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...