Technology & Engineering
Hydrostatics
Hydrostatics is the study of fluids at rest and the forces they exert on solid surfaces. It deals with the principles of pressure distribution in fluids and the behavior of floating and submerged bodies. Key concepts in hydrostatics include Pascal's law, Archimedes' principle, and the calculation of buoyant force. Understanding hydrostatics is essential in various engineering applications, such as designing ships and hydraulic systems.
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12 Key excerpts on "Hydrostatics"
- Melvyn Kay(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
27 Chapter 2 Water standing still Hydrostatics 2.1 INTRODUCTION Hydrostatics is the study of water when it is not moving; it is standing still. It is important to civil engineers who are designing water storage tanks and dams. They want to work out the forces that water creates in order to build reservoirs and dams that can resist them. Naval architects designing submarines want to understand and resist the pressures created when they go deep under the sea. The answers come from understanding Hydrostatics. The science is simple both in concept and in practice. Indeed, the theory is well established and little has changed since Archimedes (287–212 bc) worked it out over 2000 years ago. 2.2 PRESSURE The term pressure is used to describe the force that water exerts on each square metre of some object submerged in water, that is, force per unit area. It may be the bottom of a tank, the side of a dam, a ship or a submerged submarine. It is calculated as follows: pressure force area = . Introducing the units of measurement . pressure (kN/m ) force (kN) area (m ) 2 2 = Force is in kilo-Newtons (kN), area is in square metres (m 2 ) and so pres- sure is measured in kN/m 2 . Sometimes pressure is measured in Pascals (Pa) in recognition of Blaise Pascal (1620–1662) who clarified much of modern 28 Practical Hydraulics and Water Resources Engineering day thinking about pressure and barometers for measuring atmospheric pressure. 1 Pa = 1 N/m 2 . One Pascal is a very small quantity and so kilo-Pascals are often used so that 1 kPa = 1 kN/m 2 . Although it is in order to use Pascals, kN/m 2 is the measure of pressure that engineers tend to use and so this is used throughout this text (see example of calculating pressure in Box 2.1). 2.3 FORCE AND PRESSURE ARE DIFFERENT Force and pressure are terms that are often confused.
eBook - PDF- William Graebel(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
41 chapter 2 Hydrostatics and Rigid-Body Motions Chapter Overview and Goals The subjects of hydro statics and rigid-body motions are special cases of fluid dynamics where the fluid is at rest, is undergoing a constant linear acceleration, or is being rotated at a constant angular velocity. Our study of these topics will introduce the concepts of surface and body forces, pressure prism, pressure centroid, and pressure center. The theory we will introduce is the law of Hydrostatics, which is a special case of the momentum equation (Newton’s second law). As applications of our theory, we consider manometers (used for measuring pressures and pressure differences), forces on plane and curved surfaces, linear uniform acceleration, and constant angular rotation. At the end of your study you should understand these subjects sufficiently to work problems covering these topics. While this chapter is a special case of the theory presented in Chapter 3, it is singled out for special treatment so that you can concentrate on the physical principles and methods of analysis, which are clearer in these simpler cases. 1. The Hydrostatic Equation Hydrostatics is the study of the pressure field in a fluid either at rest or moving with a constant and uniform velocity so that the fluid is in rigid-body motion. There is no relative deformation of the fluid, so that all stresses due to viscosity vanish. On any surface that we examine in a static fluid, all stresses locally act normal to that surface. Furthermore, the stresses are all compressive. That is, they act to increase the density of the fluid. The standard convention for stress is that normal stresses are positive if they are tensile, that is, if they are acting to stretch a fluid element. In Hydrostatics, the stresses are almost always compressive.
