r5g.netlify.app

<p>November 14, 2008</p><p>Applied HydraulicsJohn FentonInstitut fr Hydromechanik, Universitt Karlsruhe Kaiserstrasse 12, 76131 Karlsruhe, Germany</p><p>AbstractThis course of lectures is an introduction to hydraulics, the traditional name for uid mechanics in civil and environmental engineering where sensible and convenient approximations to apparentlycomplex situations are made. An attempt is made to obtain physical understanding and insight into the subject by emphasising that we are following a modelling process, where simplicity, insight, and adequacy go hand-in-hand. We hope to include all important physical considerations, and to exclude those that are not important, but with understanding of what is being done. It is hoped that this will provide a basis for further sophistication if necessary in practice if a problem contains unexpected phenomena, then as much advanced knowledge should be used as is necessary, but this should be brought in with a spirit of scepticism.</p><p>Table of Contents1. The nature and properties of uids, forces, and ows . . . 1.1 Units . . . . . . . . . . . . . . . . 1.2 Properties of uids . . . . . . . . . . . . 1.3 Forces acting on a uid . . . . . . . . . . 1.4 Turbulent ow and the nature of most ows in hydraulics Hydrostatics . . . . . . . . . . . . . 2.1 Fundamentals . . . . . . . . . . 2.2 Forces on planar submerged surfaces . . . 2.3 Forces on submerged surfaces of general shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . 5 . 5 . 13 . 14 . . . . . . . . 24 24 31 34 39 39 41 42</p><p>2.</p><p>3.</p><p>Fluid kinematics and ux of quantities . . . . . . . . . . 3.1 Kinematic denitions . . . . . . . . . . . . . 3.2 Flux of volume, mass, momentum and energy across a surface 3.3 Control volume, control surface . . . . . . . . . . Conservation of mass the continuity equation Conservation of momentum and forces on bodies . . . . . . . . . . . . .</p><p>4. 5. 6.</p><p>. 43 . 44 . . . . . 49 49 51 53 56</p><p>Conservation of energy . . . . . . . . . . . . . . 6.1 The energy equation in integral form . . . . . . . . 6.2 Application to simple systems . . . . . . . . . . 6.3 Energy conservation along a streamline Bernoullis equation 6.4 Summary of applications of the energy equation . . . . . 1</p><p>Applied Hydraulics</p><p>John Fenton</p><p>7.</p><p>Dimensional analysis and similarity . . . . . . 7.1 Dimensional homogeneity . . . . . . . 7.2 Buckingham theorem . . . . . . . . 7.3 Useful points . . . . . . . . . . . 7.4 Named dimensionless parameters . . . . . 7.5 Physical scale modelling for solving ow problems</p><p>. . . . . .</p><p>. . . . . .</p><p>. . . . . .</p><p>. . . . . . . . . . .</p><p>. . . . . . . . . . .</p><p>. . . . . . . . . . .</p><p>. . . . . . . . . . .</p><p>56 56 57 57 59 61 62 62 66 68 70</p><p>8.</p><p>Flow in pipes . . . . . . . . . . . . . . . . 8.1 The resistance to ow . . . . . . . . . . . . 8.2 Practical single pipeline design problems . . . . . . 8.3 Minor losses . . . . . . . . . . . . . . . 8.4 Total head, piezometric head, and potential cavitation lines</p><p>2</p><p>Applied Hydraulics</p><p>John Fenton</p><p>ReferencesColebrook, C. F. (1938) Turbulent ow in pipes with particular reference to the transition region between the smooth and rough pipe laws, J. Inst. Civ. Engrs 11, 133156. Colebrook, C. F. &amp; White, C. M. (1937) Experiments with uid friction in roughened pipes, Proc. Roy. Soc. London A 161, 367381. Haaland, S. E. (1983) Simple and explicit formulas for the friction factor in turbulent pipe ow, J. Fluids Engng 105, 8990. Jirka, G. H. (2005) Hydromechanik, Lecture Notes, Institute fr Hydromechanik, Universitt Karlsruhe. http://hydro.ifh.uni-karlsruhe.de/download.htm Montes, S. (1998) Hydraulics of Open Channel Flow, ASCE, New