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PPT – Fluid Mechanics and Energy Transport BIEN 301 Lecture 2 Introduction to Fluids, Flow Fields, and Dimensional Analysis PowerPoint presentation | free to download - id: 6fa018-Y2FkN

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Fluid Mechanics and Energy TransportBIEN

301Lecture 2 Introduction to Fluids, Flow

Fields, and Dimensional Analysis

- Juan M. Lopez, E.I.T.
- Research Consultant
- LeTourneau University
- Adjunct Lecturer
- Louisiana Tech University

History of Fluid Mechanics

- White 1.14 shows us how Fluid Mechanics has

evolved in a helical fashion, returning to its

roots, with improvements each time. - Pre-historic and early history aqueducts and

waterworks Empirically Designed and Built - Archimedes (200s B.C.) and Buoyancy / Vector

addition Theoretical work with Experimental

roots - 200s B.C. to Renaissance ship and canal building

Empirical advances, no great amount of

experimental work - Leonardo da Vinci first formulated the

one-dimensional conservation of mass equation

Theoretical stemming from empirical observations.

History of Fluid Mechanics

- Mariotte (1600s) built the first wind tunnel

Testing theoretical ideas with experimental work. - Isaac Newton (1600s-1700s) generated the

mathematics which allowed fluid momentum to be

studied. - Bernoulli, DAlembert, Euler, Lagrange, Laplace,

all developed their work in frictionless fluids,

and showed the need for a formulation that would

do away with the paradox of an object with no

drag immersed in a moving stream, a natural

result of frictionless fluid assumptions

Theoretical advances mostly. - These theoretical results were unsatisfactory to

engineers, so as a natural backlash, hydraulics

was developed as an almost purely experimental

form by Pitot, Borda, Poiseuille, etc.

History of Fluid Mechanics

- Late 1800s, finally there was a trend towards

the unification between experimental hydraulics

and theoretical hydrodynamics by the likes of

Froude, Raylegh, and Reynolds. All of these

gentlemen have dimensionless groups named after

them due to the importance of their work. - Navier and Stokes began to more fully explore

viscous flow in the mid to late 1800s, setting

the stage for Prandtl. - In the early 1900s, Prandtl developed boundary

layer theory, one of the most important advances

in fluid mechanics, identified by White as the

single most important tool in modern flow

analysis.

History of Fluid Mechanics

- The past tied to the present
- These past examples of development in fluid

mechanics remain important due to the individual

contributions each advance has made to our

current understanding. - In fact, we continue to study many of these

individual ideas as simplified examples of fluid

behavior. - Fluid mechanics encompasses almost every field of

physical systems, and a basic understanding of

the mathematics, terminology, and usage will

greatly benefit you in any engineering field.

What is a Fluid?

- Matter that is unable to resist shear by a static

deflection. (White, 1.2)

- Fluid will deflect under shear unless opposed by

some external force. The rate of strain to stress

is dependent on the viscosity of the fluid.

What is a Fluid?

- This lack of resistance to shear explains why

fluid take the shape of their containers, or

spill when there is no body to contain them.

What is a Fluid?

- Mechanical Description Mohrs Circle

What is a Fluid?

- As with everything, we make some assumptions in

our definition- - Continuum (White 1.3)
- Infinitely Divisible All divisions have same

properties in homogeneous fluid - For real systems, there are uncertainties brought

about by volumes that are too small or too large. - Physical properties are defined and have finite

values throughout the continuum - Thermal properties are defined and have finite

values throughout the continuum

Dimensions vs. Units

- We must inherently have a way to describe the

systems we are studying. We describe these

systems with Dimensions and quantify these

dimensions with Units. - Four primary Dimensions in our study of Fluid

Mechanics - Mass, M
- Length, L
- Time, T
- Temperature, T

Dimensions vs. Units

- It is imperative that you learn consistency in

your dimensional analysis. Fluid mechanics lends

itself to some extremely awkward units,

especially in the British system. - For this course, we will primarily stick with the

International System (SI), but we will refresh

our memories from time to time on how to interact

with the British Gravitational (BG) units. - The use of tables is an inherent task in

engineering work. Become familiar with the tables

such as White, Table 1.1, 1.2, and Appendix

Tables A.1-A.6, and how to properly use them.

Dimensions vs. Units

- Using the tables, perform the following

conversion

Dimensions vs. Units

Dimensional Consistency

- Dimensional Homogeneity (White 1.4)
- Theoretical Equations dimensionally homogeneous

Dimensional Consistency

- However, much work in fluid mechanics has been

empirical, and this can lead to problematic

situations.

