MAEG 3030 Topic 1_v1

7/26/2019 MAEG 3030 Topic 1_v1

1/36

MAEG 3030 Topic 1: Introduction to Fluids

Prof. Shih-Chi Chen

Tel: 3943 4136

Office: ERB 307

https://elearn.cuhk.edu.hk/

MAEG 3030

Fluid Mechanics
http://moodle.cuhk.edu.hk/http://moodle.cuhk.edu.hk/

7/26/2019 MAEG 3030 Topic 1_v1

2/36


Message from Dean

2

7/26/2019 MAEG 3030 Topic 1_v1

3/36


Student/Faculty Mutual Expectations

PROPOSED AGREEMENT

A. PREAMBLE The Engineering Faculty of CUHK believes that it is important to

continually strive for an atmosphere of mutual respect,acknowledgement, and responsibility between faculty membersand the student body. Therefore, the CUHK Engineering

community strives here to enumerate the specific expectationsof each side. However, this document is not intended to beeither comprehensive or limiting in regards to theUniversitystatutes. In the end, simple respect for knowledge,hard work, and cordial interactions will help build theenvironment we seek. Therefore, we remain committed to the

ideals of CUHK Engineering, agree to abide by these principles inour time here, and will encourage each other to uphold theseresponsibilities.

3

7/26/2019 MAEG 3030 Topic 1_v1

4/36



B. STUDENT EXPECTATIONS1. a positive, respectful, and engaged academic environment inside and outside the

classroom;

2. to attend classes at regularly scheduled times without undue variations, and toreceive before term-end adequate make-ups of classes that are canceled due toleave of absence of the instructor;

3. to receive a syllabus which should include an outline of the course objectives,entire course content and schedule, evaluation criteria, and any otherrequirements for successful completion of each course on the first day of classand to be clearly informed of any changes made to the syllabus during the

semester with reasonable time to adjust to these changes;4. to consult with concerned faculty members and course tutors outside of usual

classroom times through regularly scheduled office hours or a mutuallyconvenient appointment;

5. to have reasonable access to University facilities and equipment in order tocomplete course assignments and/or objectives;

6. to have access to guidelines on Universitys definition of academic misconduct

within any course;7. to have reasonable access to grading instruments and/or grading criteria for

individual assignments, projects, or exams and to review graded material in atimely fashion;

8. to consult with each courses faculty member regarding the petition process forgraded coursework.

4

7/26/2019 MAEG 3030 Topic 1_v1

5/36



C. FACULTY EXPECTATIONS1. a positive, respectful, and engaged academic environment inside and outside the

classroom;

2. students to appear for class meetings in a timely fashion;

3. to select qualified course tutors in consultation with Department Chairmen aswell as the right to delegate grading, laboratory instruction, tutoring, and otheracademic activities to these individuals;

4. students to appear at office hours or a mutually convenient appointment forofficial matters of academic concern;

5. full attendance at examination, midterms, presentations, and laboratories, withthe exception of formal pre-approved excused absences or emergency situations;

6. students to be prepared for class, appearing with appropriate materials andhaving completed assigned readings and homework;

7. full engagement within the classroom, including meaningful focus during lectures,appropriate and relevant questions, and class participation (for instance,engagement in conversation or phone-calls not related to the lecture topic athand should be avoided);

8. to cancel class due to emergency situations and to cover missed material duringsubsequent class meetings;

9. students to act with integrity and honesty.

5

7/26/2019 MAEG 3030 Topic 1_v1

6/36


Syllabus

6

7/26/2019 MAEG 3030 Topic 1_v1

7/36


Textbooks

Fluid Mechanics 9th Edition, Robert Fox, Wiley, 2015

Introduction to Fluid Dynamics, Nakayama, Yokendo

Co. LTD, 1998.

Fluid Mechanics 4th Edition, Frank M. White, 2006

7

7/26/2019 MAEG 3030 Topic 1_v1

8/36


Tutors & tutorial sessions

Liang Zhuojian ERB 217 34228 [email protected]

Wang Zengyue ERB 302 34233 [email protected]

Zheng Wangbin ERB 301 38042 [email protected]

Office hours: Every Tuesday 3-5pm (ERB 307)

Tutorial hours survey and scheduling Time: TBD

Location: TBA

8

7/26/2019 MAEG 3030 Topic 1_v1

9/36


Why study engineering?

Intellectual development

Smarter!

Challenge

Throughout your study and career

Real world problems are open-ended

Creativity

Most jobs dont allow you to be creative!

Entrepreneurship

Be your own boss!

