Hydraulics

The study of the behavior of water and other liquids in motion and at rest that deals primarily with the properties and behavior of liquids at rest against or in motion relative to boundary surfaces and objects.

Overview

Hydraulics is a branch of fluid mechanics that deals with the behavior of water and other liquids at rest against or in motion relative to boundary surfaces and objects. Hydraulic laws apply to gases as well, but only insofar as they are resistant to compression--that is, where density fluctuations are negligible. Such situations occur only where the velocity of the moving gas is significantly less than the speed of sound. Hydraulics is concerned only with the study of homogeneous and continuous bulk liquids at the macroscopic level and thus ignores molecular structure. The study of hydraulics and the physical laws that describe it is best understood in the examination of its two component parts: hydrostatics and hydrodynamics.

Hydrostatics is the most abstract of the two constituent parts of hydraulics, for it deals only with those liquids that are at rest and is thus a special case of the more general hydrodynamics. When liquids are at rest, there are no shearing or deforming forces, so that the primary phenomena of concern are the pressures and forces exerted by the mass of the liquid upon its container. Since pressure is defined as a force per unit area, the forces exerted by a bulk liquid at rest can be determined mathematically by knowing the pressure of the liquid and the area of the surface containing the liquid. This is possible because only forces caused by gravity influence the liquid, making the pressure force uniform over horizontal cross sections of the liquid. The pressure of a liquid at rest acts equally in all directions; as a result, the forces on the boundary (container) are perpendicular to its surfaces. Pressure forces can be divided into two categories: forces on plane (flat) surfaces and forces on curved surfaces. Examples include liquid storage tanks, dams, underwater tunnels, and pressure-measuring devices.

Hydrostatic forces on plane surfaces can be characterized by the angle at which the surface of the liquid is penetrated by the boundary surface, the density and depth of the liquid, and the surface area of the plane boundary. By knowing these parameters, the scientist or engineer can easily determine the force caused by liquid pressure at any point on the plane surface. Such determinations are made mathematically by using formulas known as differential equations. Such formulas allow the scientist to calculate the effect of liquid pressure over the entire surface of the boundary by summing up the pressure effects on minute portions of the boundary surface known as "differential areas."

While the same parameters apply for the determination of pressure forces on curved surfaces, in general, such determinations are mathematically difficult, as the curved surface may be highly irregular, making the definition of differential areas rather unwieldy. In addition, forces act in parallel lines on plane surfaces; such is not the case for curved surfaces. Most commonly, however, the curved surface is either a cylinder or a sphere, such as a pipe, in which case the problem is quite tractable because of the regular and circular geometry of these surfaces. For these surfaces, the force resulting from liquid pressure is calculated for either tension or compression, depending upon whether the liquid is on the inner or outer part of these closed surfaces, respectively.

Hydrodynamics is more complicated and general in its scope than hydrostatics, for it deals with the behavior and effects of liquids in motion. Hydrokinematics is a branch of hydrodynamics concerned with liquids in motion, but without regard for the forces responsible for setting the fluid into motion. Hydrodynamics proper, on the other hand, attempts to explain, describe, and predict liquid motion, the forces on both the liquid and its boundary surfaces, and any accompanying energy changes.

At its most basic level, hydrodynamic phenomena are characterized by two mathematical equations that describe two commonly understood physical principles: a "continuity equation," or mass conservation equation, which describes the condition of the liquid, and an equation of motion, which describes the conservation of momentum or energy in the moving liquid. As was the case with hydrostatics, these laws are described by differential equations. Scientists and engineers can make predictions of the behavior of hydraulic phenomena from these two physical principles. These phenomena include the various types of hydraulic flow that may occur in natural phenomena, such as coastlines, groundwater, rivers and streams, and floods; manmade structures such as irrigation canals; chemical processing facilities; mechanical devices such as hydraulic vehicle brakes; and in the construction of dams, dikes, and spillways.

Liquid flow is described mathematically as a liquid flow "field" by expressing the moving liquid's velocity, pressure, density, and temperature as a function of positions, or coordinates, in space and time. That is, the macroscopic physical properties of a liquid are described geometrically for ease in mathematical analysis. The principle of the conservation of mass states that the net rate of mass increase into a fixed volume is equal to the net rate of mass flow into that same volume. This principle is quite intuitive, for it simply says that no more or less mass accumulates in a given volume than is actually flowing into that same volume. By knowing the volume and the density of the liquid, one can determine the mass of the liquid; knowing its velocity allows a determination of the flow of mass per unit time--the rate of mass increase. Any particle of mass that moves at a constant velocity has the property known as momentum; an object's momentum is equal to the product of its mass and its velocity. Liquids can be regarded as a continuous, many-particle system where all particles behave in the same way. Just as mass is conserved, so is momentum.

