Lecture Notes Chapter 1 Intro Sept 5

8/4/2019 Lecture Notes Chapter 1 Intro Sept 5

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Lecture Slides ChE 3O04 2011 1

INTRODUCTION TO FLUIDMECHANICS

Department of ChemicalEngineering

CHEM ENG 3O04Course Notes


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Fluid MechanicsWhere Used?

Oil Recovery/Refining/Pipelines

Gas wells/Transportation

Materials Processing (Metal Casting, Plastics Extrusion,

Injection Molding) Biomedical Engineering (Blood Flow, Artificial Hearts,

Kidney Dialysis)

Environmental Engineering (Water and Air Pollution,Particulate Dispersion)


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Fluid Mechanics (cont)

Meteorology (Weather Forecasting,

Tornadoes, Hurricanes)

Aerodynamics of Aircraft, Cars, Trucks etc

(Airfoil Design, Lift and Drag, FuelEconomy)

Power Generation (Nuclear, Conventional)

And many many more applications


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Fluid: a substance that alters its shape inresponse to any force.

Molecular diameters are very small, typically

less than 10-8 cm In other words, even in very small volumes

there are very large numbers of molecules

Define some measures of material pervolume:

==volumemassDensity


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==volumeweightS Weightpecific

Continuum Hypothesis:

A fluid is considered as an infinitely divisiblesubstance (no molecules or voids) so that the density

has a definite value at each point in the fluid. On the diagram, at low volumes individualmolecules and spaces can be seen, but above a

certain critical volume the density becomes constant(a continuum).

..waterofdensity

densityS GSGravitypecific ==


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Types of Forces

Normal Forces

Fn

Tangential (shear)

Forces

Fs

Area A Area A

Forces exerted on incompressible solids and fluidsa) Normal Forces Fnb) Tangential (shear forces) Fs


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Area

Force==StressNormal

Area

Force==StressShear

The NO SLIP Hypothesis:

The top plate drags the fluid along. A fluid in contact with a surface sticks to it and does not slip.

Fig. 1.3 A fluid subjected to shearing between two parallel plates.

The top plate drags the fluid along.

Gap, h


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The two parallel plates are placed a distance apart and the spacebetween them is filled with a fluid.

When a shear force, F is applied the top plate drags with the fluidwhile bottom one remains fixed.

h

UAF

where,F is forceU is velocityA is area in contact with the fluidh is the gap between the two plates

h

U

A

F==StressShear


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The proportionality constant, the resistant to flow, is called theviscosity, .

Newtons Law of Viscosity

dy

du=

The top plate drags the fluid along.

Gap, h

Fig. 1.3 A fluid subjected to shearing between two parallel plates.


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Fig. 1.4 Concentric cylinder viscometer. Torque and revolutionsper min (rpm) are directly measured.


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Viscosity (absolute, kinematic)

Absolute Viscosity in SI Units:

Pa s is Pascal second

is the Greek symbol mu.

Kinematic Viscosity:

is the Greek symbol nu. SI units:

[ ] sPasmN

m

sm mN === 2

2

//

density

viscosity==

s

m2=


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Pressure effect on viscosity. For gases, which are compressible, the viscosity increases with

pressure For liquids, which are incompressible, the viscosity is ~independent

of pressure.

Temperature has a strong effect on viscosity. For gases, viscosity increases with increase in temperature because

of the increase in frequency of intermolecular collisions. For liquids, viscosity decreases with increase in temperature

because of decreased intermolecular interactions with increasedmolecular vibrations.

Some typical values of viscosity for common substances: water = 10-3 Pa s lubricants = 10-1 - 1 Pa s skin oil = 5 Pas molten plastics = 103 104 Pa s


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Some basic notation:

Surface Tension at the fluid interfaces ().

No-slip condition at a solid surface (wall)

Vapor Pressure of liquids is due to molecules escaping and re-entering a liquid surface (Pr).

Compressibility is the sensitivity of density to changes in pressure.

Note: Even gases can be treated as incompressible fluidswhen velocities are less than 100 m/s

wallfluid =


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Non-Newtonian Fluids

Fluids that do not obey the linear relationship between stress ()and shear rate (du/dy) are called non-Newtonian fluids.

Typical examples are molten plastics, human blood, pastes,suspensions etc.

Some common types are:


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Ideal Bingham plastic

Power law model

here m, n are constants

If: n 1 this model describes a dilatant (shear thickening)fluid.

o00 if

dy

du >+=

oif0dy

du=

n

dum

=

dy

See the following Figures:


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Fig. 1.5 Some typical shear stress versus shearrate results for a Newtonian fluid.


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Fig. 1.6 Shear stress () versus shear rate (du/dy) for various fluids


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Fig. 1.7 Apparent viscosity (a) versus shear rate (du/dy).


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Fig. 1.8 Entangled polymer molecules subjected to shearingbetween two parallel plates.

Reynolds Number less)(dimensionRe =

=

DVavg

where is the density of the fluid,

Vavg is the average flow velocity, D is the diameter, and is the viscosity.


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Fig. 1.11 Schematic diagram of Osborne Reynolds Experiment.

When

When , the flow becomes turbulent.2300Re


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Fig. 1.10 Transition from laminar toturbulent flow in the smoke from aburning cigarette.

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Lecture Notes Chapter 1 Intro Sept 5

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