Download - Chapter 1 Fluid Mechanics
-
1FLUID MECHANICS
CHAPTER 1
LECTURER: Sarah Asif
-
2SYLLABUS
1.0 INTRODUCTION TO HYDRAULICS
1.1 Units and dimensions
1.2 Ideal and Newtonian fluid
1.3 Properties of fluid: density, specific weight,
specific gravity, viscosity, bulk modulus,
shear force, surface tension and
capillarity.
-
31.0 Introduction
- This subject is focus on scientific study related to
fluid flow in closed conduit (e.g pipe) and open
channel (e.g river).
-
4Fluid engineering applications is enormours; which are flow
in pipelines and channels, movements of air and blood
in the body, air resistance, wind loading on buildings,
motion of projectiles, jets, shock waves, lubrication,
combustion and irrigation.
The knowledge of fluid mechanics and hydraulics is required
to properly design water supply systems, wastewater
treatment facilities, spillways, pumps, turbines, air
conditioning systems and etc.
Contd
1.0 Introduction
-
51.1 Units and Dimension
Notes: British Gravitational (BG) system used English unit, while
System International (SI) used metric units.
Quantity Dimension SI BG
Mass M kg Lb
Length L m ka
Time T S s
Temperature oC oF
-
61.2 Ideal & Newtonian Fluid
Fluid can be divided into 2 (two) :
1) Liquid
- Able to flow and does not have specific form.
- Change to another form or shape if shear force
involved.
- Assumed as uncompressible fluid.
(Compressibles value has been ignored - too small)
Contd
-
71.2 Ideal & Newtonian Fluid
2) Vapor / gas
- Compressible fluid.
- Density of gas/vapor is different based on
temperature and pressure required.
Contd
-
81.2 Ideal & Newtonian Fluid
Ideal Fluid
Known as perfect fluid
This fluid has no friction, surface tension and
compressiblity.
Although this fluid does not exist in reality, a lot
of researchers used it in analysis and
calculation of fluid.
Contd
-
91.2 Ideal & Newtonian Fluid
Real Fluid
In real fluid, either liquid or gas, tangential or shearing
forces always develop whenever there is motion relative
to a body, thus creating fluid friction.
Newtonian fluid
is a fluid for which the constant of proportionality
(where, shear stress proportional to the time rate of
(angular) deformation) does not change with rate of
deformation.
Contd
-
10
1.2 Ideal & Newtonian Fluid
Real Fluid
Water, air, gasoline, and oils (Newtonian fluids)
Blood and liquid plastics (non-Newtonian fluids)
Contd
-
11
Density ()
Depends on temperature and pressure
Density = mass per unit volume or = m/V
SI Unit = kg/m3.
Example: density of water = 998 kg/m3 1000 kg/m3
1.3 Properties of FluidContd
-
12
Specific Weight ()
Specific weight = weight per unit volume or
= W/V N/m3 or
= g N/m3
Example: specific weight of water
= 1000 x 9.81 = 9.81 kN/m3
where, accelaration of gravity = 9.81 ms-2
Contd
1.3 Properties of Fluid
-
13
Specific Gravity (s.g)
Specific gravity = specific weight of substance/
specific weight of water at 4oC
s.g = substance / water at 4o
C
Where, specific weight of water is 9.81 kN/m3
Contd1.3 Properties of Fluid
-
14
Relative Density (rd)
The relative density of a substance /liquid is
defined as the ratio of its mass density to the mass
density of water taken at atmospheric of 4C.