Both the conservation of mass and momentum continuity relations ignore thermodynamic effects, which are described by the first law of thermodynamics. This law relates the temperature, heat, and internal energy of a moving liquid and thus takes into account the mechanical conditions and effects of its motion. Parameters such as elasticity and viscosity have profound influences upon the effects of a liquid's motion, especially in confined motion situations such as pipes and other conduits. For example, it requires far more energy to pump a given volume of crude oil through a pipe than it does distilled water, all other factors remaining equal, because crude oil is more viscous than water and thus resists the shearing stresses that move it.

In order to calculate the conservation of energy in a moving liquid, the scientist must balance the rate of increase of the internal energy of a fixed volume of liquid with the net rate of internal energy and work energy flow into the liquid. Such calculations require the scientist to gather large amounts of data regarding the temperature and flow rate of the liquid in question. In addition, scientists must conduct highly controlled experiments in order to disallow any extraneous sources of heat energy to enter the energy balance equation.

Applications

Just as the theoretical side of hydraulics was divided into hydrostatics and hydrodynamics, its applications are divided also. Hydraulics applications abound in the fields of chemical, civil, and mechanical engineering in areas as diverse as the measurement of the most minute of flow rates and the construction of dams and hydroelectric facilities. Hydrostatic applications vary as widely as the plethora of structures that humans have placed under water.

The laws of hydrostatics apply to all the following structures and devices but are not limited to them: storage tanks, underwater gates, tunnels, walls and pipes, sheetpiling and bulkheads for bridges and similar structures, and pressure measuring devices. Since the laws of hydrostatics deal only with pressure effects, only the circumstances of application change. Therefore, two examples will be discussed: pressure measuring devices and underwater gates.

The most common device used for the measurement of the pressure of a moving liquid is the manometer. Manometers are an application of the laws of hydrostatics--that is, the physics of stationary liquids--to the phenomena of hydrodynamics. Manometers are essentially tubes, usually constructed of glass or strong plastic, which are attached to liquid reservoirs, pipes, or channels. The tubes are most commonly U-shaped and graded in either inches or millimeters.

Pressure is measured by noting the difference in liquid height between the two "legs" of the U. A manometer with one end open to the atmosphere to act as a reference is known as a barometer.

Liquids will flow only from higher pressures to lower pressures. Therefore, moving liquids act under what is known as a pressure difference or a "pressure gradient." In order to determine the pressure difference under which the liquid is moving, the scientist examines the manometer and notes the difference in the height of the liquid from the high-pressure end and the low-pressure end. If the two "legs" of the U-shaped tube have equal levels of liquid, there is no pressure difference and the liquid is not flowing. A lower level in a leg is indicative of a flowing liquid and also indicates the direction of flow. The pressure difference itself is determined by multiplying the difference in height between the two legs by the density of the liquid. Recall that the basic hydrostatic relation required the use of liquid height and density to calculate pressure.

Manometers are among the most common pressure-measuring devices and are often the first instruments used by chemical and civil engineering students.

Apart from the use of hydrostatics in measuring devices, the most common use of hydrostatics is in civil and chemical engineering in the design of structures used either to contain or restrain bodies of stationary liquids. One very common and practical application is in the calculation of the water pressure on the surfaces of pipes. Such calculations determine the stability of such structures, which in turn help to determine their safety. Since hydrostatics gives an indication that the pressure at any point on a surface is perpendicular to that surface, pressures on both the inside and the outside of pipes result in "tangential stresses," forces that could tear the pipe apart, endangering safety and wasting resources. By calculating or measuring the pressure of the liquid in and out of the pipe and determining the diameter of the pipe, the stress on the pipe becomes a function of the material of which the pipe is made.

The applications of hydrodynamics involve liquids in motion and run the range from understanding and determining the motion of liquids in pipes, to the flow of water in open channels such as rivers and streams, to the migration of pollutants in groundwater. The flow of liquids in pipes is the most common of all hydrodynamic applications and is one of the most basic calculations in the field of chemical engineering design.

