Transcript Fundamental Properties of Water Chapter 1 The Islamic University of Gaza

The Islamic University of Gaza
Faculty of Engineering
Civil Engineering Department
Hydraulics - ECIV 3322
Chapter 1
Fundamental Properties of Water
Hydraulic
• Hydraulic comes from the Greek word hydraulikos
= water.
• Hydraulics is the science of studying the
mechanical behavior of water at rest or in motion.
• Hydraulic Engineering is the application of
fundamental principles of fluid mechanics on water.
• Hydraulic systems
Systems which are designed to accommodate water
at rest and in motion.
Hydraulic
• Hydraulic Engineering Systems:
Involve the application of engineering principles
and methods to :
– planning,
– control,
– transportation,
– conservation, and
– utilization of water.
Examples of Hydraulic Projects
• Water pipelines,
• Water distribution systems,
• Sewer systems,
• Dams and water control structures,
• Storm sewer systems,
• Rivers and manmade canals,
• Coastal and Harbour structures,
• Irrigation and Drainage Projects,
Surface tension variation
• Directly affects the evaporation loss from a
large water body in storage;
• Variation of water viscosity with temperature is
important to all problems involving water in
motion.
The Earth's Atmosphere and Stratosphere
• The earth's atmosphere layer thickness is approximately
1500 km of mixed gases.
• Nitrogen makes up ~ 78% of the atmosphere,
• Oxygen makes up ~ 21%,
• The remaining 1 % consists mainly of water vapor, argon,
and trace amounts of other gases.
• The Stratosphere is the second layer from the Earth.
• The jet stream is in the Stratosphere, which is where jets fly,
because of high wind speeds.
• Stratosphere is about 28 km.
• The ozone layer is also in the Stratosphere
Atmospheric Pressure
• The total weight of the atmospheric column exerts a
pressure on every surface with which it comes in contact.
• At sea level, under normal conditions, the atmospheric
pressure is 1.014 • l05 N/m2 or 1 bar. (1 Pascal)
• In the atmosphere, each gas exerts a partial pressure
independent of the other gases.
• The partial pressure exerted by the water vapor in the
atmosphere is called the vapor pressure.
Phases of Water
• The amount of energy holding the molecules
together depends on the temperature and
pressure.
• Depending on its energy content, different forms of
water are called three phases:
1. Solid (snow and ice)
2. Liquid (the most commonly recognized form)
3. Gaseous form in air (Moisture, water vapor)
Change of water from one phase to
another phase
• Energy must either be added or taken away from the
water.
• Latent energy : the amount of energy required to change
water from one phase to another.
• To Melt ice requires a latent heat (heat effusion) of 79.71
cal/g.
• 79.71 cal of heat energy must be taken out of each gram of
water to freeze.
• Evaporation requires a latent heat (heat of vaporization) of
597 cal/g.
• Under standard atm.P, water boils at 100°C.
Properties of water
• Understand the physical properties of water to
solve problems in hydraulic engineering
systems.
• Main Water properties:
1- Density (r),
2- Surface tension
3- Viscosity (n)
1. Density and Specific Weight of water
• Density (r): mass per unit volume (kg/m3).
• Density depends on size and weight of the molecules
and the mechanisms by which these molecules are
bonded together.
• Water expands when it freezes. The expansion of
freezing water causes stresses on the container walls.
These stresses are responsible for the bursting of
frozen water pipes, chuck holes in pavement, and for
the weathering of rocks in nature.
Density and Specific Weight of Water
• Water reaches a maximum density at 4°C. It
becomes less dense when heated.
• Density of sea water about 4% more than that of
fresh water. Thus, when fresh water meets sea
water without sufficient mixing, salinity increases
with depth.
TABLE 1.2: Variation of Density and Specific Weight of Water
with temperature
Temperature
(°C)
Density ( r , kg/m3)
Specific Weight
(g, N/m3)
0°(ice)
917
8996
0° (water)
999
9800
4°
1000
9810
10°
999
9800
20°
998
9790
30°
996
9771
40°
992
9732
50°
988
9692
60°
983
9643
70°
978
9594
80°
972
9535
90°
965
9467
100°
958
9398
Variation of Density in a Large Reservoir
Change of density with T causes water in a lake to
stratify:
1.
During summer, water tends to stratify, with warmer
water on the surface.
2.