Think about Google, Apple

Discovery

9

7/26/2019 MAEG 3030 Topic 1_v1

10/36


Why is studying fluid mechanics important?

Broad engineering applications

Agilent lab-on-a-chip cartridge

10

7/26/2019 MAEG 3030 Topic 1_v1

11/36


Resources available

CUHK Library

Internet:

Google / Google scholar / Google patent

Wolfram Alpha

Howstuffworks.com

Youtube

Wikipedia (Can I use Wiki as a reference?)

Fluid websites

iFluids (http://web.mit.edu/fluids-modules/www/)

Films(http://web.mit.edu/hml/ncfmf.html)

MIT OCW

11
http://web.mit.edu/fluids-modules/www/http://web.mit.edu/hml/ncfmf.htmlhttp://web.mit.edu/hml/ncfmf.htmlhttp://web.mit.edu/fluids-modules/www/

7/26/2019 MAEG 3030 Topic 1_v1

12/36


Fluid mechanicsNavier-Stokes Equations

= +

2

3 + 2

+

+

+

+

= +

2 23

+ +

+ +

= +

+

+ 2

3 + 2

+

+

= +

2 23

+ +

+ +

= +

+

+

+

+ 2

3 + 2

= + 2

23

+ +

+ +

7/26/2019 MAEG 3030 Topic 1_v1

13/36


Fluid

Fluids are divided into liquids and gases.

A liquid is hard to compress and as in the ancient saying Watertakes the shape of the vessel containing it, it changes its shapeaccording to the shape of its container with an upper freesurface.

Gas on the other hand is easy to compress, and fully expands tofill its container. There is thus no free surface. Consequently, an

important characteristic of a fluid from the viewpoint of fluidmechanics is its compressibility.

Another characteristic is its viscosity. Whereas a solid shows itselasticity in tension, compression or shearing stress, a fluid doesso only for compression. In other words, a fluid increases its

pressure against compression, trying to retain its originalvolume. This characteristic is called compressibility.Furthermore, a fluid shows resistance whenever two layers slideover each other. This characteristic is called viscosity.

13

7/26/2019 MAEG 3030 Topic 1_v1

14/36


Fluid

In general, liquids are called incompressible fluids and gasescompressible fluids.

Nevertheless, for liquids, compressibility must be taken into accountwhenever they are highly pressurized, and for gases compressibilitymay be disregarded whenever the change in pressure is small.

Meanwhile, a non-existent, assumed fluid without either viscosity orcompressibility is called an ideal fluid or perfect fluid.

Blood?

Blood is complicated. In vertebrates, it is composed of blood cellssuspended in a liquid called blood plasma. Plasma, which constitutes55% of blood fluid, is mostly water (92% by volume), and contains

dissipated proteins, glucose, mineral ions, hormones, carbon dioxide(plasma being the main medium for excretory product transportation),platelets and blood cells themselves.

14

7/26/2019 MAEG 3030 Topic 1_v1

15/36


Basic properties

Units SI units (metric system): There are seven fundamental SI units, namely:

meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere(A) for electric current, kelvin (K) for thermodynamic temperature, mole(mol) for mass quantity and candela (cd) for intensity of light. Derivedunits consist of these units.

Basic fluid properties for quantitative description Density (

) [kg/m3]

Viscosity () [Pa*s ] Conductivity (k) [W/mK]

Heat capacity (C=) [J/K] Diffusivity ( = ) [m2/s] Pressure (P) [Pa] Temperature (T) [K]

Volume (V) [m3]

Mass (m) [kg]

15

7/26/2019 MAEG 3030 Topic 1_v1

16/36


Dimension

All physical quantities are expressed in combinations of base units. The index number of the

combination of base units expressing a certain physical quantity is called the dimension, as

follows. In the absolute system of units the length, mass and time are respectively expressed

by L, M and T. Put Qas a certain physical quantity and c as a proportional constant, and

assume that they are expressed as follows:

= where ,, and are respectively called the dimensions of Q for L, M, T.

