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baconossifiedMechanics

Oct 29, 2013 (3 years and 7 months ago)

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UNI T 1:

I NTRODUCTI ON AND FLUI D PROPERTI ES

Fluid mechanics

Aug
-
Dec 2013

Professor

Dr. Luis E. Lesser Carrillo

Hydrogeologist
/
Environmental

Engineener


Why have a lecture in English?

(my own experience is…)


My own goal as professor (not TEC
´
s) is to inspire
my students to pursue a graduate degree abroad
(Canada, USA, Australia, maybe Europe)


I will be glad to help planning it!


2

By appointment


At Tec
-

before and after class


Out of Tec


in my office

Class schedule at Tec:

Tutoring hours:

3

Monday

Tuesday

Wednesday

Thursday

Friday

7
-
10 AM*

7
-
10 AM*

7
-
10PM**

*
Laboratorio

de
hidráulica
.
Edificio

1 (1401)

**
Classroom 3210

Dr. Luis E. Lesser Carrillo


luis_lesser@prodigy.net.mx


Ph. office: 223
-
1515 and 223
-
3361


Address office:
Río Guadalquivir # 3
. Col
.
Pathé


4

Starbucks


Çengel
, Y.A. and
Cimbala
, J.M.,
2006.
Fluid
Mechanics, fundamentals and applications
, 2
nd

edition,
McGraw
-
Hill, 980 pp.

Textbook

5


The book was requested to “
Librería

Lexis” (Tec
´
s
bookstore). However I do not know how many copies they
have. Gandhi and
Librerias

del Cristal may also have
some copies


I recommend the version in English, but you are welcome
to buy the one in Spanish if you prefer.

6


Streeter, V.L., Wylie, E.B. and Bedford, K.W., 1998.
Fluid Mechanics, 9
th

Edition
,
McGraw
-
Hill, 740 pp.


Finnemore

E.J. and
Franzini
, J.B., Fluid Mechanics with
Engineering Applications, 10
th

Edition, McGraw
-
Hill,
790 pp.


Any fluid mechanics textbook will work!

Other References

Partial test:


80 %

Assignments: 20 %

Final Grade:

7

Partial test 1: 20 %

Partial
test
2: 20 %

Homework: 20 %

Final exam: 40 %

Partial Grades:

Note:

For final grade, the reported partial grades won
´
t be used

8

Exams schedule


1
st

Partial test: September
10


2
nd

Partial test: October 29

o
Last session: November 26


Final
test:
TBA

9

Class Policies


Attendance


Maximum 3 absences allowed

o
Why do we miss classes?

o
Audit/sit in


Lateness
(activities as soon as class begins)


Cel
. Phones


Suggestions for new class dynamics using
new technologies

Course

Contents

1.
Introduction and properties
(Ch. 1 & 2
Çengel
; Ch. 1 Streeter)

2.
Pressure and fluid statics
(Ch. 3
Çengel
; Ch.
2 Streeter)

3.
Mass and Energy Conservation Equations
(Ch.
4, 5
& 6
Çengel
; Ch.
3, 4
Streeter)

4.
Dimensional
Analisis

(Ch. 7
Çengel
; Ch.
5
Streeter)

5.
Turbomachinery

(Ch.
14
Çengel
; Ch.
11
Streeter
)*

6.
Open
channel flow
(
Ch.
13
Çengel
; Ch.
13
Streeter
)

10

mcargnel

11

Solids, Liquids and Gases show very different
intermolecular forces and distances

Unit 1: Introduction and properties

mcargnel

12

Liquids and Gases are Fluids

-

Their behavior in a container is
different

-

Different densities

-

Both can be deformed by
tangential stresses

mcargnel

13

Density = mass / volume

Depends on temperature and pressure

Relative Density:

Water at 4
°
C is usually taken as
r
REF


Some useful characteristics/definitions of fluids

mcargnel

14

Correlation for the density of liquid water

In industrial practice can be considered independent from pressure. Ex:
Calculate the liquid water density at different temperatures using the
above equation

Temperature range:

mcargnel

15

Correlation for the density of liquid water

How do these calculated results compare to those by Streeter?

mcargnel

16

Specific volume = volume / mass

Specific Weight:

Other useful definitions

Specific Gravity:

Pressure:

Which are the dimensions of pressure?

mcargnel

17


Capillarity


Surface tension

Other useful definitions


Vapor Pressure


Cavitation


Continuum approach

mcargnel

18

Ideal Gas
E
quation

Where:

P = absolute pressure

T = absolute temperature

R
s

=
gas
constant

R = universal gas constant

V= volume

v
s

= specific
volume

r
= density

n = number of moles

mcargnel

19

Ideal Gases

general equation

Where:


n = number of moles

m = mass (g)

