Engineering Equations, Numbers, Diagrams and Charts: Reynolds Number

Introduction

The Reynolds Number expresses the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces and consequently quantifies the relative importance of these two types of forces for given flow conditions. The Reynolds number is a dimensionless number. High values of the parameter (on the order of 10 million) indicate that viscous forces are small and the flow is essentially inviscid.

$\mathrm{Re} = \dfrac{ \mbox{inertial forces} }{ \mbox{viscous forces} } = {{\rho {\mathbf v} L} \over {\mu}} = {{{\mathbf v} L} \over {\nu}}$

For Pipes

$\mathrm{Re} = {{\rho {\mathbf v} D_H} \over {\mu}} = {{{\mathbf v} D_H} \over {\nu}} = {{{\mathbf Q} D_H} \over {\nu}A}$

${D_H}$ = Hydraulic Diameter (m)

${\mathbf Q}$ = Volumetric flow rate (m3/s)

${A}$ = Pipe cross-sectional area (m²)

${\mathbf v}$ = Mean Velocity of the Fluid (m/s)

${\mu}$ = Dynamic Viscosity of the fluid (Pa·s = N·s/m² = kg/(m·s)).

${\nu}$ = Kinematic Viscosity of the fluid (

\nu = \mu /{\rho})

(m²/s).

Explanation

At relatively low values of the Reynolds number, the viscous force is relatively more important, and disturbances in the flow are damped out by viscosity. Thus, it is difficult for disturbances to grow and sustain themselves. On the other hand, at relatively large values of the Reynolds number, the damping of disturbances by viscosity is less effective, and inertia is more important, so that disturbances can perpetuate themselves. This is the basic reason why the Reynolds number serves as a measure for determining whether the flow is laminar or turbulent.

Application

They are used to characterize different flow regimes within a similar fluid, such as laminar or turbulent flow:

laminar when Re < 2300

transient when 2300 < Re < 4000

turbulent when Re > 4000

Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion, while Turbulent Flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce random eddies, vortices and other flow fluctuations.

Turbulent flow is a flow regime in which the movement of the fluid particles is chaotic, eddying, and unsteady.

Due to the complex nature of turbulent flows, scientists and engineers use empirical rather than theoretical approaches to model and design processes and machinery involving fluids.

Engineering Equations, Numbers, Diagrams and Charts

Labels

Thursday, 6 November 2014

Reynolds Number

Introduction

Explanation

Application

No comments:

Post a Comment