Technical Terms Fluid Mechanics

Overview

Engineering reference data for Technical Terms Fluid Mechanics in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Glossary of Key Terms

Acoustic Theory

The mathematical description of sound waves, fundamental to acoustical engineering and noise control in HVAC systems.

Aerodynamics

The study of the flow of gases, particularly as it relates to the design of vehicles and structures moving through air.

Boundary Layer

The thin layer of fluid in the immediate vicinity of a bounding surface where viscous effects are significant. The boundary layer can be laminar, transitional, or turbulent.

Cavitation

The formation and collapse of vapor bubbles in a liquid when local pressure drops below the vapor pressure. Characterized by Net Positive Suction Head (NPSH) requirements in pump systems.

Coanda Effect

The tendency of a fluid stream to stay attached to a convex surface rather than follow its original straight-line trajectory.

Conservation Laws

Fundamental principles stating that measurable properties of an isolated physical system (mass, energy, momentum) remain constant as the system evolves.

Froude Number

A dimensionless number defined as the ratio of flow inertia to gravitational forces:

$Fr = \frac{v}{\sqrt{gL}}$

where $v$ is flow velocity, $g$ is gravitational acceleration, and $L$ is characteristic length.

Euler Number

A dimensionless number representing the relationship between pressure forces and inertial forces:

$Eu = \frac{\Delta p}{\rho v^2}$

Hydraulics

The branch of science and engineering concerned with the mechanical properties and use of liquids, particularly water.

Hydrodynamics

Fluid dynamics applied specifically to liquids such as water, alcohol, and oil.

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Dimensionless Numbers Reference

Number	Formula	Ratio	Application
Froude	$Fr = v/\sqrt{gL}$	Inertia to gravity	Free-surface flows
Euler	$Eu = \Delta p/(\rho v^2)$	Pressure to inertia	Pressure drop analysis
Reynolds	$Re = \rho vL/\mu$	Inertia to viscosity	Flow regime determination

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Flow Regime Classification

Fluid flow can be classified based on the Reynolds number:

Flow Type	Reynolds Number Range	Characteristics
Laminar	$Re < 2300$	Smooth, orderly layers
Transitional	$2300 < Re < 4000$	Intermittent turbulence
Turbulent	$Re > 4000$	Chaotic, mixing occurs

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Conservation of Mass

The law of conservation of mass states that mass can neither be created nor destroyed. For fluid mechanics, this is expressed through the continuity equation:

$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0$

For incompressible flow ($\rho = \text{constant}$), this simplifies to:

$\nabla \cdot \mathbf{v} = 0$

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Viscosity Types

Type	Symbol	SI Unit	Description
Dynamic (Absolute)	$\mu$	Pa·s	Resistance to shear stress
Kinematic	$\nu$	m²/s	Dynamic viscosity divided by density

The relationship between viscosity types:

$\nu = \frac{\mu}{\rho}$

Common unit conversions:

• 1 cP (centipoise) = 0.001 Pa·s
• 1 cSt (centistoke) = 10⁻⁶ m²/s

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Flow Coefficient Standards

Standard	Symbol	Definition	Region
US	$C_v$	Flow rate (gpm) at 1 psi differential	North America
International	$K_v$	Flow rate (m³/h) at 1 bar differential	Europe/Asia

Conversion between standards:

$K_v = 0.857 \times C_v$

References

• Original Source