Fluid Mechanics
Lecture 1
Dr. M. Coley
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Fluid Characteristics
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Course Outline & Description
6 lectures
11/2 questions – Paper 1
Textbooks
Unit Operations of Chemical Engineering
Warren L. McCabe, J. Smith & P. Harriot
McGraw-Hill
Introduction to Chemical Engineering
Walter Badger & Julius Banchero
McGraw-Hill
Fluid Mechanics – 9th ed
J.F. Douglas, J. Gasiorek & J. Swaffield
ELBS Longman
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What is a Fluid?
 A fluid is a substance that may flow.
 A fluid is a substance that deforms continuously
when subjected to a shear stress.
 Characteristics:

Its constituent particles may continuously change
their positions relative to one another.

A fluid offers no lasting resistance to the
displacement of one layer over another.

If a fluid is at rest, no force tangential to the surface
on which it acts (shear force) can exist in it.
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Fluid Characteristics
 Any fluid, no matter how viscous, will flow, even
imperceptibly, when a net shear force is applied.
 A fluid will continue to flow as long as such force is
applied.
 A solid, even if very plastic, will not flow unless a net
shear force exceeds a certain value.
T=0
Liquid element
T = Δt
• no relative motion between
fluid and boundary, i.e.,
fluid in contact with lower
plate is stationary,
• fluid in contact with upper
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plate moves at speed U.
Solids & Liquids
Liquids:
 Closely spaced molecules with large intermolecular forces
 Retain volume and take shape of container
Gases:
 Widely spaced molecules with small intermolecular forces
 Take volume and shape of container
gas
liquid
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Fluid Mechanics
Most chemical processes are conducted in the
fluid phase
Reasons:
- cheaper to handle
- easier to react
- easier to transport
Solids often fluidized for easier handling
Fluid Statics
Properties of fluids at rest
Fluid Mechanics
Fluid Dynamics
Properties of fluids in motion7
Fluid Statics?
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Effects of Fluid Dynamics?
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Fluids & their Properties
A fluid is defined as a substance which deforms
continuously under the action of shearing forces
Shearing force: force that is tangential to the
force on which it acts
- shearing forces cause particles of fluid to change position
- layers of fluid slide over one another, fluid deforms & flow
- fluid offers limited resistance to deforming force
Fluid at Rest
- no shear forces are acting
- forces acting must be perpendicular
to planes they act on
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Fluid in Motion
Layers of
fluid slide
over each
other
Fluid under
shear
stress
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Fluids & their Properties cont’d
gases
Fluids
both will flow
liquids
All fluids will flow regardless of viscosity
Liquids
• takes shape of container - leaves free space
• Shape will change if shear stress exists
• No stress at ≡M
– deforms in response to shear stress
Gases
•
•
Occupy entire container
Expand continuously unless restrained
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Fluid in Motion - Gas
Easy to compress
Large volume change
when pressure changes
Temp. change affects
volume & pressure
No fixed volume
Gas expands to fill
container
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Comparing Solids & Fluids
Solids
 Displacement of layers
may occur
 ‘Flow’ will not be sustained
 Resist shear forces when
at rest
 Greater the displacement,
greater the forces
resisting displacement
Types of Fluids
 Compressible & Incompressible
 Newtonian & Non-Newtonian
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Newtonian & Non-Newtonian Fluids
Fluid Layer 1
F
F
Fluid Layer 2
 Upper layer moving faster, & will draw lower layer with a force F.
 Lower layer will retard upper layer with equal, opposite force F
Newton’s Hypothesis
For the straight & parallel motion of a given fluid, the tangential stress
between two adjoining layers is proportional to the velocity gradient in
a direction perpendicular to the layers.
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Newtonian & Non-Newtonian Fluids
 ‫ = ح‬F/A ≈ du/dy
‫ = ح‬μ(du/dy)
‫ = ح‬shear stress acting on fluid
 Absolute Viscosity – μ - ratio of shear stress to a velocity gradient
 Kinematic viscosity – ν - ratio of absolute viscosity to density
 Stress – ratio of force to area over which it acts
 Velocity gradient
– ratio of increase in velocity to distance
over which increase occurs
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Newtonian & Non-Newtonian Fluids
Rheology
Science that describes relationship between
shear stress & shear rate of a fluid
Time Independent Fluids
Properties unchanged with length of time force is applied
Newtonian Fluids
•
Viscosity independent of rate of shear
•
Viscosity independent of magnitude of shear stress
•
Fluid viscosity is constant with pressure applied & rate of flow
•
Time independent fluid – viscosity unchanged with time of force
•
Eg. most fluids, water
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Newtonian & Non-Newtonian Fluids
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Non-Newtonian Fluids
Bingham Plastic




Resist small shear stress
Flow readily if larger stress is applied
Flow with large stress is Newtonian
Eg. toothpaste, jellies
Pseudo-plastic






Includes most non-Newtonian fluids
Curve passes through origin but bends downwards
Fluid more viscous at low shear stress
Less viscous at high stress
Attraction between particles diminish - disrupted
Called shear-thinning fluids
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Non-Newtonian Fluids
Dilatant
 Viscosity increases with velocity gradient
 Shear thickening fluids
 Eg. starch suspensions
Time Dependent Flow
 Change in viscosity related to length of time stress is applied
 Thixotropic fluids
-
viscosity decrease with time
fluids expands or structure breaks down
interaction between particles reduces
eg. paints
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Non-Newtonian Fluids
Rheopectic Fluids
 Viscosity increases as shear rate increases
 Behavior is opposite to thixotropic
 Eg: gypsum suspension
Visco-elastic fluids
 Have elastic properties
 Will spring back when stress is released
 Eg: egg white
Fluids return to original behavior on standing
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 Discuss implications of fluid behavior on process design
Time – Dependent Flow
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