Fluid Mechanics Introduction: Solids vs Fluids, Stress Types

Fluids are classified as Newtonian or Non-Newtonian based on whether they obey Newton's Law of Viscosity. Newtonian fluids (water, kerosene, mercury) have linear stress-strain rate relationship. Non-Newtonian fluids are further divided into time-independent (dilatant, Bingham plastics, pseudoplastic) and time-dependent (thixotropic, rheopectic) categories. Time-independent fluids show immediate response to shear rate changes, while time-dependent fluids show viscosity changes over time under constant shear. This classification is essential for predicting fluid behavior in engineering applications.

Fluids are classified based on their response to shear stress according to Newton's law of viscosity. Newtonian fluids follow τ = μ(du/dy) with n=1, producing a straight line through the origin. Non-Newtonian fluids deviate from this linear relationship. Pseudoplastic (shear-thinning) fluids have n<1 and decrease in viscosity under shear, while dilatant (shear-thickening) fluids have n>1 and increase in viscosity under shear. Examples of Newtonian fluids include air, water, and kerosene; examples of pseudoplastic fluids include blood, paint, and alcohol; examples of dilatant fluids include cornstarch and honey.

Fluids are classified based on their viscosity behavior. Real fluids have finite viscosity and develop stress when moving tangentially over surfaces. They are divided into Newtonian and non-Newtonian fluids. Newtonian fluids obey Newton's law of viscosity, showing linear stress-velocity gradient relationships with constant viscosity (slope of graph). Non-Newtonian fluids do not obey this law, showing curved graphs with variable viscosity. The mathematical model τ = K(du/dy)^n describes non-Newtonian behavior, where K is consistency index and n is flow behavior index. Classification based on n: n > 1 indicates dilatant/shear-thickening fluids (become thicker under shear), while n < 1 indicates pseudoplastic/shear-thinning fluids (become thinner under shear). Examples include water (Newtonian) and milk/blood (non-Newtonian).

Fluids are classified into four basic types: Ideal Fluid, Real Fluid, Newtonian Fluid, and Non-Newtonian Fluid. An Ideal Fluid is defined as having no viscosity and being incompressible; however, such a fluid does not exist in practice. Real Fluids are compressible and possess some viscosity, with examples including kerosene, petrol, and castor oil. Newtonian Fluids obey Newton’s law of viscosity, meaning their viscosity depends solely on temperature and pressure, and not on the applied shear stress or rate of shear. Examples of Newtonian fluids include water, air, emulsions, petrol, and diesel. Non-Newtonian Fluids do not follow Newton’s law of viscosity; their viscosity changes with the applied shear stress or shear rate. Examples of non-Newtonian fluids include blood, ink, and toothpaste. This classification is fundamental in fluid mechanics and is relevant for competitive engineering examinations such as SSC JE, GATE, ESE, UKSSSC, UPPSC, and UKPSC.

Fluids are classified into two main categories based on their shear stress behavior. Newtonian fluids follow τ = μ(du/dy), where shear stress is directly proportional to the rate of shear strain. Non-Newtonian fluids follow the Power Law model τ = K(du/dy)^n, where apparent viscosity changes with deformation rate. Specific types include: Dilatant fluids (n>1, viscosity increases with shear rate, e.g., concentrated sugar solution), Bingham plastics (require minimum yield stress to flow, e.g., toothpaste), and Pseudo-plastic fluids (n<1, viscosity decreases with shear rate, e.g., paint).

In a static fluid under gravity, horizontal pressure distribution is uniform (∂p/∂x = 0) because no horizontal body forces or accelerations exist. Vertically, the equation -∂p/∂z = ρg leads to hydrostatic pressure distribution: p_B - p_A = ρgh. This assumes constant density and gravitational acceleration. The principle that pressure varies only with depth explains why pressure measurements at the same elevation are equal in connected fluid systems, forming the basis for manometer operation and pressure measurement techniques.

Pressure units: Pascal (N/m²), kgf/cm², Bar (10⁵ Pa), PSI. Pressure in fluid column: P = ρgh. Types: absolute (from zero), gauge (relative to atmospheric), vacuum (negative gauge). Measurement devices: barometer (atmospheric pressure using mercury), piezometer (gauge pressure using standpipe), manometer (pressure difference using U-tube). Hydrostatic force on plane surface: F = ρg h̄ A, center of pressure depth: hcp = h̄ + (Icg sin²θ)/(h̄A). For curved surfaces: horizontal force Fh = ρg h̄ A_proj, vertical force Fv = ρg V. Archimedes' principle: buoyant force equals weight of displaced fluid. For floating: body density < fluid density. Effective weight: W_eff = W - Fb. Metacentric height GM = I/V - BG determines stability: GM > 0 stable, GM < 0 unstable, GM = 0 neutral. Time period of oscillation: T = 2π√(k²/(gGM)). Rolling (about longitudinal axis) is more critical than pitching.