- Melvyn Kay(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
Chapter 2Water standing still
Hydrostatics2.1 INTRODUCTION
Hydrostatics is the study of water when it is not moving; it is standing still. It is important to civil engineers who are designing water storage tanks and dams. They want to work out the forces that water creates in order to build reservoirs and dams that can resist them. Naval architects designing submarines want to understand and resist the pressures created when they go deep under the sea. The answers come from understanding Hydrostatics. The science is simple both in concept and in practice. Indeed, the theory is well established and little has changed since Archimedes (287–212 BC ) worked it out over 2000 years ago.2.2 PRESSURE
The term pressure is used to describe the force that water exerts on each square metre of some object submerged in water, that is, force per unit area. It may be the bottom of a tank, the side of a dam, a ship or a submerged submarine. It is calculated as follows:pressure =Introducing the units of measurementforce area.pressure(=kN/m 2).force( kN )area(m 2)Force is in kilo-Newtons (kN), area is in square metres (m2 ) and so pressure is measured in kN/m2 . Sometimes pressure is measured in Pascals (Pa) in recognition of Blaise Pascal (1620–1662) who clarified much of modern day thinking about pressure and barometers for measuring atmospheric pressure.1 Pa = 1 N/m2 .One Pascal is a very small quantity and so kilo-Pascals are often used so that1 kPa = 1 kN/m2 .Although it is in order to use Pascals, kN/m2 is the measure of pressure that engineers tend to use and so this is used throughout this text (see example of calculating pressure in Box 2.1 ).2.3 FORCE AND PRESSURE ARE DIFFERENT
Force and pressure are terms that are often confused. The difference between them is best illustrated by an example:
eBook - PDF- Minoo H Patel(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Chapter 7 Hydrostatics of floating bodies Hydrostatic pressures within a fluid at rest can exert very large forces on the submerged parts of offshore structures, particularly at large water depths. Hydrostatic pressures also impart rather more subtle properties which affect the stability of floating bodies. Both of these features have a profound influence on the design of floating and fixed offshore structures and are considered here in more detail. 7.1 Basic properties of a fluid at rest A fluid may be defined as a substance that deforms due to the effect of a shear stress, however small. It follows from this statement that no shearing stresses can exist in a fluid at rest with the reactions between adjacent layers of fluid being confined to normal stresses only. These normal stresses are called pressures and are defined as the normal force per unit area on an infinitesimal plane surface at any orientation in the fluid. By resolving pressure induced forces on an infinitesimal tet-rahedral fluid element with three mutually perpendicular faces, it can readily be shown that the pressure at a point in a fluid in equilibrium is the same in all directions. This is also true for a fluid in bulk motion in which there are no shearing stresses. The pressure at a point in a fluid undergoing generalized motion is considered further in Section 3.5 Although the above properties apply both to liquids and gases, the Hydrostatics of offshore structures is principally concerned with liquids of large density (compared to gases) which induce substantial pressure gradients in the Earth's gravitational field - see, for example, Figure 2.6(b) for such gradients in the oceans and the atmosphere. A qualitative characteristic that distinguishes hquids from gases is the fact that a gas will expand in volume indefinitely to fill its containing volume fully, whereas a hquid will be of an essentially constant volume with no definite shape.
eBook - ePub- Richard Gentle, Peter Edwards, William Bolton(Authors)
- 2001(Publication Date)
- Newnes(Publisher)
The purpose of this chapter is to teach you the fundamentals of engineering fluid mechanics in a very general manner so that you can understand the way that forces are produced and transmitted by fluids that are, first, essentially at rest and, second, in motion. This will allow you to apply the physical principles behind some of the most common applications of fluid mechanics in engineering. Most of these principles should be familiar – conservation of energy, Newton’s laws of motion – and so the chapter concentrates on their application to liquids.Objectives By the end of this chapter, the reader should be able to:• recognize some fluid properties and types of flow; • understand the transmission of pressure in liquids and its application to hydraulics; • use manometry to calculate pressures; • calculate hydrostatic forces on plane and curved submerged surfaces; • understand Archimedes’ principle and buoyancy; • employ the concept of continuity of flow; • define viscosity; • calculate pressure drops in pipe flow; • use Bernoulli’s equation to measure flow rate and velocity; • apply the momentum principle to liquids in jets and pipes.3.1 Hydrostatics – fluids at rest
The first half of this chapter is devoted to Hydrostatics, the study of fluids at rest. It is a subject that is most commonly associated with civil engineers because of their interest in dams and reservoirs, but it is necessary for mechanical engineers too as it leads on to the subject of hydrodynamics, fluids in motion.What are fluids?