Contd
water
sub
waterofDensity
substance ofDensity
(Formula for rd and sg are similar if gravitys value is same)
1.3 Properties of Fluid
-
15
Contd
Example 1 :
A reservoir of glycerin as a mass of 1200 kg and a
volume of 0.952 m3. Find the glycerins weight (W), mass density ( ), specific weight ( ) and
specific gravity (s.g)
1.3 Properties of Fluid
-
16
W = mg = (1200)(9.81) = 11770N atau 11.77kN
= m/V = 1200/0.952 = 1261 kg/m3
= g = (1261)(9.81) = 12.37 kN/m3 (atau W/V)
s.g = substance / water at 4oC = 12.37k/9.81k = 1.26
Contd
Answer 1:
1.3 Properties of Fluid
-
17
Answer :
W = 4905 N, = 1587 kg/m3, =15.57 kN/m3,
s.g =1.59
Contd
A reservoir of carbon tetrachloride (CCl4) has a
mass of 500 kg and a volume of 0.315 m3. Find the
carbon tetrachlorides weight, mass density, specific weight and specific gravity.
1.3 Properties of Fluid
Question 1
-
18
Specific Volume (vs)
Defined as the reciprocal of the mass density or
volume per unit mass
SI Unit is m3/kg
Contd
1
sv
1.3 Properties of Fluid
-
19
Contd
If the specific volume of a certain gas is 0.73 m3/kg,
calculate its specific weight.
1.3 Properties of Fluid
Example 2 :
vs = 0.73 m3/kg = 1/vs = 1/0.73 =1.37 kg/m
3
= g = 1.37 x 9.81 = 13.44 N/m3
Answer 2 :
-
20
Viscosity
is a property that represents the
internal resistance of a fluid to
motion or the fluidity.
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
on viscosity.
Contd1.3 Properties of Fluid
-
21
Viscosity
To obtain a relation for viscosity,
consider a fluid layer between
two very large parallel plates (or
equivalently, two parallel plates
immersed in a large body of a
fluid) separated by a distance.
Contd1.3 Properties of Fluid
-
22
Viscosity
Now a constant parallel force F is applied to the
upper plate while the lower plate is held fixed. After
the initial transients, it is observed that the upper
plate moves continuously under the influence of
this force at a constant velocity V.
The fluid in contact with the upper plate sticks
to the plate surface and moves with it at the same
velocity.
Contd1.3 Properties of Fluid
-
23
Viscosity
Force which are needed to make a constant flow is
where is dynamic viscosity,
Contd1.3 Properties of Fluid
y
AuF
rate stressshear
stressshear /
yu
AF
The shear stress acting on this fluid layer is ( = F/A) where
A is the contact area between the plate and the fluid.
Note that the fluid layer deforms continuously under the
influence of shear stress.
-
24
The shear stress can also shows as
SI Unit = Ns/m2 or kg/ms or Pa.s or Poise
(10 Poise = 1Ns/m2)
Contd
dy
du
1.3 Properties of Fluid
-
25
Kinematic viscosity is defined as the ratio of
dynamic viscosity to mass density,
SI units : m2/s or stokes
(10,000 stokes = 1 m2/s)
Contd
density
viscositydynamic
1.3 Properties of Fluid
-
26
1.3 Properties of FluidContd
Example 3 :
A plate separated by 0.5 mm from a fixed plate
moves at 0.5 m/s under a force per unit area of 4.0
N/m2. Determine the viscosity of fluid between the
plates.
-
27
1.3 Properties of FluidContd
Answer 3 :
dy
du
4.0 N/m2
0.5 m/s
0.0005 m
2/004.00005.0
5.0)0.4( mNs
du
dy
-
28
Compressibility and Bulk Modulus
All fluid are compressible when subjected to
applied forces, they will exprience a reduction
in volume.
Volume reduction in gases are much more
compressible compared to liquids. Hence, gases
are much more compressible compared to
liquids.
Contd1.3 Properties of Fluid
-
29
The change in volume which accompanies the
change in pressure is given;
where, K is the bulk modulus of substance
Bulk modulus is limitation for substance to
resist compressibility.
Contd1.3 Properties of Fluid
V
dVKdp
-
30
The bulk modulus for solids
and liquids remains fairly
constant over the ranges of
pressure and volume changes.
Liquids are considered
incompressible as the volume
change is very small.
