Real Fluids

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  • Topic: Viscosity, Fluid dynamics, Reynolds number
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16/11/2011

Fluid Mechanics - 4 Real Fluids

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Contents

Introduction Objectives Real Fluid Types of Flow Laminar Flow Turbulent Flow

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Introduction
 In the earlier chapter, the basic equations of continuity and energy were introduced and applied to fluid flow cases where the assumption of frictionless flow (or ideal fluid flow) was made.  It is now necessary to introduce concepts which enable the extension of the previous work to real fluids in which viscosity is accepted and frictional effects cannot be ignored.  The concept of Reynolds number as an indication of flow type will be used extensively.

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Real Fluid
• In a real fluid viscosity produces resistance to motion by causing shear or friction forces between fluid particles and between these and boundary walls. • Due to this viscous effects, fluid tends to ‘stick’ to solid surfaces and have stresses within their body. • The inclusion of viscosity allows the existence of two physically distinct flow regimes, known as laminar and turbulent flow.

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Types of Flow
• Theoretically the physical nature of fluid flow can be categorized into three types, i.e. laminar, transition and turbulent flow. • To predict whether the flow will be laminar, transition or turbulent, it is necessary to explore the characteristics of flow in each of these region. • This phenomenon has been studied in detailed by Osborne Reynolds (1883) using the apparatus shown in the next slide.

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Schematic diagram of Reynolds apparatus

In this experiment,  a filament of dye was injected to the flow of water.  The discharge was carefully controlled, and passed through a glass tube so that observations could be made.  Reynolds discovered that the dye filament would flow smoothly along the tube as long as the discharge is low.  By gradually increased the discharge, a point is reached where the filament became wavy.  A small further increase in discharge will cause vigorous eddying motion, and the dye mixed completely with water. 6

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3 (THREE) distinct patterns of flow were recognized:
Viscous or Laminar – in which the fluid particles appear to move in definite smooth parallel path with no mixing, and the velocity only in the direction of flow. Transitional Turbulent – in which some unsteadiness becomes apparent (the wavy filament). – in which the flow incorporates an eddying or mixing action. The motion of a fluid particle within a turbulent flow is complex and irregular, involving fluctuations in velocity and directions. 7

Flow Pattern
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• Reynolds experiment also revealed that the initiation of turbulence was a function of fluid velocity, viscosity, and a typical dimension. This led to the formation of the dimensionless Reynolds Number (Re).

Re 

inertia forces VD  viscous forces 

where

 = density  = dynamic viscosity V = mean velocity D = pipe diameter 9

• It can be seen that it has no units. A quantity that has no units is known as a non-dimensional (or dimensionless) quantity. Thus the Reynolds number, Re, is a nondimensional number. • Realizing that the kinematic viscosity can be represented with the dynamic viscosity over density , the Re can also be written as ;

Re 

uD


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Types of Flow
• The physical nature of fluid flow can be categorized into three types, i.e. laminar, transition and turbulent flow. Reynolds Number (Re) can be used to characterize these flow. Re  VD VD   

In general, flow in commercial pipes have been found to conform to the following condition: Laminar Flow: Re Re < 4000; • Re > 4000; • 'medium' velocity; and • 'high' velocity; • Dye stream wavers in • Dye mixes rapidly and water - mixes slightly. completely; • Particle paths completely irregular; • Average motion is in the direction of the flow; • Changes/fluctuations are very difficult to detect; • Mathematical analysis very difficult...
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