Fluids are any substances which can flow. We normally think of fluids as either liquids or gases, but there are also cases where solids such as fine powders can behave as fluids. For example, much of the ground in Japan is made up of fine ash produced by the many volcanoes which were active on the islands until quite recently. Earthquakes are still common there and the buildings run the risk of not only collapsing during the tremors but also sinking into the ground as the powdery ash deposits turn into a sort of fluid due to the vibration. Nevertheless we shall only consider liquids and gases for simplicity, and most of the time we shall narrow the study down even further to liquids because we can look at the basic principles without the complications that apply to gases because of their compressibility. There are only a few major differences between liquids and gases, so let us have a look at them first.
eBook - ePub- Ted G. Byrom(Author)
- 2013(Publication Date)
- Gulf Publishing Company(Publisher)
CHAPTER 2Basic Calculations and Hydrostatics
2.1 Introduction
Hydrostatics is a subject so simple we should not even have to devote space to it. If you actually believe that, then you have not worked in the oil field for very long. The truth is that Hydrostatics is a relatively simple subject, but the problem is that its simplicity is often deceptive. Most texts and courses on fluid mechanics devote very little space or time to Hydrostatics because the interesting part of fluid mechanics is fluid dynamics not fluid statics, consequently many authors and instructors treat fluid statics as trivial. And I suppose it might justifiably be considered trivial relative to hydrodynamics and other more difficult topics, but the net result is that too many engineers get through it with little more than a superficial understanding. Too often, some of the simplifying assumptions become imbedded as axioms of truth. For instance many engineers (and even a few distinguished professors) go through their entire careers believing that water is incompressible. And in our particular discipline, the concept of buoyancy, for example, has led to all sorts of incredible nonsense, some of which has even been published in textbooks and peer-reviewed literature. Take a look at the example in Figure 2-1 to illustrate a bit about buoyancy.Figure 2-1 Smooth tube suspended in a vertical wellThe figure shows a smooth tube suspended vertically in an idealized, vertical well. The tube has a sliding seal assembly on the bottom that allows frictionless vertical motion in a concentric packer. It is supported entirely at the surface, where a weight indicator measures its suspended weight. Both cases are identical, except in case A the annular space is filled with air and in case B the annular space is filled with water. Now,1. Will the weight indicator show that the weight of A is greater than B, less than B, or the same? 2. Suppose the tube in both cases is 4½-in. API ST&C casing, will the weight indicator show that the weight of A is greater than B, less than B, or the same?
- Allan D. Kraus, James R. Welty, Abdul Aziz(Authors)
- 2011(Publication Date)
- CRC Press(Publisher)
12 Fluid Statics Chapter Objectives • To develop the basic equation of fluid statics. • To describe the use of manometers to measure pressure. • To evaluate hydrostatic forces on planar and nonplanar surfaces immersed in a fluid. • To develop the concept of buoyancy. • To examine the stability of floating objects. • To describe hydrostatic forces under conditions of uniform rectilinear acceleration. 12.1 Introduction In Chapter 11, we defined a fluid according to its response to a shearing stress and we commented that a fluid at rest would therefore not be subjected to shear stresses. In this chapter we will consider the behavior of fluids at rest, that is, in a static condition. We should distinguish, at the outset, between inertial and noninertial reference frames. In general, we will consider a static situation to be one that is stationary relative to the earth’s surface; this is what is meant by an inertial reference frame. If a fluid is stationary relative to a coordinate system that has some acceleration of its own, such a reference frame is termed noninertial. An example of a noninertial reference frame would be a fluid inside an aircraft as it executes a maneuver. Our considerations will be, in general, for inertial reference frames and we will note, as exceptions, those occasions where noninertial reference frames are employed. 12.2 Pressure Variation in a Static Field In the absence of shear stresses a fluid will experience only gravitational and pressure forces. A representative fluid element of differential size in a static fluid is shown in Figure 12.1. Its dimensions, as indicated, are dx, dy , and dz . Fluid pressure, P ( x, y, z ), which acts on all six faces of the element, will produce force components in each of the coordinate directions. Because pressure always acts inward, the x -component pressure forces, which result from the pressure exerted on the x -faces are 361
