Overview of Fluid Mechanics for MCAT

Apr 25, 2025

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}} ).

4.2 Hydrostatics

  • 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.

4.3 Fluid Dynamics

  • 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.

4.4 Fluids in Physiology

  • 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.