K unit = N/m2
Contd1.3 Properties of Fluid
-
31
Contd
Example 4 :
A liquid compressed in a cylinder has a volume of
1000 cm3 at 1 MN/m2 and a volume of 995 cm3 at 2
MN/m2. What is its bulk modulus of elasticity (K)?
MPa2001000/)1000995(
12
VV
pK
Answer 4:
1.3 Properties of Fluid
-
32
Question 2
Answer :
K = 13.2 MPa
Contd
If K for water is 22 GPa, what pressure required to
reduce a volume by 0.6 percent.
1.3 Properties of Fluid
-
33
Surface Tension ( )
This property takes place at the interface between a
liquid and a gas, i.e., at the liquid surface, and at
the interface between two immiscible liquids.
The out of balance attraction force between
molecules forms an imaginary surface film which
exerts a tension force in the surface.
Contd
1.3 Properties of Fluid
-
34
This force acts in the plane of the surface, normal to any line drawn in the surface and its tends to reduce the surface area of liquid body.
Effect of surface tension is to reduce the liquid area to minimum level and increase the internal forces thus, surface tension force must be in equilibrium.
= 0.073 N/m for air-water interface
= 0.480 N/m for air -mercury interface
Contd1.3 Properties of Fluid
-
35
Unit : N/m
For interior of liquid cylinder,
A spherical droplet,
The pressure difference between 2 surfaces of soap
bubbles,
Contd1.3 Properties of Fluid
RP
RP
2
RP
4
-
36
An atomizer forms water droplets 45m in diameter. Find the excess pressure within these droplets for
water at 30oC.
Example 5 :
Contd1.3 Properties of Fluid
PaxR
P 63292/)1045(
)0712.0(226
Answer 5 :
-
37
Question 3
Answer :
P = 67.5 Pa
Contd
What is the pressure difference between the inside
and outside of a cylindrical water jet when the
diameter is 2.2 mm and the temperature is 10oC
1.3 Properties of Fluid
-
38
Capillarity
When a liquid comes into contact with a solid
surface, then the adhesion forces between solid and
liquid as well as the cohesion forces within the liquid
must be considered. It is also because of surface
tension of liquid.
If adhesion forces > cohesion forces, the
meniscus in glass tube will show maximum curve
,i.e, mercury.
Contd1.3 Properties of Fluid
-
39
While, if cohesion forces > adhesion forces, the
meniscus will behave differently, i.e. water
1.3 Properties of FluidContd
-
40
Increasing of liquids level in tube can be estimated if angle, which is between wall and liquid are
known. Here is the formulae;
1.3 Properties of FluidContd
rh
cos2
Where : - angle
- specific weight
- surface tension
r - radius
-
41
Find the capillary rise in the tube for a mercury-air-
glass interface with 130oC if the tube radius is 1mm
and the temperature is 20oC.
Example 6 :
Contd1.3 Properties of Fluid
Answer 6 :
mr
ho
005.0)1000/1)(81.9)(13570(
)130)(cos514.0(2cos2
-
42
Question 4
Answer :
h = 14.8 mm
Contd
Find the capillary rise in the tube for a water-air-glass interface ( =0o) if the tube radius is 1 mm and the temperature is 20oC. Given w = 0.0728 N/m
1.3 Properties of Fluid
-
43
Contd1.3 Properties of Fluid
Next slides (pg 44- pg 48) are show the properties of
air, water dan common gases at standard sea-level
atmosphere pressure.