M = molar mass (g/
mol
)

mcargnel

20

Universal Gas Constant

mcargnel

21

Example 2
-
1 (
Çengel
, 2006)

Determine the density, specific gravity (relative density), and mass
of the air in a room whose dimensions are 4 m
×

5 m
×

6 m at 100
kPa

and 25
°
C. Use:

mcargnel

22

Example 5.15 (Ravel and
Navidi
, 1990)

The pressure in an oxygen tank is 10
atm

at 0
°
C. What pressure will
develop in the tank if stored in a furnace room
at
45
°
C?

mcargnel

23

Example 1
-
6 (with different data)

In order to calculate the volume flow rate of water through a hose
,
a
student measures how long it takes to fill a cylindrical bucket

Determine the volumetric flow rate during the experiment (in L/min)

Bucket diameter

23.0 cm

Height of water

collected

12.0 cm

Filling time

38.0 s

mcargnel

24

Physical Transport Properties


(Coefficient of) viscosity


Transport of Momentum


(Coefficient of) thermal conductivity


Conduction Heat Flow


Coefficient of diffusivity


Chemical species diffusion in others

mcargnel

25

If this experiment is conducted first with water and
then with oil the time required to empty the container
will be different: They have different
viscosities
.

A shaft turning inside a coaxial cylinder with a fluid in the
annular space (friction bearing)

Viscosity and the mechanism of momentum transfer

A fluid is a substance that deforms continuously when
subjected to a shear stress

mcargnel

28

If the annular cavity is small is acceptable to represent
the system in Cartesian coordinates

As time proceeds from an initial transient state, the steady
state is reached and a linear velocity profile is established.

A constant force is required to maintain the motion.

The force per unit area is proportional to the velocity decrease in
the ‘
y’

direction.

The coefficient of proportionality between the tangential stress
and the velocity gradient is called viscosity.

o
The force and velocity direction is
x

o
The momentum direction is
x

o
The shear stress is exerted in the
x
-
direction on a
fluid surface of constant
y

o
The
x
-
momentum is transmitted in the
y
-
direction

In Cartesian coordinates as drawn

The force per unit area (stress) is proportional to the
negative of the local velocity gradient.

The same equation in differential form:

mcargnel

33

Graphic representation: Stress vs. Velocity gradient

(for “Newtonian” fluids: water, milk, alcohol, all gases)

The slope is the viscosity

Newton’s Law of viscosity

mcargnel

34

Newtonian vs. non
-
Newtonian fluids

UNITS

Newton’s Law of viscosity

In
cgs

system
:

Calculation of momentum flux (shear stress)

Compute the steady state momentum flux (
t
) when the lower plate
velocity is 0.3 m/s, the plate separation is 0.3 mm and the fluid
viscosity is 0.7
cP.


Remember:

Example 2
-
5
(
Çengel
, 2006)
: Determining the viscosity

37

The viscosity of a liquid is to be measured by a
Couette

viscometer constructed of two 400
-
mm
-
long cylinders. The outer diameter of the inner
cylinder is 120 mm and the gap between the two
cylinders is 1.5 mm.

The inner cylinder is rotated at 300 rpm, and the
torque (T) is measure to be 1.80 Nm. Determine
the viscosity of the fluid

Example 2
-
5
(
Çengel
, 2006)
: Determining the viscosity

38

R = radius

w
= angular velocity

n = revolutions per unit time

(Ans.: 1.58


10
-
1

Pa.s
)

Fluid


[
Pa.s
]

Air

10
-
5

Water

10
-
3

Olive oil

10
-
1

Glicerine

1

Honey (hot)

10

Syrup

100

Viscosities values in:

Figure 2
-
26,

Table 2
-
3 (Chapter 2) and

Tables A
-
3 to A
-
10 (Appendix)

in
Çengel

(2006
)

Viscosities at room temperature

(order of magnitude)

40

Problem

2
-
72
(
Cengel
)

A thin 20
-
cm x 20
-
cm flat plate is pulled at 1m/s horizontally through a
3.6
-
mm
-
thick oil layer sandwiched between two plates, one stationary
and the other moving at a constant velocity of 0.30 m/s.

41

The dynamic viscosity of oil is 0.027
Pa.s

. Assuming the velocity in
each oil layer to vary linearly. (a) find the location where the oil velocity
is zero and (b) determine the force that needs to be applied on the plate
to maintain the motion.

42

Lower region:

Upper region

43

The location where the oil velocity is zero

44

The force needed to maintain the motion