16

7/26/2019 MAEG 3030 Topic 1_v1

17/36


Density, specific gravity and specific volume

The mass per unit volume of material is called the density, which is generally

expressed by the symbol. The density of a gas changes according to the pressure,

but that of a liquid may be considered unchangeable in general. The units ofdensity are kg/m3 (SI). The density of water at 4C and 1 atm (101 325 Pa, standard

atmospheric pressure) is 1000 kg/m3. The ratio of the density of a material to the

density of waterw, is called the specific gravity, which is expressed by the symbol

s:

s =/w

The reciprocal of density, i.e. the volume per unit mass, is called the specific

volume, which is generally expressed by the symbol v:

v = 1/ (m3/kg)

Density of water and air under standard atmospheric pressure

17

7/26/2019 MAEG 3030 Topic 1_v1

18/36


Viscosity

As shown below, suppose that liquid fills the space between two parallel plates of areaA

each and gap h, the lower plate is fixed, and force Fis needed to move the upper plate in

parallel at velocity U. Whenever Uh/v < 1500 (v =/: kinematic viscosity), laminar flow is

maintained, and a linear velocity distribution, as shown in the figure, is obtained. Such a

parallel flow of uniform velocity gradient is called the Couette flow.

In this case, the force per unit area necessary for moving the plate, i.e. the shearing stress

(Pa), is proportional to U and inversely proportional to h. Using a proportional constant, it

can be expressed as follows:

=

=

The proportional constant is called the viscosity, the coefficient of viscosity or the dynamic

viscosity.

18

7/26/2019 MAEG 3030 Topic 1_v1

19/36


Viscosity

A flow where the velocity u in the x direction changes in the ydirection is

called shear flow. The left figure shows the case where the fluid in the gap

is not flowing. However, the velocity distribution in the case where thefluid is flowing is as shown in the right figure. Extending equation to such a

flow, the shear stress on the section dy, distance yfrom the solid wall, is

given by the following equation:

=

This relation was found by Newton through experiment, and is called

Newton's law of viscosity.

19

7/26/2019 MAEG 3030 Topic 1_v1

20/36


Viscosity as a function of temperature

At 1 atm

Why?

20

7/26/2019 MAEG 3030 Topic 1_v1

21/36


Viscosity

In the case of gases, increased temperature makes the molecularmovement more vigorous and increases molecular mixing so that theviscosity increases. In the case of a liquid, as its temperature increasesmolecules separate from each other, decreasing the attraction betweenthem, and so the viscosity decreases. The relation between thetemperature and the viscosity is thus reversed for gas and for liquid.

The units of viscosity are Pa-s (pascal second) in SI, and g/(cm s) in the CGSabsolute system of units. 1 g/(cm s) in the absolute system of units is

called 1 P (poise) (since Poiseuilles law, is utilized for measuring theviscosity, the unit is named after him), while its 1/100th part is 1 cP(centipoise). Thus

1 P = 100 cP = 0.1 Pa s

The value (Nu) obtained by dividing viscosity by density is called thekinematic viscosity or the coefficient of kinematic viscosity:

=

21

7/26/2019 MAEG 3030 Topic 1_v1

22/36


Rheological diagram

Newtonian fluid vs. Non-Newtonian fluid

Water vs. blood

22

7/26/2019 MAEG 3030 Topic 1_v1

23/36


Surface tension

The surface of a liquid is apt to shrink, and its free surface is in

such a state where each section pulls another as if an elastic

film is being stretched.

The tensile strength per unit length of assumed section on the

free surface is called the surface tension. Surface tensions of

various kinds of liquid are given in the table below

7/26/2019 MAEG 3030 Topic 1_v1

24/36


Review of vector calculus

7/26/2019 MAEG 3030 Topic 1_v1

25/36



7/26/2019 MAEG 3030 Topic 1_v1

26/36



7/26/2019 MAEG 3030 Topic 1_v1

27/36


Mass conservation There are two methods for studying the movement of flow. One is a method which

follows any arbitrary particle with its kaleidoscopic changes in velocity andacceleration. This is called the Lagrangian method. The other is a method by

which, rather than following any particular fluid particle, changes in velocity andpressure are studied at fixed positions in space x, y, z and at time t. This method iscalled the Eulerian method. Nowadays the latter method is more common andeffective in most cases.

Lagrangian description: Following a particle Define a particle: ()=

+ = 0

Eulerian description: Inspecting a fixed point in space

= , + = 0 Shapiro Video: Eulerian and Lagrangian Descriptions in Fluid Mechanics

http://www.youtube.com/watch?v=mdN8OOkx2ko

27

7/26/2019 MAEG 3030 Topic 1_v1

28/36


Mass conservation

How to derive+ = 0?

Approach 1: Integration

=

+ =

+ = 0

= + = 0

28

7/26/2019 MAEG 3030 Topic 1_v1

29/36


Mass conservation

How to derive+ = 0?