During the fall, the surface water drops rapidly and
sinks toward the lake bottom. The warmer water near
the bottom rises to the surface, resulting in fall
overturn of the lake.
3. In the winter (water temperature falls below 4°C, with
highest water density ), the lake surface freezes while
warmer water remains at the bottom. The winter
stratification is followed by spring overturn of the lake.
Specific Weight of Water
• The weight W = m.g
- m: mass of project (m, in grams, kilograms, etc.),
- g : the gravitational acceleration (g = 9.81 m/sec2).
• Weight is expressed in the force units of newton (N) = the
force required to accelerate 1 kg of mass at a rate of 1
m/sec2.
• The specific weight (g) = weight per unit volume of water
(N/m3)
g=rg
• Specific gravity (S): the ratio of the specific weight of any
liquid to that of water at 4°C.
Example 1.1
2. Viscosity of Water
• Consider that water fills the space between two parallel
plates at a distance y a part. A horizontal force T is applied
to the upper plate and moves it to the right at velocity V while
the lower plate remains stationary. The shear force T is
applied to overcome the water resistance R, and it must be
equal to R because there is no acceleration involved in the
process.
Shear stress (t) is the resistance per unit area of the upper plate t = RIA
Water responds to shear stress by continuously yielding in angular
deformation in the direction of the shear.
The rate of angular deformation in the fluid, d(q)ldt ,is proportional to
the shear stress, as shown in Figure 1.2.
we know that:
dx
dx
Angular deformatio n (Shear strain), q 
, and v 
dy
dt
dq
dx
dv
Rate of shear strain 


(Velocity gradient)
dt
dy.dt dy
dv
du
t  constant
t


dy
dy
The proportionally constant,  , is called the absolute viscosity of the fluid
• The absolute viscosity has the dimension of force per unit
area (stress) times the time interval considered. It is usually
measured in the unit of poise.
• The absolute viscosity of water at room temperature (20.2°C)
is equal to 1 centipoise (cP), which is one-hundredth of a
poise.
1 poise = 0.1 N • sec/m2 = 100 cP
• The absolute viscosity of air is approximately 0.018 cP
(roughly 2% of water).
Newtonian fluids and non-Newtonian fluids
Equation (1.2) is commonly known at Newton's law
of viscosity. Most liquids abide by this relationship
and are called Newtonian fluids. Liquids that do not
abide by this linear relationship are known as nonNewtonian fluids. These include most house paints
and blood.
Kinematic Viscosity
• Kinematic viscosity, nu, is obtained by dividing the
absolute viscosity by the mass density of the fluid at the
same temperature;
n =  / r.
• The kinematic viscosity unit is cm2/sec.
• The absolute viscosities and the kinematic viscosities of
pure water and air are shown as functions of temperature in
Table 1.3.
TABLE 1.3 Viscosities of Water and Air at various temperatures
Water
Air
Temperature
Absolute
Kinematic
Absolute
Kinematic
(°C)
Viscosity
Viscosity
Viscosity
Viscosity
N • sec/m2
cm2/sec
N • sec/m2
cm2/sec
0
1.781 x l0-3
.785 x 10-6
1.717 x 10-5
.329 x 10-5
5
1.518 x l0-3
.519 x 10-6
1.741 x l0-5
.371 x l0-5
10
1.307 x 10-3
.306 x l0-6
1.767x 10-5
.417 x l0-5
15
1.139 x l0-3
1.139 x l0-6
1.793 x l0-5
.463 x 10-5
20
1.002 x l0-3
1.003 x l0-6
1.817 x l0-5
.509 x 10-5
25
0.890 x 10-3
3.893 x 10-6
1.840 x l0-5
.555 x10-5
30
0.798 x l0-3
3.800 x 10-6
1.864 x 10-'
.601 x 10-5
40
0.653 x 10-3
3.658 x 10-6
1.910 x l0-5
.695 x 10-5
50
0.547 x l0-3
1553 x 10-6
1.954 x l0-5
.794 x l0-5
60
0.466 x 10-3
3.474 x 10-6
2.001 x 10-5
.886 x l0-5
70
0.404 x 10-3
3.413 x 10-6
2.044 x l0-5
.986 x 10-5
80
0.354 x 10-3
3.364 x I0-6
2.088 x 10-5
-.087 x 10-5
90
0.315 x l0-3
3.326 x l0-6
2.131 x l0-5
2.193 x l0-5
100
0.282 x 10-3
1294 x 10-6
2.174 x l0-5
-.302 x l0-5
3. Surface Tension and Capillarity
• Even at a small distance below the surface of a liquid
body, liquid molecules are attracted to each other by
equal forces in all directions.
