Physics MCAT Chapter 4: Fluids

4.1 Characteristics of Fluids

Definition: Fluids can be either gas or liquid; anything that can flow.
Shear Forces: Fluids are weak to shear (tangential) forces unlike solids.
- Example: A desk doesn't move when touched, but water ripples.
Density (ρ):
- Formula: ( \rho = \frac{\text{mass}}{\text{volume}} )
- SI Units: kg/m³; commonly used: g/cm³.
Weight of an Object:
- Formula: Weight = ρ × Volume × Gravitational Acceleration.
Specific Gravity:
- Comparison of an object's density to that of water.
- Formula: ( \text{Specific Gravity} = \frac{\rho}{1 \text{ g/cm}^3} )
Pressure (P):
- Formula: ( P = \frac{\text{Force}}{\text{Area}} )
- Units: Pascals (Pa); conversions between atm, torr, mmHg are essential for MCAT.
Types of Pressure:
- Absolute Pressure: Total pressure on an object.
- Atmospheric Pressure: Varies with altitude.
- Hydrostatic Pressure: Pressure exerted by a fluid; ( P = P_0 + \rho gh ).
- Gauge Pressure: ( P_{\text{gauge}} = P_{\text{absolute}} - P_{\text{atmosphere}} ).

Pascal's Principle:
- Pressure applied to an incompressible fluid is transmitted throughout in a closed system.
- Used in hydraulic systems for mechanical advantage.
Work and Volume Relations:
- Volume = Area × Distance.
- Work related to pressure: ( W = \text{Pressure} \times \Delta \text{Volume} ).
Archimedes' Principle:
- Buoyant Force = Weight of displaced fluid.
- Object in equilibrium: Gravitational force equals buoyant force.
Surface Tension:
- High cohesion: Convex shape.
- High adhesion: Concave meniscus.

Viscosity (η):
- Resistance to flow, units: Pascal-seconds.
- Ideal fluids are inviscid (no viscosity).
Flow Types:
- Laminar Flow: Orderly and predictable.
- Turbulent Flow: Chaotic; occurs at high velocities.
Flow Rate:
- Poiseuille's Law: ( Q = \frac{\pi r^4 \Delta P}{8 \eta L} ).
- Key aspects: Radius and pressure differences highly affect flow rate.
Critical Speed: Speed where flow becomes turbulent.
Streamlines:
- Volume flow rate is constant: ( Q = v A ).
- Velocity inversely proportional to cross-sectional area.
Bernoulli's Equation:
- Combines dynamic and static pressure: ( P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} ).
- Demonstrates conservation of energy in fluid flow.
Venturi Effect:
- Shows inverse relationship between speed and pressure in a fluid.

Applications:
- Circulatory and respiratory systems as closed loops.
- Use fluid dynamics concepts to analyze physiological functions.

Conclusion: Understanding of fluid mechanics is essential for solving problems in physics and physiology, especially relevant for the MCAT.