There are two common parameters measured in the study of liquid flow in pipes: velocity and volumetric flow. Both of these measurements depend upon whether the flow of liquid is laminar or turbulent. Laminar flow is characterized by slow moving liquids where the water is often described as smooth and glasslike. Turbulent flow is most common in nature and is characterized by rushing currents, whirls, and eddies. In a series of now-classic 1883 experiments, Osborne Reynolds discovered a numerical way of determining such flows, which is known as the "Reynolds number," R. The quantity of R is found by multiplying the density of a moving liquid (in kilograms per cubic meter), its velocity (in meters per second), and the length of the pipe, conduit, and the like (in meters) and dividing this quantity by the liquid's viscosity (in kilopascals). Reynolds numbers below 2,000 indicate laminar flow, while those greater than 4,000 indicate turbulent flow. The area from 2,000 to 4,000 is known as the transition region and is often assumed to be laminar.

There are only straightforward equations for the calculation of velocity and volumetric flow rate in laminar flow. In laminar flow, all fluid particles move in straight lines parallel to the pipe walls; as a result, flow rate is independent of the smoothness or roughness of the pipe walls.

In preliminary design work, at least, it is often assumed that the liquid is in a laminar flow regime. Both volumetric flow rate and liquid velocity depend upon the pressure drop along the length of the pipe, the radius of the pipe, the pipe's length, and the liquid's viscosity.

In turbulent flow, the liquid particles actually move in random and often unpredictable directions. As a result, the engineer must take into account the characteristics of the moving liquid as well as those of the pipe itself. In such cases, the engineer uses a series of tables that relate the Reynolds number and the pipe roughness to determine a friction factor. The value of this factor determines how much energy is lost in turbulent liquid flow through pipes of varying roughness. Such charts have been compiled for a variety of commonly processed liquids. In such cases where the charts have not been prepared, experiments must be conducted in order to determine empirically the relationship between the Reynolds number and the pipe roughness for the particular situation.

Perhaps the most common use of turbulent flow information is in the study of flowing waters in nature, particularly the large rivers such as the Nile, the Amazon, and the Mississippi.

Understanding the flow characteristics of such bodies of water has a wide range of practical applications, from harnessing the energy of the flowing water for electrical purposes to using the water itself for irrigation. Natural flow has an additional problem not encountered in pipe flow: that of an irregular flow channel. The factors contributing to turbulent flow must be accounted for in such situations; however, in order to attain accuracy, the shape of the actual river bed must be accounted for as well. The liquid velocities in such situations are thus a product of viscosity, the river bed geometry, friction caused by irregularities in the river bed, and the surface tension of the liquid.

Context

Hydraulics, like many other engineering sciences, has a dual heritage. Both practical and theoretical developments helped to shape the growth of this discipline.

Prior to any systematic studies of hydraulics, ancient civilizations such as the Chinese, Egyptians, and Mesopotamians used the properties of water to their practical advantage in such projects as irrigation and flood prevention. One example is the Sadd-el-Kafara dam, built between 2700 and 2600 B.C.

Constructed entirely of rock, the dam is 110 meters long and 14 meters high.

Archaeologists believe it to be the world's first large-scale dam for the purpose of flood protection.

Systematic theories regarding the behavior and effects of water are attributed to the Ancient Greeks, beginning with the philosopher Thales between 624 and 546 B.C.

Yet, it was not until the time of Archimedes (287-212B.C.) that the study of hydraulics took a shape resembling that of modern hydraulic science. Archimedes was, for the most part, a mathematician, so it should not be surprising that he analyzed the phenomena of hydrostatics, particularly flotation and buoyancy, in geometrical terms.

It was not until the sixteenth and seventeenth centuries, however, that the study of hydraulics gained a true scientific character--that is, the capacity for quantitative prediction and analysis. Until this time, hydraulics remained largely practical, steeped in an "artisan tradition,"

where empirical rules of thumb would be passed down from one generation of hydraulic builders to the next. This tradition saw its greatest achievements in the mammoth projects of the Roman Empire, which included water supply and sewage systems.