York. Moody, L. F. (1944) Friction factors for pipe ow, Trans. ASME 66, 671684 (including discussion). Oertel, H. (2005) Introduction to Fluid Mechanics: Fundamentals and Applications, Universittsverlag, Karlsruhe. www.ubka.uni-karlsruhe.de/cgi-bin/psview?document=2005/maschinenbau/17 Rouse, H. (1937) Modern conceptions of the mechanics of uid turbulence, Transactions ASCE 102(1965 (also published in facsimile form in Classic Papers in Hydraulics (1982), by J. S. McNown and others, ASCE)), 52132. Streeter, V. L. &amp; Wylie, E. B. (1981) Fluid Mechanics, First SI Metric Edn, McGraw-Hill Ryerson, Toronto. Swamee, P. K. &amp; Jain, A. K. (1976) Explicit equations for pipe-ow problems, J. Hyd. Div. ASCE 102, 657664. White, F. M. (1986) Fluid Mechanics, Second Edn, McGraw-Hill. White, F. M. (2003) Fluid Mechanics, Fifth Edn, McGraw-Hill, New York.</p><p>Useful reading and reference materialThe table of references which follows on the next page shows some that students might nd useful for further reading or exercises. If no Library location is shown, it is not in the Main Library of the University of Karlsruhe. However, Institute Libraries may own some of these books, so it is recommended that students search on the University Library search site (http://www.ubka.uni-karlsruhe.de/ hylib/suchmaske.html), or use the list of active search results available via our Information Page, or directly from http://www.ifh.uni-karlsruhe.de/lehre/RessEng/Hydromechanics/Books.html. One book is available on the Internet, Oertel (2005), with the location given above, written by a Professor of Mechanical Engineering in this University. For readers of German, Professor Gerhard Jirkas Lecture notes for the course equivalent to this one for German civil engineering undergraduate students at the University of Karlsruhe are at the location given in Jirka (2005) above.</p><p>3</p><p>Applied Hydraulics</p><p>John Fenton</p><p>Book Historical works Garbrecht, G. (ed.) (1987) Hydraulics and hydraulic research: a historical review, Balkema Rouse, H. and S. Ince (1957) History of hydraulics, Dover Standard uid mechanics &amp; hydraulics textbooks Brower, W. B. (1999) A Primer in Fluid Mechanics: Dynamics of ows in one space dimension, CRC Press Chadwick, A. and J. Morfett (1993) Hydraulics in Civil and Environmental Engineering, Spon Crowe, C. T., D. F. Elger and John A. Roberson (2001) Engineering Fluid Mechanics, Wiley Daily, J. W. and D. R. F. Harleman (1966) Fluid Dynamics, Addison-Wesley Douglas, J. M. Gasiorek and J. A. Swafeld (1986) Fluid Mechanics, Longman Featherstone, R.E., and C. Nalluri (1995) Civil Engineering Hydraulics: essential theory with worked examples, Blackwell Science Francis, J.R.D. and P. Minton (1984) Civil Engineering Hydraulics, E. Arnold Jaeger, C. (1956) Engineering Fluid Mechanics, Blackie Krause, E. (2005) Fluid Mechanics: With Problems and Solutions, Springer Lighthill, M. J. (1986) An Informal Introduction to Theoretical Fluid Mechanics, Oxford Olson, R. M. and S. J. Wright (1990) Essentials of Engineering Fluid Mechanics, Harper &amp; Row Rouse, H. (1946) Elementary Mechanics of Fluids, Wiley Street, R. L., G. Z. Watters, and J. K. Vennard (1996) Elementary Fluid Mechanics, Wiley Streeter, V. L. and E. B. Wylie (1983) Fluid Mechanics, McGraw-Hill White, F. M. (1979) Fluid Mechanics, McGraw-Hill Worked solutions Alexandrou, A. N. (1984) Solutions to problems in Streeter/Wylie, Fluid Mechanics, McGraw-Hill Crowe, C. T., D. F. Elger and John A. Roberson (2002) Engineering Fluid Mechanics: Student Solutions Manual, Wiley Douglas, J. F. (1962) Solution of problems in uid mechanics, Pitman Paperbacks Open channel hydraulics Chow, V. T. (1959) Open-channel Hydraulics, McGrawHill Henderson, F. M. (1966) Open Channel