Textbook

Fundamentals of Hydraulic Engineering SystemsBy Ned Hwang & Robert Houghtalen

CE 351 –Hydraulic- Spring 2007

http://engg.kaau.edu.sa/ ~sagutb

Course Objectives

Reviewing the basic properties of water Reviewing the basic principles of hydrostatics Reviewing the basic principles of fluid in motion (conservation

of mass, momentum and energy) Analyzing, understanding and designing of water flow in

pipes and pipes networks. Analyzing, understanding and designing water flow in open

channels under different conditions. Learning the basic theory of hydromachines (pumps in

particular). Learning different techniques for measuring velocity, pressure

and flowrate in both pipe and open channel flows. Understanding similitude and its applications in hydraulic

modeling

Chapter 1

Fundamental Properties of Water

Hydraulic Hydraulic Comes from the Greek word hydraulikos, meaning

water. Hydraulics is the science of studying the mechanical

behaviour 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 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 Cooling systems Etc.

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

Water properties such as:- the density(), - the surface tension - the viscosity

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.**We will focus on the fundamental physical properties of

water.

Density in a large reservoir. Change of density with T causes water in a lake to

stratify: During summer, water tends to stratify, with warmer water on the

surface. During the fall, the surface water T 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.

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.

The Earth's Atmosphere and

Atmospheric Pressure The earth's atmosphere layer thickness is

approximately 1500 km of mixed gases. Nitrogen makes up ~ 78% of the atmosphere, oxygen makes up ~ 21%, and the remaining 1 % consists mainly of water

vapor, argon, and trace amounts of other gases.

DIFFERENT ATMOSPHERES

BACK

THE STRATOSHPERE

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.

BACK

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 • l0^5 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

water molecule is a stable chemical bond of oxygen and hydrogen atoms.

The amount of energy holding the molecules together depends on the T & P.

Depending on its energy content, water may appear in either solid, liquid, or gaseous form.

Different forms of water (are called three phases ): Solid form of water-- Snow and ice Liquid is it most commonly recognized form; Gaseous form of water in air -- Moisture, water vapor

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. ( in the form of heat or pressure) Heat energy units is: calories (cal). One cal is the energy required to increase the T of 1 g of

water, in liquid phase, by 1 °C. Specific heat of a substance: the amount of energy required to raise the T of a substance

by 1 °C. Under standard atmospheric pressure, the specific heat of - water is 1.0 cal/g •°C - ice is 0.465 cal/g •°C.

change water from one phase to another phase

Specific heat of water vapor under const. P is 0.432 cal/g •°C,

Specific heat of water vapor at constant vol. is 0.322 cal/g •°C. To melt 1 gram of ice requires, a latent heat (heat effusion) of 79.71 cal. To freeze water, 79.71 cal of heat energy must be taken

out of each gram of water.

Evaporation requires, a latent heat (heat of vaporization) of 597 cal/g. Under standard atm.P, water boils at 100°C. At higher elevations, where the atm. P is less, water

boils at T lower than 100°C. -This phenomenon may be explained best from a

molecular-exchange viewpoint.

At the gas-liquid interface:

there is a continual interchange of molecules Net evaporation occurs when more molecules are

leaving than are entering the liquid; Net condensation occurs when more molecules

are entering than are leaving the liquid. vapor pressure

when continuous impingement of vapor molecules on the liquid surface creates P on the liquid surface (this partial P combined with the partial P created by other gases in the atmosphere makes up the total atm.P).

Vapor pressure increases

when the molecular energy is raised due T of the liquid, which causes a large number of molecules to leave the liquid, which, in turn, increases the vapor pressure.

Boiling

as T reaches a point (known as the boiling point of the liquid ) where the Pv is equal to the ambient atm.P, evaporation increases drastically, and boiling in liquid takes place.

For water at sea level, the boiling point is 100°C. The Pv of water is shown in Table 1.1 above.

Temperature

Vapor PressureTemperatur

e

Vapor Pressure

(°C) atm N/m1 (°C) atm N/m2

-5 0.004162 421 55 0.15531 15745

0 0.006027 611 60 0.19656 19924

5 0.008600 873 65 0.24679 25015

10 0.012102 1266 70 0.30752 31166

15 0.016804 1707 75 0.38043 38563

20 0.023042 2335 80 0.46740 47372

25 0.031222 3169 85 0.57047 57820

30 0.041831 4238 90 0.69192 70132

35 0.055446 5621 95 0.83421 84552

40 0.072747 7377 100 1.00000 101357

45 0.094526 9584 105 1.19220 120839

50 0.12170 12331 110 1.41390 143314

TABLE 1.1 Vapor Pi Vapor Pressure

Cavitation In a closed system, (i.g, in pipelines or pumps),: water vaporizes rapidly in regions where the (P

drops below Pv). = is known as cavitation.

The vapor bubbles formed in cavitation usually collapse in a violent manner when they move into higher pressure regions. This may cause considerable damage to a system.

