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Basic Concepts

Mechanics: the science which seeks an explanation

for the motion of bodies based upon models grounded

in well defined axioms.Static: the force analysis on a fixed body.

Kinematics: a description of the motion of a body.

Dynamics: the study of a bodys motion and its

causing forces.

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A matter phase that cannot withstand any tendency

for applied forces to deform it in such a way that

volume is left unchanged.

A substance that deforms continuously whensubject to a shear stress of any magnitude.

Simply:

Gases and liquids

are fluids.

What is a Fluid?

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Fluid mechanics: the science that concern with the

behavior of fluids (liquids or gases) at rest or in

motion.

Classification of fluid mechanics:

The study of fluid mechanics goes back at least to the

days of ancient Greece; Archimedes' Principle.

o Hydrodynamics: flow of liquids.

o Gas dynamics: flow of gases.

o Aerodynamics: flow of air.

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DIMENSIONS AND UNITSAny physical quantity can be characterized by

dimensions.

The magnitudes assigned to the dimensionsare called units.

SI system:A simple and logical system basedon a decimal relationship between the various

units.English system: It has no apparent systematicnumerical base. Major confusion in this systemis the Force;

.

Dimensional homogeneityAll equations must be dimensionally homogeneous; each term in the

equation must have the same dimension, e.g. V=Vo+at.

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PRIMARY AND SECONDARY DIMENSIONS

Some basic dimensions are selected asprimary dimensions, such as:mass m, length L, time t, and temperature T.

Others, expressed in terms of the primarydimensions and are called secondary

dimensions, such as velocity V, force F,energy E,etc.

Scalar and Vector Quantities

Scalar quantity has only magnitude.(e.g. mass, density, speed.)

Vector quantity has both magnitude and direction.(e.g. weight, Force, velocity.)

Work = Force Displacement

Force = Mass Acceleration

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Fluid as a continuum

Matter is made up of atoms that arewidely spaced in the gas phase.

Yet it is very convenient todisregard the atomic nature of a

substance and view it as acontinuous, homogeneous matterwith no holes, that is, a continuum.

In this course we will limit ourconsideration to substances thatcan be modeled as a continuum.

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FLUID PROPERTIES

Specific gravity: The ratio of the density of a substance to the density ofa standard substance at a specified temperature.

For liquids, water at 4oCr =1000kg/m3.

For gases, airr =1.205kg/m3.

Density: The mass per unit volume of a substance.

Specific weight: The weight of a unit volume of a substance.

Specific volume: The volume per unit mass of a substance.

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Temperature: A measure of the internal energy level of a fluid.

Celsius scale: SI unit system s temperature scale.

Kelvin scale:A temperature scale that is independent of the propertiesof any substance.

The reference point in the Kelvin scale was changed

from the ice point, 273.15 K, to a much more precisely

reproducible point, the triple point, 273.16 K.

Fahrenheit scale: BG unit system s temperature scale.

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Pressure: A normal force exerted by a fluid per unit

area; the compression stress at a point in a

static fluid.

Atmospheric pressure: The weight of an air column on

a unit area.

Absolute pressure: The actualpressure at a given position.

Gage pressure: The differencebetween the absolute pressure and

the local atmospheric pressure.

Vacuum pressures: Pressures belowatmospheric pressure.

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State equation: : Any equation that relates the thermodynamic

properties of a substance to each other.

e.g. ideal gas law: , .

Specific heat: The energy required to raise a unit mass of a substance

one degree. For gasses, it is cp if the process occur at

constant pressure, or cv if the process occur at constant

volume.

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As a consequence of compressibility, disturbances in the

fluid propagate at a finite velocity.

Speed of sound: The rate of propagation of a sound

wave through a fluid; (i.e. acoustic velocity).

For ideal gases:=

. = .

Compressibility: Fluid s density changes caused by the flow.

Compressibility coefficient:

For gases, the relation between pressure and density is

=

1

.

=1

,Bulk modulus of elasticity: when dealing with liquids.

=

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Viscosity: Theproperty which determines the amount of its resistance

to a shearing force due to the interaction between fluid

molecules. It describes the fluidity of the fluid, i.e. how

easily it flows.

For small time increment:

where is the dynamic coefficient of viscosity.

tan .

, and

.

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No slip condition: The velocity of fluid is zero at the stationary boundary.

The magnitude of depends on:

The cohesive force between molecules (dominant for liquid).

The momentum interchange between colliding molecules (dominant

for gases).

As the temperature increase, the viscosity of a gas increases and

viscosity of a liquid decreases.

For liquids, Andrade Eq.:

For gases: Sutherland Eq.:

.

.

.

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Velocity Distribution:

Since depends on the velocity distribution,finding is the key for fluid dynamics

problems.

15

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If P drops below Pv, liquid is locally

vaporized, creating cavities of vapor

and bubbles. Collapse of cavities is a

violent process which can damage

machinery, CAVITATION.

Vapor pressure ( Pv ) : The pressure at which a liquid boils and is in

equilibrium with its own vapor.

Newtonian vs. Non-Newtonian fluid

Fluids are classified based on

the relation between theapplied shear stress and the

deformation rate.

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Surface Tension ( ): the magnitude of tension exerted by liquid surface on a

unit area of the objects that are in contact with the surface.

Liquid molecules near the

surfaces have a greater

attraction (stronger

intermolecular forces) to

each other.

The balance between intermolecular cohesive forces and the fluid-solid

adhesion forces.

The curved free surface in the tube is call the meniscus.

Water meniscus curves up ( 0 ); Mercury meniscus curves down up

( 130 ).

Capillary effect: the rise or fall of a liquid in a

small-diameter tube.