• The molecules on the surface, however, are not able to
bond in all directions and therefore form stronger bonds
with adjacent water molecules. This causes the liquid
surface to seek a minimum possible area by exerting
surface tension (s) tangent to the surface over the
entire surface area.
• The rise or fall of liquid in capillary tubes are the results
of surface tension.
“Wetted”
“Non-Wetted”
Adhesion
Cohesion
Adhesion
Cohesion
Adhesion > Cohesion
Water
Cohesion > Adhesion
Mercury
• Most liquids adhere to solid surfaces.
• The adhesive force varies depending on the nature of the
liquid and of the solid surface.
• If the adhesive force between the liquid and the solid
surface is greater than the cohesion in the liquid
molecules, the liquid tends to spread over and wet the
surface, as shown in Figure 1.3(a).
• If the cohesion is greater, a small drop forms, as shown in
Figure 1.3(b).
• Water wets the surface of glass, but mercury does not.
If we place a small vertical glass tube into the free surface of
water, the water surface in the tube rises (capillary rise ).
The same experiment performed with mercury will show that
the mercury falls. The phenomenon is commonly known as
capillary action.
• Capillary effect is the rise or fall of a liquid in a smalldiameter tube. It is caused by surface tension.
• The magnitude of the capillary rise (or depression), h, is
determined by the balance of adhesive force and the weight
of the liquid column above (or below) the liquid-free surface.
• The angle (q) at which the liquid film meets the glass
depends on the nature of the liquid and the solid surface.
• The upward (or downward) motion in the tube will stop
when the vertical component of the surface tension force
around the edge of the film equals the weight of the raised
(or lowered) liquid column.
• The weight of the fluid is balanced
with the vertical force caused by
surface tension.
• The very small volume of liquid above
(or below) the base of the curved
meniscus is neglected
(sD) sin q 
h

4
D 2 (gh)
4s sin q
gD
• The surface tension (s) of a liquid is usually expressed in
the units of force per unit length.
• Its value depends on the temperature and the electrolytic
content of the liquid. Small amounts of salt dissolved in
water tend to increase the electrolytic content and, hence,
the surface tension. Organic matter (such as soap)
decreases the surface tension in water and permits the
formation of bubbles.
• The surface tension of pure water is listed in Table 1.4.
Elasticity of Water
• Under ordinary conditions, water is commonly assumed to be
incompressible. In reality, it is about 100 times as compressible as
steel.
• It is necessary to consider the compressibility of water when water
hammer problems are involved.
• The compressibility of water is inversely proportional to its volume
modulus of elasticity, Eb, also known as the bulk modulus of elasticity,
• The pressure-volume relationship:
• Where:
- Vol is the initial volume,
- D(P) and D(Vol) are the corresponding changes in pressure and volume,
respectively
Elasticity of Water
• The negative sign means that a positive change in pressure will
cause the volume to decrease.
• The bulk modulus of elasticity (Eb) of water varies both with
temperature and pressure.
• Typical value: Eb = 2.2 x 109 N/m2 (300,000 psi)
• Large values of the bulk modulus indicate incompressibility
• Incompressibility indicates large pressures are needed to
compress the volume slightly
Example 1.2
Forces in a Fluid Field
• Various types of forces may be exerted on a body of water at rest
or in motion. These forces usually include:
- the effects of gravity,
- inertia, elasticity,
- friction,
- pressure, and
- surface tension.
• These forces may be classified into three basic categories
according to their physical characteristics:
1. body forces
- force per unit mass (N/kg) or force per unit volume (N/m3).
- act on all particles in a body of water as a result of some external
body or effect but not due to direct contact.
- an example …gravitational force and Inertial forces and forces
due to elastic effects.
Forces in a Fluid Field
2. Surface forces
- force per unit area (N/m2)
- act on the surface of the water body by direct contact.
- may be either external (Pressure forces and friction forces)
or internal (viscous force inside a fluid body).
3. line forces.
- force per unit length (N/m).
- Surface tension is thought of as the force in the liquid
surface normal to a line drawn in the surface. Thus, it may
be considered as a line force.