Science of Water : Concepts and Applications

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Water Hydraulics 69 • • • • • • V 1 2 /2g y 1 z 1 1 Energy grade line Hydraulic grade line V 1 Piezometers Center line of pipe Datum Pipe flow V 2 2 h L V 2 1 /2g V 2 2 /2g y 2 z 2 Open channel flow V 2 2 /2g and the velocity head V 2 /2g. Figure 3.15 shows the energy grade line or energy gradient, which represents the energy from section to section. In the absence of frictional losses, the energy grade line remains horizontal, although the relative distribution of energy may vary between the elevation, pressure, and velocity heads. In all real systems, however, losses of energy occur because of resistance to fl ow, and the resulting energy grade line is sloped (i.e., the energy grade line is the slope of the specifi c energy line). Specifi c energy (E)—Sometimes called specifi c head, is the sum of the pressure head y and the velocity head V 2 /2g. The specifi c energy concept is especially useful in analyzing fl ow in open channels. Steady fl ow—Occurs when the discharge or rate of fl ow at any cross section is constant. Uniform fl ow—Occurs when the depth, cross-sectional area, and other elements of fl ow are substantially constant from section to section. Nonuniform fl ow—Occurs when the slope, cross-sectional area, and velocity change from section to section. The fl ow through a Venturi section used for measuring fl ow is a good example. Varied fl ow—Flow in a channel is considered varied if the depth of fl ow changes along the length of the channel. The fl ow may be gradually varied or rapidly varied (i.e., when the depth of fl ow changes abruptly), as shown in Figure 3.16. Slope (gradient)—The head loss per foot of channel. y 1 z 1 1 Energy grade line Water surface Channel bottom FIGURE 3.15 Comparison of pipe fl ow and open-channel fl ow. (Adapted from Metcalf & Eddy, Wastewater Engineering: Collection and Pumping of Wastewater, McGraw-Hill, New York, 1981.) FIGURE 3.16 Varied fl ow. RVF GVF RVF GVF RVF GVF RVF Sluice gate Hydraulic jump RVF – Rapidly varied flow GVF – Gradually varied flow V 1 Flow over a weir V 2 2 h L y 2 z 2 Hydraulic drop
70 The Science of Water: Concepts and Applications MAJOR HEAD LOSS Major head loss consists of pressure decreases along the length of pipe caused by friction created as water encounters the surfaces of the pipe. It typically accounts for most of the pressure drop in a pressurized or dynamic water system. Components of Major Head Loss The components that contribute to major head loss are roughness, length, diameter, and velocity. Roughness Even when new, the interior surfaces of pipes are rough. The roughness varies, of course, depending on pipe material, corrosion (tuberculation and pitting), and age. Because normal fl ow in a water pipe is turbulent, the turbulence increases with pipe roughness, which, in turn, causes pressure to drop over the length of the pipe. Pipe Length With every foot of pipe length, friction losses occur. The longer the pipe, the more the head loss. Friction loss because of pipe length must be factored into head loss calculations. Pipe Diameter Generally, small diameter pipes have more head loss than large diameter pipes. This is the case because in large diameter pipes less of the water actually touches the interior surfaces of the pipe (encountering less friction) than in a small diameter pipe. Water Velocity Turbulence in a water pipe is directly proportional to the speed (or velocity) of the fl ow. Thus, the velocity head also contributes to head loss. √ Note: For the same diameter pipe, when fl ow increases, head loss increases. Calculating Major Head Loss Darcy, Weisbach, and others developed the fi rst practical equation used to determine pipe friction in about 1850. The equation or formula now known as the Darcy–Weisbach equation for circular pipes is: h f LV 2 f D2 g In terms of the fl ow rate Q, the equation becomes: where h f = head loss, ft f = coeffi cient of friction L = length of pipe, ft V = mean velocity, ft/s D = diameter of pipe, ft g = acceleration due to gravity, 32.2 ft/s 2 Q = fl ow rate, ft 3 /s fLQ hf gD 8 2 2 5 (3.20) (3.21)
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Second Edition THE SCIENCE OF WATER
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Cover Image: Falling Spring at Fall
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Contents Preface ..................
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Contents ix Velocity Head .........
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Contents xi Specifi c Conductance .
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Contents xiii (5) Beetles (Order: C
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Contents xv Chlorine Residual Testi
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Contents xvii Water Filtration Calc
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To the Reader In reading this text,
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1 Introduction When color photograp
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Introduction 3 On second look, we s
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Introduction 5 As mentioned earlier
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Introduction 7 This scream of lost
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Introduction 9 Metcalf & Eddy, Inc.
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12 The Science of Water: Concepts a
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Page 76 and 77: Water Hydraulics 51 √ Important P
Page 78 and 79: Water Hydraulics 53 FIGURE 3.4 Thru
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Page 102 and 103: Water Hydraulics 77 Slope (S) The s
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Page 108 and 109: Water Hydraulics 83 TYPES OF DIFFER
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Page 112 and 113: Water Hydraulics 87 Meter backpress
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Page 118 and 119: Water Hydraulics 93 Solution: 1200g
Page 120: Water Hydraulics 95 Water and Waste
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120 The Science of Water: Concepts
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6 Water Ecology The subject of man
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Water Ecology 157 The environment i
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Water Ecology 159 FIGURE 6.2 Notone
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Water Ecology 161 H 2 O O 2 FIGURE
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Water Ecology 163 FeS FIGURE 6.6 Th
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Water Ecology 165 Algae FIGURE 6.8
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Water Ecology 167 2. Likewise, biom
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Water Ecology 169 Population densit
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Water Ecology 171 succession can be
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Water Ecology 173 dark winter month
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Water Ecology 175 In rain events wh
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Water Ecology 177 long profi le, cr
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Water Ecology 179 THE FLOODPLAIN A
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Water Ecology 181 It is important t
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Water Ecology 183 Specifi c Adaptat
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Water Ecology 185 serve to indicate
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Water Ecology 187 UNITS OF ORGANIZA
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Water Ecology 189 FIGURE 6.20 Stone
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Water Ecology 191 FIGURE 6.22 Midge
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Water Ecology 193 FIGURE 6.25 Riffl
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Water Ecology 195 They push their m
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Water Ecology 197 FIGURE 6.32 Damse
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Water Ecology 199 Darwin, C., 1998.
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10 Water Treatment Calculations Gup
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