This section covers fluid mechanics including pressure calculations (P = F/S for contact pressure, P = ρgh for hydrostatic pressure), buoyancy (Archimedes' principle: F_A = ρ_liquid × g × V_submerged), and hydrostatic principles. The content demonstrates calculating contact areas from pressure, determining hydrostatic pressure at depth, computing buoyant forces for submerged objects in liquids and gases, and finding submerged volumes for floating objects. Key applications include brick contact area calculations, water pressure at depth, and buoyant force determination for various objects.

This comprehensive segment covers fundamental fluid statics concepts. Hydrostatic pressure is explained as P = P₀ + ρgh, with pressure changing only in the direction of gravity. Barometers measure atmospheric pressure using P = ρgh, while manometers measure pressure differences. Archimedes' principle states buoyant force equals the weight of displaced fluid (F = ρVg), always acting opposite to gravity. The instructor emphasizes that pressure changes only vertically, not horizontally, and that ρ represents the density of the liquid or air being measured.

Fluid statics examines fluids at rest. Core concepts include: (1) Absolute pressure equals atmospheric plus gauge pressure (P_abs = P_0 + P_gauge); (2) Standard atmospheric pressure is 1 atm = 1.013 × 10^5 Pa = 101 kPa = 760 mmHg; (3) For connected fluids of same type at same level, pressures are equal; (4) Buoyancy force equals weight of displaced fluid (F_B = ρ_fluid × V_displaced × g); (5) Pascal's principle states pressure applied to confined fluid is transmitted undiminished throughout. These principles enable analysis of pressure distribution, floating bodies, and hydraulic systems.

This comprehensive section covers the fundamental principles of fluid flow analysis essential for refrigeration and air conditioning systems. The three conservative equations are conservation of mass, conservation of momentum, and conservation of energy. Conservation of mass leads to the continuity equation (A1V1 = A2V2 for steady incompressible flow). Conservation of linear momentum (Newton's Second Law for control volumes) is applied to find forces on nozzles, bends, and pipe walls. Bernoulli equation relates pressure, velocity, and elevation along streamlines under assumptions of steady, one-dimensional, incompressible, and inviscid flow. For real fluids, it is modified with a head loss term. Practical applications include Venturi meter flow measurement and pump/fan power calculations. The section also covers compressible vs incompressible flow, with incompressible assumption valid when Mach number < 0.3.

Fluid kinematics studies fluid motion without considering forces, using Eulerian approach (fixed space coordinates) rather than Lagrangian (tracking individual particles). Flow types include steady/unsteady (time-dependent), uniform/non-uniform (space-dependent), rotational/irrotational (particle spin), and laminar/turbulent (mixing behavior). Streamlines (imaginary lines showing velocity direction) never intersect, while pathlines and streaklines can. Bernoulli's equation (P/ρg + V²/2g + z = constant) describes energy conservation in fluid flow, with Venturi meter being a key application for measuring discharge.

Fluid flow follows two fundamental conservation laws. First, conservation of mass (A₁V₁ = A₂V₂) states that flow rate remains constant, so narrower pipes have higher velocities. Second, Bernoulli's equation (P + ½ρv² + ρgh = constant) represents energy conservation, showing that increased velocity reduces pressure. These principles explain phenomena like airplane lift, pipe flow behavior, and pressure changes in varying pipe diameters.

This comprehensive section covers the foundational principles of fluid dynamics. The conservation of mass for incompressible fluids states that mass flow rate (A × v) remains constant throughout a tube, meaning when cross-sectional area decreases, velocity increases proportionally. Flow rate, defined as volume per unit time, is constant at all cross-sections. Bernoulli's principle states that swiftly moving fluid exerts less pressure than slowly moving fluid, explaining phenomena like airplane lift, sailboat movement, and baseball curves. Bernoulli's equation (P + ½ρv² + ρgh = constant) mathematically expresses conservation of energy in fluids, showing that pressure energy, kinetic energy, and potential energy sum to a constant value along a streamline.

Bernoulli's Equation (P + ρgy + ½ρv² = constant) describes the conservation of energy in a moving fluid, where pressure energy (P), potential energy (ρgy), and kinetic energy (½ρv²) are interrelated; as fluid velocity increases, pressure decreases, which explains phenomena like curveballs (where spin creates differential airspeeds causing pressure differences that curve the ball) and why docks use piling instead of solid structures (to prevent high-pressure water buildup against boats).