eBook - PDF- Xixi Wang(Author)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
2 Overview of Hydromechanics 2.1 Engineering Properties of Water 10 2.2 Hydrostatic Pressure and Force 12 2.3 Energy in Still and Flowing Water 18 2.4 Governing Laws of Flowing Water 20 2.5 Flow Regime 33 2.6 Dimensional Analysis and Similitude 41 Problems 43 This chapter provides a broad overview of the basics of hydromechanics (also referred to as fluid mechanics) that are needed as background for subsequent chapters. The purpose of this chapter is to highlight fundamental concepts and equations rather than to substitute for textbooks of fluid mechanics. The overview covers water properties, hydrostatic pressure and force, conservations of mass, energy and momentum in flowing water, and dimensional analysis and similitude. 2.1 Engineering Properties of Water Five properties of water are used extensively in the field of water resources and hydraulic engi- neering. These properties are density, specific weight, dynamic viscosity, kinematic viscosity, and saturation vapor pressure. They are functions of atmospheric pressure and water tempera- ture. Table 2.1 lists the values of the properties at standard atmospheric pressure (Finnemore and Franzini, 2002). Density is defined as the mass per unit volume of water, whereas specific weight is defined as the weight per unit volume of water. In consistent units, they are related as: γ = ρg (2.1) specific weight [lbf ft −3 ; N m −3 ] density [slug ft −3 ; kg m −3 ] gravitational acceleration (= 32.2 ft sec −2 ; 9.81 m s −2 ) Dynamic viscosity (also known as absolute viscosity) is the shear stress between two layers of water per unit velocity gradient. It can be computed as: 10 2.1 Engineering Properties of Water 11 Table 2.1 Properties of water at standard atmospheric pressure.
eBook - PDF- Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Roberson(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
Hydrostatic Equilibrium • A hydrostatic condition means that the weight of each fluid particle is balanced by the net pressure force. • The weight of a fluid causes pressure to increase with increasing depth, giving the hydrostatic differential equation. The equations that are used in Hydrostatics are derived from this equation. The hydrostatic differential equation is dp _ dz = −γ = −ρg • If density is constant, the hydrostatic differential equation can be integrated to give the hydrostatic equation. The meaning (i.e., physics) of the hydrostatic equation is that piezometric head (or piezometric pressure) is constant everywhere in a static body of fluid. p _ γ + z = constant Pressure Distributions and Forces Due to Pressure • A fluid in contact with a surface produces a pressure distribution, which is a mathematical or visual description of how the pressure varies along the surface. • A pressure distribution is often represented as a statically equivalent force F p acting at the center of pressure (CP). • A uniform pressure distribution means that the pressure is the same at every point on a surface. Pressure distributions due to gases are typically idealized as uniform pressure distributions. • A hydrostatic pressure distribution means that the pressure varies according to dp/dz = −γ. Force on a Flat Surface • For a panel subjected to a hydrostatic pressure distribution, the hydrostatic force is F p = _ p A • This hydrostatic force • Acts at the centroid of area for a uniform pressure distribution. • Acts below the centroid of area for a hydrostatic pressure distribution. The slant distance between the center of pressure and the centroid of area is given by y cp − _ y = _ I _ _ y A Hydrostatic Forces on a Curved Surface • When a surface is curved, one can find the pressure force by applying force equilibrium to a free body comprised of the fluid in contact with the surface.
