CHAPTER 1 INTRODUCTION - Universiti Teknologi Malaysiafkm.utm.my/~ummi/SME1313/Chapter 1.pdf ·...

SME 1313 Fluid Mechanics I

CHAPTER 1 INTRODUCTION

ByUmmikalsom Abidin

C24-316FKM, UTM


IntroductionFluid Mechanics

Fluid Statics- fluid at rest

- deals with forces applied by fluids at rest

Fluid Dynamics- fluid in motion

Hydrostatic forces on submerged bodies

e.g dam, tanks storing fluid, automation actuators

Buoyant force applied by fluids on submerged or floating bodies

e.g ships, submarines

Hydrodynamics

e.g liquid flow in pipes and open channel (hydraulics), pumps,hydroturbines, water cooling system

Gas dynamics

e.g gas turbines, flow of air over a body (aerodynamics) –aircraft, rockets, automobiles


Introduction

Naturally occuring flowsMeteorologyOceanographyHydrology


What is fluid?Fluid is a substance that deforms continuously under the application of a shear (tangential) stress no matter how small the shear stress may be.

t1 t2

F Ft0

t2>t1>t0

(a) (b)

Behavior of (a) solid and (b) fluid, under the action of a constant shear


What is fluid?

Fluids comprise the liquid and gas (or vapor) phases Distinction between solid,liquid and gas

StrongestMolecules are relatively fixed position

Solid

WeakestMolecules move about at random in the gas phase

Gas

ModerateGroups of molecules move about each other in the liquid phase

Liquid

Intermolecular bonds

Atom Arrangement


What is fluid?Normal to surface

Force acting on area dA

Tangent to surface

Fn

dA Ft

Normal stress: σ = Fn/dA

Shear stress: ι = Ft/dA

The normal stress and shear stress at the surface of a fluid element. For fluids at rest, the shear stress is zero and the pressure is the only normal stress


No-slip ConditionA fluid in direct contact with a solid “sticks” to the surface due to viscous effects, and there is no slip.The flow region adjacent to the wall in which the viscous effects(and thus the velocity gradients) are significant is called boundary layer.

Uniform approach

velocity, V

Relative velocities of

fluid layers

Zero velocity at the surface

Plate

A fluid flowing over stationary surface comes to a complete stopat the surface because of the no-slip condition


Classification of Fluid FlowsViscous vs. Inviscid Regions of Flow

Viscous Flow Region – flows in which the frictional effect is significantInviscid Flow Region – viscous forces are negligibly small compared to inertial or pressure forces

Inviscid flow region

Viscous flow

region

Inviscid flow region

The flow of an originally uniform fluid stream over a flat plate, and the regions of viscous flow (next to the plate on both sides) and inviscid flow (away from the plate)


Classification of Fluid Flows

Internal vs. External FlowInternal flow – flows in which the fluid is completely bounded by solid surface

e.g flow in a pipe or ductDominated by the influence of viscosity throughout the flow field

External flow – flows in which the fluid is unbounded over

solid surfacese.g flow over a plate, wire, sphere objectViscous effects are limited to boundary layers near solid surfaces and to wake regions downstream of bodies

* Open-channel flow – the flow of liquids in a duct in which the liquid is partially filled and there is a free surface e.g rivers, irrigation channels


Classification of Fluid FlowsCompressible vs. Incompressible Flow

Incompressible Flow – density of the fluid remains nearly constant throughout

liquids, gases at low speedsdensity changes of gas flows are under 5% or when Ma<0.3

Compressible Flow – density changes of the fluid is significant

gases at high speedsdensity changes of gas flows are above 5% or when Ma>0.3

Mach number,Ma = V = Speed of flow

c Speed of soundMa=1 (Sonic), Ma<1 (Subsonic), Ma>1(Supersonic), Ma>>1 (Hypersonic)

(Speed of sound=346 m/s)


Classification of Fluid FlowsLaminar vs. Turbulent Flow

In 1880s, Osborn Reynolds conducted an experiment to see flow patterns

Tank arranged as above with a pipe taking water from the centre into which dye is injected through a needle


Classification of Fluid FlowsFilament of dye

Laminar (viscous)

Transitional

Turbulent


Classification of Fluid Flows

Reynolds number,Re =ρud

µ

Laminar flow Re<2000Transitional flow 2000<Re<4000Turbulent flow Re>4000


Classification of Fluid FlowsNatural (or unforced) vs. Forced Flow

Forced Flow – fluid is forced to flow over a surface or in a pipe by external means such as pump or a fanNatural Flow – any fluid motion is due to natural means such as buoyancy effect, where warmer (and thus lighter) fluid rises and cooler (and thus denser) fluid falls

Schlieren image of a hot water (left) and ice water (right) in a glass


Classification of Fluid FlowsSteady vs. Unsteady Flow

Steady Flow – no change of fluid properties (velocity, pressure) at a point with time

Devices that are intended for continuous operation e.gturbines, pumps, boilers, condensers

Unsteady Flow – fluid properties change at a point with timeTransient – used for developing flows

t1=5 s

V1=10 m/s

t2=10 s

V2=10 m/s

t1=5 s

V1=10 m/s

t2=10 s

V2=11 m/s


Classification of Fluid FlowsUniform vs. Non-uniform Flow

Uniform Flow – no change of fluid properties with location over a specified region

Non-uniform Flow – if at a given instant, fluid properties change with location over a specified region

