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
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