Flow, Macmillan Books which deal more with practical design problems Mays, L. W. (editor-in-chief) (1999) Hydraulic Design Handbook, McGraw-Hill Novak, P. et al. (1996) Hydraulic Structures, Spon Roberson, J. A., J. J. Cassidy, M. H. Chaudhry (1998) Hydraulic Engineering, Wiley</p><p>Location in Library Magazin Signatur: 87 E 711 Magazin Signatur: V A 6900</p><p>Comments An encyclopaedic historical overview An interesting readable history Practice-oriented </p><p>Lesesaal Technik, Fachgruppe: mech 6.0, Signatur: 99 A 598 Lehrbuchsammlung, Lesesaal Technik, Fachgruppe: mech 6.0, Signatur: 2004 A 1594(7) Magazin, Signatur: 2006 A 1209 Magazin, Signatur: 79 A 2384(2) </p><p>Well-known Well-known, students seem to like it Practically-oriented, with examples A clear and brief presentation A classic of sophisticated theory </p><p> Lesesaal Technik, Fachgruppe: mech 6.0, Signatur: 2005 A 11571 Magazin, Signatur: 87 A 2002 Magazin, 672(5) Magazin, Signatur: 88 A 1213 Magazin, Signatur: 80 A 695 Signatur: 74 A</p><p>Mathematical and clear treatment Clear and high-level explanation of the basics Standard hydraulics textbook A very good book, at a high level A very good book, at a high level </p><p> Lehrbuchsammlung, Lesesaal Technik, Fachgruppe: mech 6.0, Signatur: 2003 A 13185(7) </p><p>Magazin, Signatur: V A 5786 Magazin, Signatur: 73 A 1763</p><p>Classical and lengthy work on open channels Classical and readable work on open channels Encyclopaedic Practice-oriented Practice-oriented</p><p>4</p><p>Applied Hydraulics</p><p>John Fenton</p><p>1. The nature and properties of uids, forces, and ows1.1 UnitsThroughout we will use the Systme Internationale, in terms of metres, kilograms and seconds, the fundamental units of mass (M), length (L) and time (T) respectively. Other quantities are derived from these. All are set out in Table 1-1. Some of the derived quantities will be described further below.Quantity mass length time temperature linear velocity angular velocity linear acceleration volume ow rate mass ow rate linear momentum force work, energy power pressure, stress surface tension dynamic viscosity kinematic viscosity Dimensions Units Fundamental quantities M kg L m T s C or K = C + 273.15 Derived quantities LT1 m s1 T1 s1 2 LT m s2 3 1 L T m3 s1 1 MT kg s1 M L T1 kg m s1 2 MLT 1 kg m s2 = 1 N (Newton) 2 2 ML T 1 N m = 1 J (Joule) 1 J s1 = 1 W (Watt) ML2 T3 ML1 T2 1 N m2 = 1 Pa (Pascal) = 105 bar 2 MT N m1 1 1 ML T 1 kg m1 s1 = 10 Poise L2 T1 1 m2 s1 = 104 Stokes</p><p>Table 1-1. Quantities, dimensions, and units</p><p>1.2 Properties of uids1.2.1 Denition of a uid</p><p>(a) Liquid</p><p>(b) Gas</p><p>(c) Liquid with other molecule</p><p>Figure 1-1. Behaviour of typical molecules (a) of a liquid, (b) a gas, and (c) a different molecule in a liquid</p><p>A uid is matter which, if subject to an unbalanced external force, suffers a continuous deformation. The forces which may be sustained by a uid follow from the structure, whereby the molecules are able to move freely. Gas molecules have much larger paths, while liquid molecules tend to be closer to each other and hence are heavier. Fluids can withstand large compressive forces (pressure), but only negligibly small tensile forces. Fluids at rest cannot sustain shear forces, however uids in relative motion do give rise to shear forces, resulting 5</p><p>Applied Hydraulics</p><p>John Fenton</p><p>from a momentum exchange between the more slowly moving particles and those which are moving faster. The momentum exchange is made possible because the molecules move relatively freely. Especially in the case of a liquid, we can use the analogy of smooth spheres (ball bearings, billiard balls) to model the motion of molecules. Clearly they withstand compression, but not tension.Molecular characteristic Spacing Activity Solids Liquids Small (material is heavy) Very little Vibratory Fluids Gases Large (light) Great, molecules moving at large velocities and colliding If conned, elastic in compression, not in tension or shear. Molecules free to move and slip past one another. If a force is applied it continues to change the alignment of particles. Liquid resistance is dynamic (inertial and viscous).