1: Fluid definition and properties

Section 1: Fundamental Concepts

1: Fluid Definition and Properties

A fluid is a substance that continuously deforms (flows) under the application of a shear stress, no matter how small that stress may be. This fundamental characteristic distinguishes fluids (liquids and gases) from solids. Solids resist shear stress with static deformation, while fluids flow indefinitely. Liquids maintain a relatively fixed volume and form a free surface under gravity, whereas gases expand to fill any container.

Key Properties Governing Fluid Behavior:

1. Density ($\rho$):
   Defined as mass per unit volume ($\rho = m/V$), measured in kg/m³ (SI) or slugs/ft³ (US Customary). Density is a measure of how tightly packed the fluid molecules are. Liquids are generally incompressible (constant density under most conditions), while gases are highly compressible (density varies with pressure and temperature).
2. Specific Weight ($\gamma$):
   Represents the weight per unit volume ($\gamma = \rho g$), where $g$ is gravitational acceleration. Units are N/m³ or lb/ft³. It indicates the fluid's weight density under gravity.
3. Specific Gravity ($SG$):
   A dimensionless ratio of the fluid’s density to the density of water at a standard reference condition (typically 4°C, where $\rho_{\text{water}} \approx 1000$ kg/m³). $SG = \rho_{\text{fluid}} / \rho_{\text{water}}$. For example, mercury has $SG \approx 13.6$.
4. Viscosity ($\mu$, $\nu$):
   Quantifies a fluid's resistance to shearing motion or internal friction.
   • Dynamic Viscosity ($\mu$): Relates shear stress ($\tau$) to the rate of shear strain ($du/dy$) via Newton’s law of viscosity: $\tau = \mu (du/dy)$. Units: Pa·s (N·s/m²) or lb·s/ft² (slug/ft·s). Higher $\mu$ means greater resistance to flow (e.g., honey vs. water).
   • Kinematic Viscosity ($\nu$): Defined as $\nu = \mu/\rho$. Units: m²/s or ft²/s. Accounts for both viscous and inertial effects, crucial in dynamic similarity (e.g., Reynolds number).
     Newtonian fluids (water, air) follow Newton’s law; non-Newtonian fluids (ketchup, blood) do not.

Other Critical Properties (Briefly):

• Compressibility: Measures change in volume/density with pressure (important for gases and high-speed liquid flows).
• Surface Tension: Causes liquid surfaces to minimize area (relevant for droplets, bubbles, capillary action).
• Vapor Pressure: Pressure at which a liquid boils at a given temperature; critical for cavitation analysis.

Understanding these properties is essential for analyzing fluid statics, predicting flow behavior, applying conservation laws, and designing fluid systems. Density and viscosity, in particular, appear ubiquitously in equations governing fluid motion and scaling (dimensional analysis).