CH1 Introduction

FLUID MECHANICSLichuanqi

Shandong University

AFD EFD CFD

Information and Introduction

Instructor

Li chuanqi

E-mail : [email protected]

Tel: 13864163006

Textbook

Fluid Mechanics with Engineering Applications

E.John Finnemore Joseph B. Franzini

Homework

One of the best ways to learn something is through practice and repetitionTherefore, homework assignments are extremely important in this class!Homework sets will be carefully designed, challenging, and comprehensive. If you study and understand the homework, you should not have to struggle with the exams

Course Topics

Fluid Properties Fluid Statics

Pressure at a Point Force on Surfaces

Concepts of Fluid Flow Types of Flow

Laminar and Turbulent Flow Steady Flow and Uniform Flow Path Lines, Streamlines, and Streak Lines

Course Topics

The fundamental equations of fluid dynamics Equation of Continuity Bernoullis Equation momentum equation

Pipe Flow

Open Channel Flow

My Goals for the next 14 weeks

That each of you develop an intuition for the fundamental principles of fluid mechanicsThat you leave this course saying,

Fluids makes sense and I can tackle fluids problems.That we have an enjoyable 14 weeks

learning together

CH 1 Introduction

Outline

What is Fluid Mechanics?Why is Fluid Mechanics Important?Applications of Fluid Mechanics. Dimension systems and analysis.

1.1 Fluid Mechanics Overview

Gas Liquids Statics Dynamics

Air, He, Ar, N2, etc.

Water, Oils, Alcohols, etc.

0= iF

Viscous/InviscidSteady/Unsteady

Compressible/

Incompressible

0> iF

Laminar/

Turbulent

, Flows

Compressibility Viscosity Vapor

Pressure

Density

Pressure BuoyancyStability

Chapter 1: Introduction Chapter 2: Fluid Statics Fluid Dynamics:

Rest of Course

Surface

Tension

Fluid Mechanics

Definition of Fluid Mechanics: Fluid mechanics is the science of the mechanics of liquids and gases. It involves many of the same principles of solid Statics and Dynamics, but fluids is a more complex subject because solids involve the study of forces on discrete bodies, while in fluids bodies flow together.

The analysis is based on the fundamental laws of mechanics, which relate continuity of mass and energy with force and momentum.

An understanding of the properties and behavior of fluids at rest and in motion is of great importance in engineering.

Used in the design of : Water supply system -- waste water treatment Dam spillways -- valves, flow meters Shock absorbers, brakes -- automatic transmissions ships, submarines -- breakwaters, marinas Aircrafts, rockets -- computer disk drives

Windmills, turbines -- pumps, HVAC systems Bearings -- artificial organs Sport items: Golf balls Race cars

Scope of Fluid Mechanics

z Science of the mechanics of liquids and gasesz Based on same fundamental principles as solidMechanics z More complicated subject, however, since in fluidsseparate elements are more difficult to distinguishz We'll solve problems of fluids on the surface ofthe Earth, within reasonable ranges of pressure andtemperature.

Scope of Fluid Mechanics

Branches: Fluid statics: fluids at rest Fluid kinematics: velocities and streamlines Fluid dynamics: velocity & accelerations forces

Classical hydrodynamics Mathematical subject Deals with ideal frictionless fluids

Classical hydraulics: Experimental science Deals with real fluids

Scope of Fluid Mechanics

Classical hydrodynamics and hydraulics are now combined into FLUID MECHANICS

Modern Fluid Mechanics: Combines mathematical principles with experimental data Experimental data used to verify or complement theory or mathematical analysis

Computational Fluid Dynamics (CDF) Numerical solutions using computers Methods:Finite differences * finite elementsBoundary elements * analytic elements

Why is Fluid Mechanics Important?

Knowledge of fluid mechanics in needed to properly design many engineering projects, including water pipe systems, storm water drainage systems, aircraft, brake systems, heating and air conditioning systems, golf balls, boats, and cars. Therefore, most of you will use Fluid Mechanics in your work.

