
- Volume $V$ calculated using: $V = rac{4}{3} imes ext{π} imes r^3$
- Mass from density $m = ho V$ .

Pressure (P): Defined as force per unit area: $P = rac{F}{A}$ (N/m² or Pa).
Calculate pressure using:
- Example: For a person’s feet covering area of 0.050 m² weighing 60 kg at 9.8 m/s² -> $P = rac{mg}{A}$ .
Fluid Pressure: Exerts equally in all directions and acts perpendicularly on surfaces.
Fluid Pressure Variation with Depth:
- At depth $h$ : $P = ho g h$
- Concepts of pressure due to weight of fluid.

Atmospheric Pressure: Average at sea level: 1 atm = $1.013 imes 10^5 ext{N/m}^2$ .
Gauge Pressure: Pressure above atmospheric pressure: $P = P_G + P_0$ , where $P_G$ is gauge pressure.

Pascal’s Principle: External pressure on a confined fluid transmits uniformly throughout the fluid.
Applications of hydraulic systems in applications such as car brakes, with force ratios dependent on cross-sectional areas.

Measuring Pressure with Device Types:
- Open-Tube Manometer: Relation $P = P_0 + ho g ext{height}$ .
- Aneroid Barometer: Measures altitude and various pressure readings.

Buoyant Force: Exerts upward force on submerged objects, equal to weight of fluid displaced. Archimedes’ principle applies to all objects (submerged or floating).

Flow Types: Streamline (laminar) and turbulent flow.
Equation of Continuity: $A_1 v_1 = A_2 v_2$ ; for fluids in pipes, constant mass flow rate if incompressible.

Real-world examples include: Torricelli’s theorem for spigots, lift on airplane wings, blood flow dynamics, etc.

Viscosity (η): Measure of a fluid's internal friction; defined via $F = A rac{dv}{dy}$ .
SI units of viscosity are Pa·s.

Poiseuille’s Equation: $Q = rac{ ho R^4 riangle P}{8 heta L}$ ; describes flow rate of viscous fluids in cylindrical tubes.

Surface Tension (γ): Force per unit length at the liquid's surface, defined by $ext{SV} = rac{F}{l}$ .
Capillarity: Varies with adhesive versus cohesive forces, determines how far liquids rise in narrow tubes.

Common Phases of Matter: Solid, Liquid, Gas.
Solid: Maintains fixed size and shape, requires large force to change volume or shape.
Liquid: Takes shape of its container, flows, not readily compressible, volume changes only with large force.
Gas: Neither fixed shape nor volume, expands to fill container.
Plasma: Fourth phase at high temperatures, consists of ionized atoms. Plasma contains free electrons and ions, typically found in stars, including the sun.
Colloids/Liquid Crystals: Some argue for separate classifications. Colloids have particle sizes between those of solutions and suspensions, while liquid crystals exhibit properties of both liquids and solids, often found in LCD screens.