eBook - PDF- A. Douglas Davis(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
1 2 FLUI D MECHANIC S 12. 1 Introductio n As in al l o f mechanics , w e ca n focu s ou r attentio n o n fluids at rest (whic h w e cal l Hydrostatics) o r w e ca n stud y fluids in motion (whic h w e cal l hydrodynam-ics). A fluid is define d a s a substanc e tha t doe s no t hav e a fixed shap e an d tha t ca n flow. Therefore , bot h liquid s an d gase s ar e fluids. Bu t ther e ar e als o importan t difference s betwee n liquid s an d gases . Liquid s ar e no t readil y compressed ; w e ca n usuall y conside r thei r volume s o r densitie s a s fixed. Gase s ca n b e compresse d fa r mor e easily . Liquid s hav e a distinc t surfac e wherea s gase s completel y fill u p a container . We wil l find Newton' s Secon d Law , F = ma , an d al l th e earlie r idea s o f energ y conservatio n t o b e quit e usefu l whe n discussin g fluids. O f cours e thi s shoul d b e so , a s a fluid is merel y a collectio n o f particle s (bu t suc h a larg e collectio n tha t it is no t o f muc h us e t o as k for th e detail s o f energy , force , acceleration , o r mas s o f eac h individua l particle) . 12. 2 Hydrostatics : Fluid s a t Res t Th e ide a o f pressure is useful , eve n essential , in discussin g fluids. Pressur e is th e forc e exerte d o n a n are a divide d b y tha t area : (12.2.1 ) SECTIO N 12. 2 / Hydrostatics : FLUID S AT RES T 34 7 Figur e 12.2. 1 Pressure . 3 g Pressure , however , is no t a vecto r quantity . Experimentally , it is observe d tha t th e magnitud e o f th e forc e exerte d o n som e smal l are a is th e sam e for an y directio n o r orientatio n o f tha t area . Thi s is show n schematicall y in Figur e 12.2.1 . Yo u hav e experience d thi s if yo u hav e dive d int o a swimmin g poo l o r th e ocean—whe n yo u div e yo u fee l th e increase d pressur e o n al l part s o f you r body . W e ma y sa y tha t a fluid exerts pressure equally in all directions.
- Michael Clifford, Kathy Simmons, Philip Shipway(Authors)
- 2009(Publication Date)
- CRC Press(Publisher)
Water will not wet a greasy surface. In engineering, surface tension is not usually a significant force except where the dimensions of the volume of water are small compared with the area of the surface with which it is in contact, and it is the reason for the phenomenon of capillary action. From experience it is known that water will tend to be drawn along a piece of string and this is due to surface tension. Surface tension is only of significance in this chapter when considering the measurement of pressure using a manometer tube and will be dealt with in that section. An Introduction to Mechanical Engineering: Part 1 142 Key points from Section 3.1 ● A fluid is shaped by external forces (i.e. a fluid takes up the shape of its container). ● A fluid at rest cannot support a shear stress. ● In fluid mechanics, all fluids are treated as having local properties that are the same as the bulk properties and do not vary with time (continuum). ● Pressure in a fluid is associated with molecular motion. ● When pressure is constant over an area, F pA . ● Absolute pressure (relative to vacuum) and gauge pressure (relative to atmospheric pressure) are both used in engineering. ● The perfect gas equation of state can be used to obtain gas properties. ● Liquids can usually be treated as incompressible but gases cannot. 3.2 Fluids at rest – Hydrostatics Hydrostatics is the study of fluids at rest, but can also concern fluids in uniform motion such that all the fluid has the same velocity throughout, i.e. there is no motion of one part of the fluid relative to another part or to a surface. For example, liquid inside a road tanker moving along may be analysed as a Hydrostatics problem if there is no relative motion within the fluid.
- John I. Hochstein, Andrew L. Gerhart(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
35 35 • calculate the hydrostatic pressure force on a plane or curved submerged surface. • calculate the buoyant force and determine the stability of floating or submerged objects. • determine the pressure at various locations in a fluid at rest. • explain the concept of manometers and apply appropriate equations to determine pressures. LEARNING OBJECTIVES After completing this chapter, you should be able to: In this chapter, we will consider an important class of problems in which the fluid is either at rest or moving in such a manner that there is no relative motion between adjacent particles. In both instances there will be no shearing stresses in the fluid, and the only forces that develop on the surfaces of the particles will be due to the pressure. Thus, our principal concerns are to investigate pressure and its variation throughout a fluid and the force on submerged surfaces due to that pressure variation. The absence of shearing stresses greatly simplifies the analysis and, as we will see, allows us to obtain relatively simple solutions to many important practical problems. 2.1 Pressure at a Point As we briefly discussed in Chapter 1, the term pressure is used to indicate the normal force per unit area at a given point acting on a given plane within the fluid mass of interest. A question that immediately arises is how the pressure at a point varies with the orientation of the plane passing through the point. To answer this question, consider the free-body diagram, illustrated in Fig. 2.1, that represents a small triangular wedge of fluid from some arbitrary location within a fluid mass. Since we are considering the situation in which there are no shearing stresses, the only external forces acting on the wedge are due to the pressure and gravity. For simplicity the forces in the x direction are not shown, and the z axis is taken as the vertical axis so gravity acts in the negative z direction.
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