Historical development (1)

Ancient civilizations: irrigation, ships Ancient Rome: aqueducts, baths (4th century

B.C.) Ancient Greece: Archimedes buoyancy (3rd

century B.C.) Leonardo (1452-1519): experiments, research

on waves, jets, eddies, streamlining, flying

Historical development (2)

Newton (1642-1727): laws of motion, law of viscosity, calculus

18th century mathematicians: solutions to frictionless fluid flows (hydrodynamics)

17th & 18th century engineers: empirical equations (hydraulics)

Late 19th century: dimensionless numbers, turbulence

Historical development (3)

Prandtl (1904): proposes idea of the boundary layer Flow fields of low-viscosity fluids divided into two zones:A thin, viscosity-dominated layer near solid surfacesAn effectively inviscid outer zone away from boundaries Explains paradoxes Allow analysis of more complex flows

20th century: hydraulic systems, oil explorations, structures, irrigation, computer applications

Historical development (4)

Beginning of 21st century: No complete theory for the nature of turbulence Still a combination of theory and experimental data

History

Faces of Fluid Mechanics

Archimedes(C. 287-212 BC)

Newton(1642-1727)

Leibniz(1646-1716)

Euler(1707-1783)

Navier(1785-1836)

Stokes(1819-1903)

Reynolds(1842-1912)

Prandtl(1875-1953)

Bernoulli(1667-1748)

Taylor(1886-1975)

Significance

Fluid Mechanics is omnipresent Weather & climate Aerodynamics Combustion Energy generation Geology Hydraulics and Hydrology Hydrodynamics Ocean and Coastal Engineering Water Resources Sports & recreation numerous other examples

Weather & Climate

Tornadoes

HurricanesGlobal Climate

Thunderstorm

Aerodynamics

Energy generation

Geology

River Hydraulics

Hydraulic Structures

Hydrodynamics

Water Resources

Environmental

London Sewer

Environmental

Stream Habitat

Transportation

Culverts

Geotechnical

Groundwater and Seepage

Structural

Snow Load

Structural

Wind Load

Analytical Fluid Dynamics

The theory of mathematical physics problem formulation

Control volume & differential analysis Exact solutions only exist for simple geometry and

conditions Approximate solutions for practical applications

Linear Empirical relations using EFD data

Analytical Fluid Dynamics

Lecture Part of Fluid Class Definition and fluids properties Fluid statics Fluids in motion Continuity, momentum, and energy principles Surface resistance Flow in conduits

Analytical Fluid Dynamics

Schematic

Example: laminar pipe flow

Exact solution :2 21( ) ( )( )4

pu r R rx = Friction factor:

88 64Re2 2

w

dudywf

V V

= = =

Assumptions: Fully developed, Low Approach: Simplify momentum equation, integrate, apply boundary conditions to determine integration constants and use energy equation to calculate head loss

xgyu

xu

xp

DtDu +

+

+= 2

2

2

2

Head loss:1 2

1 2 fp pz z h + = + +

2

2

322f

L V LVh fD g D

= =

UD 2000Re

Experimental Fluid Dynamics (EFD)

Definition:Use of experimental methodology and procedures for solving fluids engineering systems, including full and model scales, large and table top facilities, measurement systems (instrumentation, data acquisition and data reduction), uncertainty analysis, and dimensional analysis and similarity.

EFD philosophy: Decisions on conducting experiments are governed by the ability of the

expected test outcome, to achieve the test objectives within allowable uncertainties.

Integration of UA into all test phases should be a key part of entire experimental program test design determination of error sources estimation of uncertainty documentation of the results

Applications of EFD

Application in research & development

Tropic Wind Tunnel has the ability to create temperatures ranging from 0 to 165 degreesFahrenheit and simulate rain

Example of industrial application

NASA's cryogenic wind tunnel simulates flight conditions for scale models--a critical tool indesigning airplanes.

Full and model scale

Scales: model, and full-scale

Selection of the model scale: governed by dimensional analysis and similarity

Computational Fluid Dynamics

CFD is use of computational methods for solving fluid engineering systems, including modeling (mathematical & Physics) and numerical methods (solvers, finite differences, and grid generations, etc.).

Rapid growth in CFD technology since advent of computer

ENIAC 1, 1946 IBM WorkStation

Modeling (example)

Free surface animation for ship in regular waves

Dimensions and Units (1)

z Units needed to properly express a physical quantityz Systems to be used: S.I. (Systeme Internationale d'Unites)

Adopted in 1960Used by nearly every major country, except the U.S.Likely to be adopted by the U.S. in the near future

B.G. (British Gravitational system)Used in the technical literature for years Preferred system in the U.S.

Dimensions and units (2)

Basic dimensions used in fluid mechanics: Length (L) Mass (M) Time (T) Temperature ()

Dimensions of acceleration: [a] = LT-2 Newton's 2nd law: F = [m][a] = MLT-2 Only 3 of the four basic units can be assigned

arbitrarily, the fourth becoming a derived unit

Derived quantities (1)

Basic dimensions: mass (M), length (L), time (T) Velocity = Length / Time Acceleration = Velocity / Time = Length / Time2 Discharge = Volume / Time Force = Mass Acceleration Pressure = Force / Area (also Stress) Work = Force Length (also Energy, Torque) Power = Work / Time = Force Velocity Angular Velocity = Angle / Time Angular Acceleration = Angular Velocity / Time

Example

Newtons second law

F = ma = MLT-2

In this case, acceleration is a derived unit, because it is derived from combining basic units.