Uncertainty

- Once we have established a way to describe these

systems, we must also account for the uncertainty

in our experimentation. (White 1.11) - Instruments and all physical measurements have

some form of uncertainty. - Accounting for all the measurements is important
- Adding them all is simply not realistic
- A simplified Root Mean Square (RMS) approach is

recommended.

Uncertainty

- RMS Formulation

Uncertainty

- RMS Example

Basic Physical Properties

- Thermodynamics (White 1.6)
- Principal components of velocity vectors
- Pressure, p
- Density, ?
- Temperature, T
- Principal components of work, heat, and energy

balance. - Internal Energy, û
- Enthalpy, h û ?/p
- Principal transport properties
- Viscosity, µ
- Thermal Conductivity, k
- Together, these define the state of the fluid.

Basic Physical Properties

- Additional Properties (White 1.6)
- Specific Weight, ? ?g
- Specific Gravity
- SGgas ?gas / ?air
- SGwater ?liquid / ?water
- Potential Energy
- -g?r
- Kinetic Energy
- 0.5 V2
- Total Energy
- e û 0.5 V2 (-g?r)

State Relationships

- State Relationships for Gases (White 1.6)
- Thermodynamic properties are related to each

other by state relationships. For gases, there is

the ideal gas law (perfect-gas law). - p ?RT where R cp cv (gas constant)
- The gas constant is related to the universal gas

constant, ? by the following equation - ? Rgas Mgas

State Relationships

- State Relationships for Liquids
- No direct analog of the ideal gas law exists for

liquids. - Why? If fluids involves liquids and gases, why

can we not get a direct correlation to a liquid

form? - Compressibility. The ideal gas law assumes

compressibility, whereas most liquids are mostly

incompressible.

State Relationships

- State Relationships for Liquids
- As an example of this lack of direct

relationship, see from White, eq. 1.19

- Where B and n are dimensionless parameters that

vary with temperature.

Velocity Fields

- For many of the problems encountered here, the

velocity field will be the solution to our given

problem, or an integral part thereof. (White 1.5) - The three-dimensional velocity field can be

expressed in a variety of ways

Velocity Fields

- Simplified problems in White, example 1.5, we

see the convective result for a 1-Dimensional

problem. The extended answer for the 3D problem

is as follows

Velocity Fields

- Dealing with partial differential equations.
- Cross out terms ahead of time, simplifies

calculations. - For the 2D problem, there are no velocity

components in the Z direction (no w magnitude,

and no d() /dz.

Velocity Fields

Application

- So, what can we do with all of this stuff? Why

re-hash over so many of the basics we have seen

in other courses over the years? - While we may have been exposed to all of these

concepts, they become integral in the study of

fluid mechanics. - Familiarity with these ideas is no longer enough,

we must master these concepts and learn to apply

them in new and effective ways.

Application

- With these basics we will be able to
- Fully describe and define the subject of our

study Fluids. - Perform dimensionally consistent calculations,

increasing the skill set required of a modern

professional engineer. - Be conversant and capable in both the BG and the

SI system, able to convert between the two as the

problem requires.

Application

- With these basics we will be able to
- Understand the basic thermodynamic concepts

required to extend our analysis from pure fluid

mechanics to true energy transport problems. - Heat Transfer
- Temperature-dependent effects
- Accurately and professionally report our

findings, accounting for our experimental error

and/or uncertainty.

Application

- As was mentioned before these skills, though

ideally common throughout all of our engineering

courses, become absolute cornerstones of success

for a subject as complex and difficult as fluid

mechanics.

Fundamental Approaches

- There are two primary approaches to problem

solving in fluid mechanics - Lagrangian and Eulerian
- Lagrangian follows a fluid particle as it moves

through a flow field. - Eulerian Observes passing fluid particles from a

stationary position relative to the flow field

Fundamental Approaches

- Examples
- Lagrangian
- A user observes traffic on the freeway as he sits

in his vehicle, travelling down the freeway along

with the traffic. Traffic jams, velocity changes,

etc, are all marked and observed to attempt to

describe the flow of traffic through a section of

freeway. - Eulerian
- A state trooper monitors freeway traffic from a

hidden location under the bridge, monitoring for

changes in traffic that could indicate potential

trouble. Multiple state troopers and cameras

along the road give a big picture perspective

to traffic managers.

Fundamental Approaches

- Eulerian will be our fundamental approach for

this course. - Probes at different points in the fluid stream

are much more easy to design and monitor for

smaller systems that well concern ourselves with

than large instrumentation designs that follow

the flow. - Can you think of an example of Eulerian

monitoring and/or Lagrangian monitoring in

biomedical systems? What are some potential

benefits of each type of system relative to this

application?

Assignment

- HW 2 has been posted on blackboard
- Project Proposals due soon!
- Individual project sign-ups will be available by

tonight on blackboard.

Questions?