-
44
1.3 Properties of Fluid (Appendix)
ContdTable A.1: Properties of air at standard sea-level atmosphere pressure
Temperature oC
Density, kg/m3
Specific weight,
N/m3
Dynamic viscosity,
Ns/m2
Kinematic Viscosity,
m2/s
0 1.29 12.7 1.72 10-5 13.3 10-6
10 1.25 12.2 1.77 10-5 14.2 10-6
20 1.20 11.8 1.81 10-5 15.1 10-6
30 1.16 11.4 1.86 10-5 16.0 10-6
40 1.13 11.0 1.91 10-5 16.9 10-6
50 1.09 10.7 1.95 10-5 17.9 10-6
60 1.06 10.4 1.99 10-5 18.9 10-6
70 1.03 10.1 2.04 10-5 19.9 10-6
80 1.00 9.80 2.09 10-5 20.9 10-6
90 0.972 9.53 2.19 10-5 21.9 10-6
100 0.946 9.28 2.30 10-5 23.0 10-6
-
45
1.3 Properties of Fluid (Appendix)Contd
Table A.2: Properties of water at standard sea-level atmosphere pressure
TemperatureoC
Density, kg/m3
Specific weight, N/m3
Dynamic viscosity, Ns/m2
Surface tension*, N/m
0 1000 9810 1.75 10-3 0.0756
10 1000 9810 1.30 10-3 0.0742
20 998 9790 1.02 10-3 0.0728
30 996 9770 8.00 10-4 0.0712
40 992 9730 6.51 10-4 0.0696
50 988 9690 5.41 10-4 0.0679
60 984 9650 4.60 10-4 0.0662
70 978 9590 4.02 10-4 0.0644
80 971 9530 3.50 10-4 0.0626
90 965 9470 3.11 10-4 0.0608
100 958 9400 2.82 10-4 0.0589
* Contact
with air
-
46
1.3 Properties of Fluid (Appendix)Contd
Fluid
TempDensity,
Specific gravity, sg
Viscosity,
Surface tension,
Bulk Modulus,
K
oC kg/m3 10 3
Ns/m2N/m 106 N/m2
Benzene 20oC 876 0.88 0.65 0.029 1030
Tetrachloride Carbon
20oC 1588 1.594 0.97 0.026 1100
Raw oil 20oC 856 0.86 7.2 0.03
Gasoline 20oC 680 0.68 0.29
Glycerine 20oC 1258 1.26 1494 0.063 4344
Hydrogen
257oC 73.7 0.074 0.021 0.0029
Table A.3: Properties of fluid at standard sea-level atmosphere pressure
-
47
1.3 Properties of Fluid (Appendix)Contd
Table A.3: Properties of fluid at standard sea-level atmosphere pressure
Fluid
TempDensity
,
Specific weight,
sg
viscosity,
Surface tension,
Bulk Modulus,
K
oC kg/m3 10 3
Ns/m2N/m 106N/m2
Kerosene 20oC 808 0.81 1.92 0.025
Mercury 20oC 13550 13.56 1.56 0.51 26200
Oxygen 195oC 1206 1.21 0.278 0.015
SAE 10 oil 20oC 918 0.92 82 0.037
SAE 30 oil 20oC 918 0.92 440 0.036
Water 20oC 998 0.999 1.00 0.073 2171
Sea water 20oC 1023 1.024 1.07 0.073 2300
-
48
1.3 Properties of Fluid (Appendix)
Contd
Table A.4: Physical properties of common gases at standard sea-level atmosphere pressure
Gas
Chemical formula
Molar Mass, M
Density,
Viscosity,
Gas Constant, R
kg/ kg-mol kg/m3 106 Ns/m2 m2/(s2K)
Air 28.96 1.205 18.0 287
Carbon dioxide
CO2 44.01 1.84 14.8 188
Carbon monoxide
CO 28.01 1.16 18.2 297
Helium He 4.003 0.166 19.7 2077
Hydrogen H2 2.016 0.0839 9.0 4120
Methane CH4 16.04 0.668 13.4 520
Nitrogen N2 28.02 1.16 17.6 297
Oxygen O2 32.00 1.33 20.0 260
Water Vapour
H2O 18.02 0.747 10.1 462
-
49
1.3 Summary of Fluids Properties
Surface Tension
Viscosity
Bulk Modulus
Density
Specific Gravity
Capillarity
Compressibility
Relative Density
Properties
of Fluid
Value of fluid
properties are
vary in different
temperatures