Faculty of Engineering

Hydraulics - ECIV 3322

Chapter 1Chapter 1

Fundamental Properties of Water (Revision)

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Hydraulic 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.

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• Hydraulic Engineering Systems:

involve the application of engineering principles and methods to:

– planning,– control,– transportation, – conservation, and – utilization of water.

Hydraulic Hydraulic

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Examples of Hydraulic ProjectsExamples of Hydraulic Projects

• Water pipelinesWater pipelines

• Water distribution systemsWater distribution systems

• Sewer systemsSewer systems

• Dams and water control structuresDams and water control structures

• Storm sewer systemsStorm sewer systems

• Rivers and manmade canalsRivers and manmade canals

• Coastal and Harbour structuresCoastal and Harbour structures

• Irrigation and Drainage ProjectsIrrigation and Drainage Projects

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The Earth's AtmosphereThe Earth's Atmosphere

• The earth's atmosphere layer thickness is approximately 1,500 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.

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• 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.

• N/m2 is also known as 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.

Atmospheric PressureAtmospheric Pressure

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Phases of WaterPhases 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)

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• 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 of fusion) 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- 0.57 T0C) cal/g.

• Under standard atm. P, water boils at 100°C.

Change of water from one phase to Change of water from one phase to another phaseanother phase

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• Surface tension variation directly affects the evaporation loss from a large water body in storage;

• Water viscosity variation with temperature is important to all problems involving water in motion.

Physical Properties of WaterPhysical Properties of Water

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It is important to understand the physical properties of water to solve problems in hydraulic engineering systems.

Main water properties:

1. Density ()

2. Viscosity ()

3. Surface tension

Physical Properties of WaterPhysical Properties of Water

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1. Density and Specific Weight of 1. Density and Specific Weight of WWaterater

• Density (): 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.

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• 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.

1. Density and Specific Weight of 1. Density and Specific Weight of WWaterater

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Table 1.2: Variation of density and specific weight of water with temperature

Temperature (°C)

Density (kg/m3)

Specific Weight (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

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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 (Summer stratification)

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.

Variation of Density in a Large ReservoirVariation of Density in a Large Reservoir

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• 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 () = weight per unit volume of water (N/m3)

= g• Specific gravity (S): the ratio of the specific weight of any

liquid to that of water at 4°C.

Specific Weight of WaterSpecific Weight of Water

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Example 1.1Example 1.1

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• 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.

2. Viscosity of Water2. Viscosity of Water

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Shear stress () is the resistance per unit area of the upper plate = 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()ldt ,is proportional to the shear stress, as shown in Figure 1.2.

dt

dxvand

dy

dx , strain),(Shear n deformatioAngular

gradient)(Velocity .

strain shear of Ratedy

dv

dtdy

dx

dt

d

constantdy

dv

dy

dv

The proportionally constant, , is called the absolute viscosity of the fluid

dt

d

Therefore,dy

dv

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• 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).

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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 non-Newtonian fluids. These include most house paints and blood.

Newtonian fluids and non-Newtonian fluidsNewtonian fluids and non-Newtonian fluids

(1.2)

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Kinematic ViscosityKinematic Viscosity

• Kinematic viscosity, , is obtained by dividing the absolute viscosity by the mass density of the fluid at the same temperature;

= /.

• 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.

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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

TABLE 1.3 Viscosities of Water and Air at various temperatures

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3. Surface Tension and Capillarity3. 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 () tangent to the surface over the entire surface area.

• The rise or fall of liquid in capillary tubes are the results of surface tension.

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“Wetted” “Non-Wetted”

Adhesion > Cohesion Cohesion > Adhesion

Adhesion

CohesionAdhesion

Cohesion

Water Mercury

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• 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.

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• Capillary effect is the rise or fall of a liquid in a small-diameter 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 () 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.

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• The surface tension () 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.

• 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

)(4

sin)( 2 hDD

Dh

sin4

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Elasticity of WaterElasticity 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,

- (P) and (Vol) are the corresponding changes in pressure and volume, respectively.

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• 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

Elasticity of WaterElasticity of Water

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Example 1.2Example 1.2

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Forces in a Fluid FieldForces 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.

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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.

Forces in a Fluid FieldForces in a Fluid Field