</p><p>Structure</p><p>Response to force</p><p>Rigid, molecules do not move relative to each other. Stress is proportional to strain Resisted continuously, static or dynamic</p><p>Table 1-2. Characteristics of solids and uids</p><p>1.2.2 Density The density is the mass per unit volume of the uid. It may be considered as a point property of the uid, and is the limit of the ratio of the mass m contained in a small volume V to that volume:= lim m . V 0 V</p><p>In fact the limit introduced above must be used with caution. As we take the limit V 0, the density behaves as shown in Figure 1-2. The real limit is V V , which for gases is the cube of the mean free path, and for liquids is the volume of the molecule. For smaller volumes considered the fact that the uid is actually an assemblage of particles becomes important. In this course we will assume that the uid is continuous, the continuum hypothesis.</p><p>If inside molecule Possible variation if the fluid is compressible</p><p>If outside molecule</p><p>V *</p><p>V</p><p>Figure 1-2. Density of a uid as obtained by considering successively smaller volumes V , showing the apparent limit of a constant nite value at a point, but beyond which the continuum hypothesis breaks down.</p><p>As the temperature of a uid increases, the energy of the molecules as shown in Figure 1-1 increases, each molecule requires more space, and the density decreases. This will be quantied below in 1.2.8, where it will be seen that the effect for water is small. 6</p><p>Applied Hydraulics</p><p>John Fenton</p><p>1.2.3 Surface tension This is an important determinant of the exchange processes between the air and water, such as, for example, the purication of water in a reservoir, or the nature of violent ow down a spillway. For the purposes of this course it is not important and will not be considered further. 1.2.4 Bulk modulus and compressibility of uids The effect of a pressure change p is to bring about a compression or expansion of the uid by an amount V . The two are related by the bulk modulus K , constant for a constant temperature, dened:p = K V . V</p><p>The latter term is the volumetric strain. K is large for liquids, so that density changes due to pressure changes may be neglected in many cases. For water it is 2.070 G N m2 . If the pressure of water is reduced from 1 atmosphere (101,000 N m2 ) to zero, the density is reduced by 0.005%. Thus, for many practical purposes water is incompressible with change of pressure. 1.2.5 The continuum hypothesis In dealing with uid ows we cannot consider individual molecules. We replace the actual molecular structure by a hypothetical continuous medium, which at a point has the mean properties of the molecules surrounding the point, over a sphere of radius large compared with the mean molecular spacing. The term 'uid particle' is taken to mean a small element of uid which contains many molecules and which possesses the mean uid properties at its position in space. 1.2.6 Diffusivity Fluids may contain molecules of other materials, such as chemical pollutants. The existence of such materials is measured by the mass concentration per unit volume c in a limiting sense as the measuring volume goes to zero. at a point, invoking the continuum hypothesis. The particles will behave rather similarly to individual uid molecules but where they re..</p>