CH 2 Properties of Fluids

1.What is the differences between solids, liquids and gases?

2. Learn definitions that specify basic fluid properties (density, specific weight, specific volume, and specific gravity) and how to use these definitions for solving problems.

3. Understand the concept of compressibility and how it applies to fluid mechanics.

4. Understand the concept of Newtonian fluids and viscosity and how to solve for forces in a Newtonian fluid.

5. Understand the concept of surface tension and vapor pressure and how to find the capillary rise of a fluid.

Section Goals

2.1 What is a fluid?

A fluid is a substance in the gaseous or liquid form Distinction between solid and fluid?

Solid: can resist an applied shear by deforming. Stress is proportional to strain

Fluid: deforms continuously under applied shear. Stress is proportional to strain rate

FA

= F VA h = FluidSolid

What is a fluid?

Stress is defined as the force per unit area.

Normal component: normal stress In a fluid at rest, the normal

stress is called pressure Tangential component: shear

stress

What is a fluid?

A liquid takes the shape of the container it is in and forms a free surface in the presence of gravity

A gas expands until it encounters the walls of the container and fills the entire available space. Gases cannot form a free surface

Gas and vapor are often used as synonymous words

What is a fluid?

solid liquid gas

Fluids can be ... liquids,

or gases!

Continuum

All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion.

However, in dealing with fluid-flow relations on a mathematical basis, it is necessary to replace the actual molecular structure by a hypothetical continuous medium, called the continuum.

Continuum

In a continuum, the physical variable at a point in space is the averaged value of the variable in a small sphere.

How good is the assumption?

10-3cm

3x1010 molecules of air

2.2 Distinction between a solid and a fluid (1)

Molecules of solid closer together than those of fluid

Solid: intermolecular forces larger than in fluid

Elastic solid

deforms under load

recovers original state when unloaded

Plastic solid:

deforms under sufficient load

continues deforming as long as load is applied

does not return to original state

Distinction between a solid and a fluid (2)

Intermolecular forces in fluid not large enough to holdelements togetherFluid flows under slightest stress and continues flowing

as long as stress is present

Distinction between a gas and a liquid (1)

Fluids: gases or liquids GAS:

Molecules farther apart Very compressible Tends to expand indefinitely

LIQUID: Relatively incompressible If external pressure removed, does not expand May have a free surface (subject to its own vapor

pressure)

2.3 Density, Specific Weight, Specific Volume, and Specific Gravity

DensityDensity of a fluid, , Definition: mass per unit volume,

slightly affected by changes in temperature and pressure.

= mass/volumeUnits: kg/m3

Typical values:Water = 1000 kg/m3; Air = 1.23 kg/m3

2.3.1 Density

vm=

The density of a fluid is defined as mass per unit volume.

Different fluids can vary greatly in density

Liquids densities do not vary much with pressure and temperature

Gas densities can vary quite a bit with pressure and temperature

Density of water at 4 C : 1000 kg/m3Density of Air at 4 C : 1.20 kg/m3

Alternatively, Specific Volume: 1=

m = mass, and v = volume.

Specific weight of a fluid, [gamma] Definition: weight of the fluid per unit volume Arising from the existence of a gravitational force The relationship and g can be found using the following:

Since = m/Vtherefore = gUnits: N/m3

Typical values:Specific weight of water at 4 C : 9.80 kN/m3Specific weight of air at 4 C : 11.9 N/m3

Specific weight

The specific gravity (or relative density) can be defined in two ways:

Definition 1: A ratio of the density of a substance to the density of water at standard temperature (4C) and atmospheric pressure, or

Definition 2: A ratio of the specific weight of a substance to the specific weight of water at standard temperature (4C) and atmospheric pressure.

Unit: dimensionless.Cw

s

Cw

sSG

==

44 @@

Specific gravity

2.3.2 Viscosity

Viscosity is a measure of a fluid's resistance to flow..

The force a flowing fluid exerts on a body in the flow direction is called the drag force, and the magnitude of this force depends, in part, on viscosity.

Viscosity is a fluids resistance to flow.

Fluid motion can cause shearing stresses

(a) Deformation of material placed between two parallel plates. (b) Forces acting on upper plate.

Behavior of a fluid placed between two parallel plates

The shearing stress is increased by P, the rate of shearing strain is increased in direct proportion,

Viscosity

Problem

Three black marbles are dropped at the same time into three different fluids - oil, water, and glycerol. Will they all fall at the same rate of speed?