V1=10 m/s V2=10 m/s

V1=10 m/s V2=11 m/s

or V=10 m/s

orV1=10 m/s

V2=10 m/s

1

2

2

1


Classification of Fluid FlowsSteady uniform flow

Conditions do not change with position and with time e.g flow of water in a pipe of constant diameter at constant velocity

Steady non-uniform flowConditions change from point to point in the stream but do not change with time e.g flow in tapering pipe with constant velocity at inlet, but velocity change along the length of the pipe toward the exit

Unsteady uniform flowAt a given instant of time, the conditions at every point are the same, but will change with time e.g pipe of constant diameter connected to a pump pumping at a constant rate which is then switched off

Unsteady non-uniform flowEvery condition of the flow may change from point to point and with time at every point e.g waves in channel


Classification of Fluid FlowsOne-, Two-, and Three-Dimensional Flows

1-D Flow – flow parameters (such as velocity, pressure, depth) vary in one primary dimensions2-D Flow - flow parameters vary in two primary dimensions3-D Flow - flow parameters vary in three primary dimensions

The development of the velocity profile in a circular pipe, V=V(r,z) and thus the flow is 2-D in the entrance region, and becomes 1-D downstream when the velocity

profile fully develops and remain unchanged in the flow direction, V=V(r)

z

Developing velocity profile, V(r,z)

Fully developed velocity profile, V(r)

r


Classification of Fluid FlowsThe dimensionality of the flow also depends on the choice of coordinate system and its orientation

Rectangular coordinates, V(x,y,z)Cylindrical coordinates, V(r,θ,z)

Higher dimensionality should be considered if only very high accuracy is required


Application Areas of Fluid Mechanics

Human body (Bio-fluid Mechanics)Cardiovascular system

Artificial heartPulmonary system

Breathing machine

BuildingWater supply systemSewerage systemHeating and air-conditioningAerodynamics forces and flow fields around structure



AutomobilesHydraulic brakes, power steering, automatic transmissionFuels line, fuel pump, fuel injectorsLubrication systemsCooling systemsAir-conditioningAerodynamics design

AircraftAerofoil designGas turbine



Ship, submarines, hovercraftHydrodynamics designBuoyancy and stability

IndustryCooling of electronicsAutomation system

RecreationalBadminton shuttle and golf ball aerodynamics

Geophysical fluid dynamicsMeteorologyOceanography


System and Control VolumesSystem – quantity of matter or a region in space chosen for studySurroundings – mass or region outside the systemBoundary – Real or imaginary surface that separates the system from its surroundings (fixed or movable)

SYSTEM

SURROUNDINGS

BOUNDARY


System and Control VolumesClosed System (Control Mass)

Consists of a fixed amount of mass, and no work, can cross the boundaryEnergy in the form of heat and work can cross the boundaryE.g piston-clinder device

Open System (Control Volume)Both mass and energy can cross the boundaryE.g compressor, turbine, nozzle, car radiator

Imaginary boundary

Real boundary

CV

(a nozzle) CV

Imaginary boundary

Imaginary boundary


Dimensions and UnitsAny physical quantity can be characterized by dimensionsMagnitude assigned to the dimensions are called unitsPrimary or fundamental dimensions

mole (mol)Amount of matter

candela (cd)Amount of light

ampere (A)Electric of current

kelvin (K)Temperature

second (s)Time

kilogram (kg)Mass

meter (m)Length

UnitDimension

The seven fundamental (or primary) dimensions and their units in SI


Dimensions and UnitsDerived or secondary dimensions are dimensions obtained from combination of primary dimensions

Most used derived dimensions


SI UnitsMetric SI (from Le Systeme International d’Unites) or International SystemSI system was produced by General Conference of Weights and Measures in 1960SI is a simple and logical system and widely being used for scientific and engineering work in most of the industrialized nations


SI Units

pico, p10-12

nano, n10-9

micro, µ10-6

milli, m10-3

centi, c10-2

deci, d10-1

deka, da101

hecto, h102

Kilo, k103

mega, M106

giga, G109

tera, T1012

PrefixMultiple

Standard prefixes in SI units


Dimensional HomogeneityIn engineering, all equations must be dimensionally homogeneous where every term in an equation must have the same unit


Problem-Solving TechniqueStep 1:Problem Statement

State briefly and concisely (in your own words) the information given and the quantities to be found

Step 2:SchematicDraw a schematic of the system or control volume to be used in the analysis.Indicate any energy and mass interactions with the surroundingsListing the given information on sketch

Step 3:Assumptions and ApproximationsState any assumptions and approximations made to simplify the problem to make it possible to obtain a solution


Problem-Solving TechniqueStep 4:Physical Laws

Apply all the relevant basic physical laws and principle and reduce them to their simplest form by utilizing the assumptions made

Step 5:PropertiesDetermine the unknown properties at known states necessary to solve the problem from property relations or tables

Step 6:CalculationsSubstitute the known quantities into the simplified relations and perform the calculations to determine the unknownPay attention to the units and unit cancellationsGive appropriate number of significant digits


Problem-Solving TechniqueStep 7:Reasoning, Verification, and Discussion

Check to make sure that the results obtained are reasonable and intuitive and verify the validity of the questionable assumptionsRepeat the calculations that resulted in unreasonable values

CHAPTER 1 INTRODUCTION - Universiti Teknologi Malaysiafkm.utm.my/~ummi/SME1313/Chapter 1.pdf ·...

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