Terminal Settling Velocity of a Solid Particle in Fluid - Maple Programming Help

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Terminal Settling Velocity of a Solid Particle in Fluid

Introduction

This application calculates the terminal velocity of a solid particle settling in a fluid.

 

Deriving the Settling Velocity

restart:

Drag force

Fd12πDia24CDρ__fv2:

Buoyancy force

Fbρ__pρ__fgπDia36:

The terminal settling velocity is reached when the drag force equals the buoyancy force. Hence, the settling velocity is given by the following equation.

 

resv__terminal=solveFb=Fd,v1

resv__terminal=23CDρ__fgDiaρ__fρ__p3CDρ__f

(2.1)

Parameters

Gravity:

g9.81:


Density of the particle:

ρ__p1800:


Fluid density:

ρ__f994.6:


Fluid viscosity:

μ0.0008931:


Particle diameter:

Dia0.000208:

 

Governing Equations

Drag coefficient:

CDRey&lcub;24ReyRey<0.124Rey1&plus;0.14Rey0.70.1Rey10000.441000Rey3500000.198104ReyRey&gt;350000&colon;

ReynoldsNumberRey&equals;Dia &rho;__f v__terminal&mu;&colon;

 

TerminalVelocityv__terminal&equals;4g&rho;__p&rho;__fDia3CDRey&rho;__f&colon;

 

Solution

fsolveReynoldsNumber&comma;TerminalVelocity&comma;v__terminal&comma;Rey&semi;

Rey=3.656696458&comma;v__terminal=0.01578618582

(5.1)