Cavitation in a closed hydraulic system can be avoided by maintaining the pressure above the vapor pressure everywhere in the system

Mass (Density) and Weight (Specific Weight) The density of a substance: is defined as mass per unit volume It is a property inherent to the molecular

structure of the substance.-- This means that density depends on (size and weight of the molecules and the mechanisms by which these molecules are bonded together [T,P]).

Because of its peculiar molecular structure, water is one of the few substances that 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.

Water maximum density reaches a maximum density at 4°C. It becomes less dense when further chilled or heated.

The density of water is shown as a function of T (see Table 1.2).

(Note that the density of ice is different from that of liquid water at the same T).

Density of sea water because sea water contains salt, the density 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 Density and Specific Weight of Water

Temperature (°C) Density (p, kg/m3) Specific Weight (y,N/m2)

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

In the S.I. system the weight of an object is defined by the product of its mass (m, in grams, kilograms, etc.), and the gravitational acceleration (g = 9.81 m/sec2 on earth).

W=m*g Weight is expressed in the force units of newton (N).

(One newton is defined as 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, = g.

The specific weight of water is a function of T (see Table 1.2).

Specific gravity (S) the ratio of the specific weight of any liquid to that of

water at 4°C.

• Consider that water fills the space between two parallel plates at a distance y apart. 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.

• The resistance per unit area of the upper plate (shear stress, = RIA = T/A) is proportional to the

rate of angular deformation in the fluid, d()ldt.

Viscosity of Water

Water responds to shear stress by continuously yielding in angular deformation in the direction of the shear. The rate of angular deformation is proportional to the shear stress, as shown in Figure 1.2.

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

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.

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).

kinematic viscosity

kinematic viscosity, nu, which 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.

WaterAir

Absolute Kinematic Absolute Kinematic

Temperature Viscosity, Viscosity, Viscosity, Viscosity,

(°C) N • sec/m2 m^sec N • sec/m2 w^sec

0 1.781 xl0-3 .785 x 10-6 1.717x10-'' .329 x 10-5

5 1.518 xl0-3 .519xl0~'' 1.741 xl0-5 .371 xl0-5

10 1.307X10-3 .306 xl0-6 1.767x 10-5 .417 xl0-5

15 1.139 xl0-3 1.139 xlO"6 1.793 xl0'5 .463 x 10-5

20 1.002 xl0-3 1.003 xl0-6 1.817 xl0-5 .509 x 10-5

25 0.890 x 10-3 3.893 x 10-6 1.840 xl0-5 .555 x10-5

30 0.798 xl0-3 3.800x10-° 1.864x10-' .601 x 10-5

40 0.653 x 10-3 3.658 x 10^ 1.910 xl0-5 .695 x 10-5

50 0.547 xl0-3 1553 x 10-6 1.954xl0~5 .794 xlO-5

60 0.466 x 10-3 3.474x10-" 2.001 x 10-' .886 xl0-5

70 0.404 x 10-3 3.413 x 10-6 2.044 xl0-5 .986 x 10-5

80 0.354 x 10-3 3.364 x ICr6 2.088 x 10-5 2 -.087 x 10-5

90 0.315 xl0-3 3.326 xl0-6 2.131 xl0-5 2 2.193 xl0-5

100 0.282 x 10~3 1294 x 10-6 2.174 xl0-5 2 -.302 xl0-5

TABLE 1.3 Viscosities of Water and Air

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.

A steel needle floating on water, the spherical shape of dewdrops, and the rise or fall of liquid in capillary tubes are the results of surface tension.

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 bore 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

These two typical cases are schematically presented in Figure 1.4(a) and 1.4(b).)

The magnitude of the capillary rise (or depression), h, is determined by the balance of adhesive force between the liquid and solid surface and the weight of the liquid column above (or below) the liquid-free surface.

The angle (theta) 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 cease 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.

When the very small volume of liquid above (or below) the base of the curved meniscus is neglected, the relationship may be expressed as

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.

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, Ep,, also known as the bulk modulus of elasticity.

The pressure-volume relationship may be expressed as

where Vol is the initial volume, and (P) and del(Vol) are the corresponding changes in pressure and volume, respectively.

The negative sign means that a positive change in pressure (i.e., increment) will cause the volume to decrease (i.e., negative change).

The bulk modulus of elasticity (Ep) of water varies both with temperature and pressure.

In the range of practical applications in typical hydraulic systems,

Ep= 2.2 x 109 N/m2 (300,000 psi)

Forces in a Fluid Field Various types of forces may be exerted on a body of

water at rest or in motion. In hydraulic practice, 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)). 2. and surface forces, (force per unit area (N/m2)). 3. line forces. (force per unit length (N/m)).

Body forces are forces that 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 of this is the gravitational force. It acts on all particles in any body of water as a result of the gravitational field of the earth,

Inertial forces and forces due to elastic effects. Surface forces act on the surface of the water body by

direct contact. These forces may be either external or internal.

Examples of external surface forces: - Pressure forces and - friction forces. Examples of internal surface force : viscous force inside a

fluid body. 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.