The marble will drop the fastest in the water and slowest in the glycerol. The reason is due to the different viscosities of the fluids.

Definition: Ratio of absolute viscosity to the density;

Appears in many problems in fluids. Called kinematic viscosity because it involves no force

(dynamic) dimensions

Units: m2/s

Typical values: Water = 1.14x10-6 m2/s; Air = 1.46x10-5 m2/s;

In general, viscosity of liquids with temperature, whereas

viscosity of gases with in temperature.

= /

Viscosity: Kinematic Viscosity

Viscosity: Newtonian vs. Non-Newtonian

Newtonian Fluids are Linear Relationships between stress and strain: Most common fluids are Newtonian.

Non-Newtonian Fluids are Non-Linear between stress and strain

Corn Starch

Latex Paint

Toothpaste

Example:AirWaterOilGasolineAlcoholKeroseneBenzeneGlycerine

Fluid Newtons lawof viscosity

Newtonian fluids obey refer

Newtons law of viscosity is given by;

dydu= (1.1)

The viscosity is a function only of the condition of the fluid, particularly its temperature.

The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of .

= shear stress = viscosity of fluiddu/dy = shear rate, rate of strain or velocity gradient

Newtonian and Non-Newtonian Fluid

Fluid Newtons lawof viscosity

Non- Newtonianfluids

Do not obey

The viscosity of the non-Newtonian fluid is dependent on the velocity gradient as well as the condition of the fluid.

Newtonian Fluids a linear relationship between shear stress and the velocity gradient (rate

of shear), the slope is constant the viscosity is constant

non-Newtonian fluids slope of the curves for non-Newtonian fluids varies

Newtonian and Non-Newtonian Fluid

2.3.3 Compressibility of Fluids: Bulk Modulus(

2.3.4 Vapor Pressure

Vapor Pressure

010002000300040005000600070008000

0 10 20 30 40

Temperature (C)

V

a

p

o

r

p

r

e

s

s

u

r

e

(

P

a

)

liquid

What is vapor pressure of water at 100C? 101 kPa

water

2.3.5 Surface Tension

Two non-mixing fluids (e.g., a liquid and a gas) will form an interface. The molecules below the interface act on each other with forces equal in all directions, whereas the molecules near the surface act on each other with increased forces due to the absence of neighbors. That is, the interface acts like a stretched membrane

Surface Tension: Capillary Action

Capillary action in small tubes which involve a liquid-gas-solid interface is caused by surface tension. The fluid is either drawn up the tube or pushed down.

h is the height, R is the radius of the tube, is the angle of contact.

Wetted Non-Wetted

The weight of the fluid is balanced with the vertical force caused by surfacetension.

Adhesion > Cohesion Cohesion > Adhesion

Adhesion

CohesionAdhesion

Cohesion

Review: Fluid Properties

Viscosity Density and Specific Weight Elasticity Vapor Pressure Surface Tension

dydu =

See you next time.

Information and Introduction Instructor Textbook HomeworkCourse TopicsCourse TopicsMy Goals for the next 14 weeksOutline1.1 Fluid Mechanics OverviewScope of Fluid MechanicsScope of Fluid MechanicsScope of Fluid MechanicsWhy is Fluid Mechanics Important?Historical development (1)Historical development (2)Historical development (3)Historical development (4)HistorySignificanceWeather & ClimateAerodynamicsEnergy generationGeologyRiver HydraulicsHydraulic StructuresHydrodynamicsWater ResourcesEnvironmentalEnvironmentalTransportationGeotechnicalStructuralStructuralAnalytical Fluid DynamicsAnalytical Fluid DynamicsExperimental Fluid Dynamics (EFD)Applications of EFDComputational Fluid DynamicsModeling (example)Dimensions and Units (1)Dimensions and units (2)Derived quantities (1)Example 2.1 What is a fluid?What is a fluid?What is a fluid?What is a fluid?ContinuumContinuum2.2 Distinction between a solid and a fluid (1)Distinction between a solid and a fluid (2)Distinction between a gas and a liquid (1)2.3 Density, Specific Weight, Specific Volume, and Specific Gravity2.3.1 DensitySpecific weightSpecific gravity2.3.2 ViscosityFluid motion can cause shearing stressesViscosityProblem Viscosity: Kinematic ViscosityViscosity: Newtonian vs. Non-NewtonianNewtonian and Non-Newtonian FluidNewtonian and Non-Newtonian Fluid2.3.3 Compressibility of Fluids: Bulk Modulus(2.3.4 Vapor PressureVapor Pressure2.3.5 Surface Tension Surface Tension: Capillary Action Review: Fluid Properties