Approach 2: Differential analysis Consider a infinitesimal cube

(mass change rate inside the cube) + (total mass flow going out) = 0

= , , , = + +

Mass change rate inside the cube: Consider X direction:

Mass flux on the left side (inlet)

Mass flux on the right side (outlet)

29

Flux rate of flow of a property per unit area

7/26/2019 MAEG 3030 Topic 1_v1

30/36


Mass conservation

Consider all three directions

(mass change rate inside the cube) + (total mass flow going out) = 0

Divide the equation by dxdydz, we have

l d b

7/26/2019 MAEG 3030 Topic 1_v1

31/36


Streamline and stream tube

A curve formed by the velocity vectors of each fluid particle at a certain

time is called a streamline. In other words, the curve where the tangent at

each point indicates the direction of fluid at that point is a streamline.Floating aluminium powder on the surface of flowing water and then

taking a photograph, gives the flow trace of the powder as shown below.

A streamline is obtained by drawing a curve following this flow trace. From

the definition of a streamline, since the velocity vector has no normal

component, there is no flow which crosses the streamline.

31

d fl d d fl

7/26/2019 MAEG 3030 Topic 1_v1

32/36


Steady flow and unsteady flow

A flow whose flow state expressed by velocity, pressure,

density, etc., at any position, does not change with time, is

called a steady flow.

= 0

A flow whose flow state does change with time is called anunsteady flow. Whenever water runs out of a tap while the

handle is being turned, the flow is an unsteady flow. On the

other hand, when water runs out while the handle is

stationary, leaving the opening constant, the flow is steady.

0

32

3 2 d 1 fl

7/26/2019 MAEG 3030 Topic 1_v1

33/36


3-D, 2-D, and 1-D flow

All general flows such as a ball flying in the air and a flow around a movingautomobile have velocity components inx, yandz directions. They arecalled three-dimensional flows. Expressing the velocity components in the

x, yandz axial directions as u, v and w, then = , , , = , , , = , , ,

Consider water running between two parallel plates cross-cut vertically to

the plates and parallel to the flow. If the flow states are the same on allplanes parallel to the cut plane, the flow is called a two-dimensional flowExpressing the velocity components in thex and ydirections as u and urespectively, then

= ,, = ,,

For one dimensional flow; consider water flowing in a tube in terms ofaverage velocity, then the flow has a velocity component in thex directiononly.

= ,

33

L i d b l fl

7/26/2019 MAEG 3030 Topic 1_v1

34/36


Laminar and turbulent flow

Laminar flow, sometimes known as streamline flow, occurs when afluid flows in parallel layers, with no disruption between the layers.

At low velocities the fluid tends to flow without lateral mixing, andadjacent layers slide past one another like playing cards. There areno cross currents perpendicular to the direction of flow, nor eddiesor swirls of fluids. In laminar flow the motion of the particles of fluid is very orderly with all

particles moving in straight lines parallel to the pipe walls. In fluiddynamics, laminar flow is a flow regime characterized by high momentumdiffusion and low momentum convection.

Turbulent flow is a flow regime characterized by chaotic andstochastic property changes. This includes low momentumdiffusion, high momentum convection, and rapid variation ofpressure and velocity in space and time. Nobel Laureate Richard Feynman described turbulence as "the most

important unsolved problem of classical physics."

Flow in which the kinetic energy dies out due to the action of fluidmolecular viscosity is called laminar flow.

34

L i d b l fl l

7/26/2019 MAEG 3030 Topic 1_v1

35/36


Laminar and turbulent flow examples

Faucet Long pipes

35

O b R ld i t

7/26/2019 MAEG 3030 Topic 1_v1

36/36


Osborne Reynolds experiment

Reynolds conducted many experiments using glass tubes of 7, 9, 15 and 27mm diameter and water temperatures from 4 to 44C. He discovered thata laminar flow turns to a turbulent flow when the value of the

nondimensional quantityvd/ reaches a certain amount whatever thevalues of the average velocity v, glass tube diameter d, water densityand water viscosity. Later, to commemorate Reynolds achievement,

= = ( is kinematic viscosity)

was called the Reynolds number. In particular, whenever the velocity isthe critical velocity vc, Re, = vcd/is called the critical Reynolds number.

The value of Re, is much affected by the turbulence existing in the fluidcoming into the tube, but the Reynolds number at which the flow remainslaminar, however agitated the tank water, is called the lower criticalReynolds number. This value is said to be 2320 by Schiller. Whenever the

experiment is made with calm tank water, Rec, turns out to have a largevalue, whose upper limit is called the higher critical Reynolds number.

Ekman obtained a value of 5 x 104 for it .

36

Documents

MAEG 3030 Topic 1_v1