It was in the Renaissance period in Europe, and in the subsequent scientific revolution, that the Archimedean ideal of a mathematical study of hydraulics was reborn. This rebirth took shape in the studies of Galileo and his student, Evangelista Torricelli. While Galileo did little work on hydraulics, his scientific method, that of developing mathematical hypotheses to be tested experimentally, made a profound impact on Torricelli, who is heralded as the founder of modern hydraulic science. One example is his study of liquid jets--high-velocity streams of water from small orifices. Torricelli applied Galileo's analysis of projectile motion to this problem, confirming that liquid jets, like moving projectiles, could be described mathematically.

By the eighteenth century, the influence of Galileo and Torricelli had combined with the new physics of Sir Isaac Newton to produce the works of Johann Bernoulli and Leonhard Euler. In 1742, Bernoulli developed the streamline equation--the relation that describes the motion of fluids in pipes as a function of pressure and density. In 1749, Euler derived the continuity equations for both compressible and incompressible fluids.

In the nineteenth century, the complete joining of the ancient traditions of hydraulic engineering and the newly developed hydraulic sciences of hydrostatics and hydrodynamics was achieved, setting the study on course to the twentieth century. This period saw the Reynolds' studies of laminar and turbulent flow, as well as Henri-Philibert-Gaspard Darcy's (1857) studies of the influence of pipe wall roughness, friction, and energy loss. In addition, engineering became known as a profession through both formal education, in the form of engineering schools in Europe and the United States and professional societies such as the American Society of Civil Engineers.

Principal terms

DENSITY: the mass of a substance per unit volume, measured in kilograms per cubic meter

FLUID: a liquid, vapor, or gas that fills the container that holds it; hydraulics limits its focus to liquids and those vapors and gases undergoing negligible changes in density

PRESSURE: the measure of the force exerted by a fluid per unit area, measured in kilopascals

SURFACE TENSION: the property of a liquid to adhere to capillary surfaces

VISCOSITY: the measure of a fluid's resistance to shearing forces, that is, those forces that deform it, measured in kilograms per meters times seconds

Bibliography

Garbrecht, Gunther, ed. HYDRAULICS AND HYDRAULIC RESEARCH: A HISTORICAL REVIEW. Rotterdam, The Netherlands: A. A. Balkema, 1987. This survey of the history of hydraulics covers the ancient artisan traditions of irrigation and land reclamation as well as trends in twentieth century hydraulic engineering, such as hydroelectric plants. This collection of articles has varying levels of technical detail. Recommended for the interested reader are E. O. Macagno on Leonardo da Vinci (pages 33-54) and C. B. Vreugdenhil et al. on the modeling of hydraulic phenomena (pages 329-354).

King, Horace Williams. HANDBOOK OF HYDRAULICS: FOR THE SOLUTION OF HYDRAULIC PROBLEMS. New York: McGraw-Hill, 1954. Although dated, the book contains technical detail and the practical side of hydraulics is discussed. Offers well-illustrated examples of practical problems solved by civil and chemical engineers. Well-organized, taking the reader from problems of hydrostatics, such as underwater barriers, to the more mathematically intricate hydrodynamics problems of fluid flow.

Parker, Sybil, ed. FLUID MECHANICS SOURCEBOOK. New York: McGraw-Hill, 1988. Hydraulics is a subdiscipline of fluid mechanics, and as such, hydraulics can be understood only in relation to fluid mechanics. Offers the layperson an excellent explication of all aspects of hydraulics, from hydrostatics to hydrodynamics. Wonderfully illustrated, with both diagrams and technical graphs. While the book does not spare mathematical detail, most equations and their variables are adequately explained, and the introductory chapters are excellent preludes to the discipline as a whole. An excellent technical source.

Rouse, Hunter. HYDRAULICS IN THE UNITED STATES: 1776-1976. Iowa City: The Institute for Hydraulic Research, University of Iowa, 1976. A good example of the history of technology as written by those who practice it. Rouse offers a retrospective of achievements in the study of hydraulics from theoretical work to the establishment of engineering research institutions in the United States. Well illustrated and nontechnical.

Singer, Charles, ed. A HISTORY OF TECHNOLOGY. 5 vols. New York: Oxford University Press, 1958. This mammoth collection presents a history of technology from ancient times to the beginning of the twentieth century. Those interested in hydraulics will have to do some looking through the subject headings in which the book is organized (for example, see "The Chemical Industry" in volume 5). For those looking for the role of hydraulics in the broader context of the growth of technology, however, this is a fine source. It is a top-notch history of technology and contains excellent illustrations.

Equation of State

Fluid Mechanics and Aerodynamics