Fluid Mechanics: Physics of Liquids and Gases

What Is Fluid Mechanics?

Fluid mechanics is the branch of physics that studies the behavior of fluids — liquids and gases — at rest and in motion. A fluid is any substance that flows and takes the shape of its container, from water and hydraulic oil to compressed air and steam. Unlike solids, fluids cannot permanently resist shear stress — any applied shear force, however small, causes them to deform continuously.

Understanding fluid mechanics is essential for designing piping systems, sizing pumps, optimizing heat exchangers, and troubleshooting pressure problems in any industrial plant.

Viscosity: Internal Resistance to Flow

Viscosity (μ) is a fluid's internal resistance to flow. It relates shear stress to the rate of deformation:

τ = μ × (du/dy)

Where τ is shear stress (Pa), μ is dynamic viscosity (Pa·s), and du/dy is the velocity gradient perpendicular to flow.

Industrial fluid viscosities:

Viscosity changes with temperature — in liquids it decreases as temperature rises (hot oil flows more easily), while in gases it increases. This explains why hydraulic systems perform differently in winter and summer.

Continuity Equation: What Goes In Must Come Out

The continuity equation expresses conservation of mass for incompressible flow in a closed conduit:

A₁ × v₁ = A₂ × v₂

Where A is cross-sectional area and v is flow velocity. When a pipe narrows, velocity increases. When it widens, velocity decreases. This principle governs the design of nozzles, diffusers, and every transition fitting in industrial piping.

Bernoulli's Equation: Energy in Fluids

Bernoulli's equation states that along a streamline in ideal (inviscid, incompressible) flow, total energy per unit volume is constant:

P + ½ρv² + ρgh = constant

Where:

• P = static pressure (Pa)
• ½ρv² = dynamic pressure — kinetic energy per unit volume
• ρgh = hydrostatic pressure — potential energy per unit volume
• ρ = fluid density (kg/m³)
• g = gravitational acceleration (9.81 m/s²)
• h = elevation (m)

Key insight: When velocity increases, pressure decreases — and vice versa. This principle explains:

• Venturi tube: A constriction increases velocity and drops pressure — used industrially to measure flow rates
• Atomizer: High-speed air creates low pressure that draws liquid upward — the principle behind industrial paint sprayers
• Aircraft lift: Air moves faster over the wing's upper surface, creating a pressure difference that generates lift

Reynolds Number: Laminar or Turbulent?

The Reynolds number (Re) is the most important dimensionless number in practical fluid mechanics. It determines whether flow is laminar (smooth, orderly) or turbulent (chaotic, mixed):

Re = ρ × v × D / μ

Where ρ is density, v is velocity, D is pipe inner diameter, and μ is dynamic viscosity.

Flow classification:

Example: Water flowing in a 50 mm pipe at 2 m/s. Density = 1000 kg/m³, viscosity = 0.001 Pa·s:

Re = 1000 × 2 × 0.05 / 0.001 = 100,000

This is clearly turbulent — which is the dominant regime in most industrial applications.

Laminar vs. Turbulent Flow

Laminar Flow

In laminar flow, fluid moves in parallel layers with no mixing. The velocity profile is parabolic — zero at the wall, maximum at the center. It follows the Hagen-Poiseuille equation:

Q = π × D⁴ × ΔP / (128 × μ × L)

Flow rate scales with the fourth power of diameter — doubling the diameter increases flow 16-fold. This explains why small-bore tubing creates severe pressure problems in hydraulic systems.

Turbulent Flow

In turbulent flow, random eddies mix the fluid vigorously. This is beneficial in heat exchangers where turbulence dramatically improves heat transfer. However, it increases pressure drop and demands more pump energy.

Pipe Flow: Practical Calculations

In industrial design, calculating pressure loss in pipes is essential for pump selection. The Darcy-Weisbach equation uses a friction factor f:

ΔP = f × (L/D) × (ρv²/2)

Where L is pipe length and D is diameter. The friction factor depends on Reynolds number and internal surface roughness, determined from the Moody chart or empirical correlations.

Beyond straight-pipe friction, minor losses occur at bends, valves, and sudden expansions:

ΔP_minor = K × (ρv²/2)

Where K is a loss coefficient depending on the fitting type — standard 90° elbow (K ≈ 0.9), fully open ball valve (K ≈ 0.05), half-closed gate valve (K ≈ 5.6).

Industrial Applications

Cooling Water Networks

In plastics factories, cooling water circulates in closed loops from chillers to molds and back. Engineers calculate total pressure loss across the network to select pumps with the correct head and flow capacity. Adding a production line requires recalculating the entire network because additional flow changes the pressure balance.

Hydraulic Systems

In metal presses and shearing machines, hydraulic oil operates at 150-350 bar. Correct design requires calculating flow velocity in every tube to keep Reynolds number within the laminar range (Re < 2300) — turbulent flow in hydraulic systems causes noise, erosion, and excessive oil heating.

Compressed Air

Compressed air networks in workshops typically operate at 6-8 bar. Leaks and undersized piping cause pressure drops that waste compressor energy. A practical rule: every 1 bar pressure drop increases energy consumption by approximately 7%. Regular leak detection saves thousands of dollars annually.

Summary of Key Equations

Fluid mechanics is not abstract theory — every pipe, pump, and valve in a plant operates by these laws. Understanding them means designing more efficient systems and catching pressure problems before they become costly failures.