FUNDAMENTALS OF FLUID MECHANICS

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WHAT IS FLUID MECHANICS?

The study of fluids in motion or at rest and the subsequent effects of the fluids on the boundaries (may be either solids surfaces or other fluids).

THE NO-SLIP CONDITION All velocity profiles must have zero

values with respect to the surface at the points of contact between a fluid and a solid surface.

CLASSIFICATION OF FLUID FLOWS

Viscous VS Inviscid regions of flows Internal VS External Flow Compressible VS Incompressible Flow Laminar VS Turbulent Flow Natural (or Unforced) VS Forced Flow Steady VS Unsteady Flow One-, Two-, Three-Dimensional Flows

VISCOUS vs INVISCID REGIONS OF FLOW

Viscous : flows in which the frictional effects are significant.

However , in many flows of practical interest, there are regions where viscous forces are negligibly small compared to inertial or pressure forces.

Neglecting the viscous term in such inviscid flow regions greatly simplifies the analysis without much loss in accuracy.

Internal VS External Flow

The flow of an unbounded by solid surfaces such as a plate, a wire, or a pipe is external flow.

The flow in a pipe or duct is internal flow if the fluid is completely bounded by solid surfaces.

Compressible VS Incompressible Flow

Compressible and incompressible flow of a fluid is depending on the level of variation of density during flow.

Incompressibility is an approximation, in which the flow is said to be incompressible if the density remains nearly constant throughout.

Mach Number Ma=V/c V: speed of flow C: speed of sound

The flow is called sonic if: Ma = 1 , subsonic Ma < 1 , supersonic Ma > 1 , hypersonic

Laminar VS Turbulent Flow Laminar : The highly ordered fluid

motion characterized by smooth layers of fluid.

Turbulent : The highly disordered fluid motion that typically occurs at high velocities and is characterized by velocities fluctuations.

Transitional : A flow that alternates between being laminar and turbulent.

Natural (or Unforced) VS Forced Flow

In forced flow, a fluid is forced to flow over a surface or in a pipe by external means such as pump or fan.

In natural flow, fluid motion is due to natural means such as the buoyancy effect.

Steady VS Unsteady Flow Steady – no change of properties,

velocity, temperature, etc. , at a point with time.

One-, Two-, Three-Dimensional Flows

A flow field is characterized by its velocity distribution, and thus a flow is said to be one-, two-, or three-dimensional if the flow velocity varies in one, two, or three primary dimensions, respectively.

SYSTEM AND CONTROL VOLUME System : a quantity of matter or a region in space chosen for study. Surrounding : the mass or region outside the system. Boundary : the real or imaginary surface that separate the system from its surroundings.

IMPORTANCE OF DIMENSIONS AND UNITS

MODELING IN ENGINEERING It can be studied either experimentally

or analytically. Example :

PROBLEM-SOLVING TECHNIQUE

Step1 : problem statement Step2 : schematic Step3 : assumptions and

approximations Step4 : physical laws Step5 : properties Step6 : calculations Step7 : reasoning, verification, and

discussion

ENGINEERING SOFTWARE PACKAGES

Engineering Equation Solver (EES) Computational fluid dynamics Software

(CFD)

ACCURACY, PRECISION, AND SIGNIFICANT DIGITS

Accuracy error : the value of one reading – true value. Precision error : the value of one reading – the average of

readings. Significant digits : the digits that are relevant and meaningful.

EXAMPLE

As shown in fig 1.21 if the fluid is glycenn at 20 ͦ C and the width between the plates is 6mm,what shear stress is required to move the upper plate at 2.5m/s.what is the reynolds number,if d is taken to be the distance between the plates

No-slip condition The properties of liquids it was found

that at 20˚C carbon tetachloride had a dynamic viscosity of 9.67x10^ ̄ 4 pas and kinematic viscosity of 6.08x10^-7m²/s.calculate its specific gravity and weight density.

Speed of sound A liquid compressedin a cylinder has a

volume of 1000cm³ at 1MN/m² and a volume of 995cm³ at 2 MN/m³.what is the buble modulus of elasticity.

Presure inside a water droplet

A soap buble 60.0mm is diameter has an internal pressure in excess of the outside presure of 25 N/m².wthat is the tension in the soap film.