Physics for Geologists, Second edition

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122 Fluids and fluid flow June 1991. This material must have been very fine; but if the terminal velocity is very small, an air current rising at the same velocity would suspend all such particles (indeed, as we have seen, it was probably carried to these heights in a rising column of warm air or gas). This may happen with rain drops in a thunderstorm, leading to a 'cloud-burst' when the uplift ceases or when the water saturation reaches some critical value. Solids in flowing fluid In liquids The murky colour of river water after heavy rains is due to the sediment carried in suspension in the water. Part of the total sediment load will be in suspension; part, in traction along the river bed. It will be clear that, although we cannot apply Stokes' Law to this problem, the principles are much the same. The finer, less dense, material will be in suspension; the coarser, denser, will be in traction; and there will be a critical size and density above which it will fall from suspension or cease to move. There may well be a critical Reynolds number at which particles of a particular size will move. The physical principle involved is that grains will move on account of the energy of the fluid until they arrive in a position in which the energy is insuf- ficient to move them farther. The energy of the water is partly transferred to the solids by virtue of the frictional resistance at the waterlsolid interface. In gases Windblown sand Once again, we cannot expect Stokes' Law to apply to windblown sand, but we can expect the principles to apply. The distinction between sediment transport in water and in air lies mainly in the smaller mass density of air, and its smaller viscosity. Equation 12.7 suggests that terminal velocity is inversely proportional to the fluid mass density and to its viscosity. So we would expect water to be able to move much larger grains than wind, if their velocities are equal. Buoyancy also plays a part. As the dimensionless ratio p,/p, decreases and approaches 1, so the terminal velocity decreases and the ease of movement by the fluid increases. See Bagnold (1941) for a classic, but rigorous treatment. Nukes ardentes, avalanches and turbidity currents When a volcano erupts, fine hot powder in hot gases may cause a plume to rise to great altitudes, as we have seen. If the amount of solids exceeds the buoyant effect of hot gases, the cloud descends from the volcano as nue'es Copyright 2002 by Richard E. Chapman
Fluids and fluid flow 123 ardentes, as happened on Mount PelCe in Martinique, West Indies, in May 1902 with the destruction of the town of St Pierre and all but one or two of the town's 30 000 inhabitants. When solids are suspended in a fluid, that fluid acquires a greater bulk density, and so tends to move to the most stable position it can reach, min- imizing the potential energy of the system. Snow avalanches and turbidity currents are similar. Bernoulli's theorem Water can be regarded for practical purposes as incompressible over the pressure changes that may take place in relatively short distances and with slow movement. Daniel Bernoulli (1700-82, of Switzerland) used this and the principle of conservation of energy to formulate an energy balance. Consider an ideal liquid flowing through a pipe of decreasing diameter (Figure 12.6). The work done on the liquid in the pipe is equal to the change of energy of the liquid. At station 1, the force applied to the liquid is equal to plA1, where p is the pressure and A is the area normal to the flow; and in moving the liquid a small distance 611 in the small interval of time St, the work done is equal to p1A1811. Likewise, the work done at station 2 is p2A2812. The weight of liquid passing station 1 during the interval of time 6t is pgA1611; and the same weight of liquid leaves station 2. The potential energy Ep per unit of mass entering at station 1 is gzl, so the potential energy of unit weight is zl and the potential energy of the liquid entering at station 1 is pgA1611z1, and that leaving at station 2 is pgA2612z2. The kinetic energy Ek per unit of weight is q2/2g, where q is the volu- metric flow rate; so the kinetic energy of the liquid entering at station 1 is pg~1611q:/2g; and that leaving at station 2 is pg~2612qi/2g. Copyright 2002 by Richard E. Chapman Figure 12.6 Bernoulli's theorem relates the energy changes in flow through a converging tube. The three terms in Equation 12.8 are the three 'heads' - pressure head, elevation head and velocity head (which is ignored) - illustrated in Figure 12.7.
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Physics for Geologists Second editi
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Copyright 2002 by Richard E. Chapma
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... vlii Contents Polarization 47 L
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Figures Copyright 2002 by Richard E
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Tables Copyright 2002 by Richard E.
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xiv Preface waves diminishes with d
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xvi Preface provides. This book is
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xviii Acknowledgements to K. Whaler
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xx Symbols mass refractive index bu
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2 Basic concepts Table 1.1 Dimensio
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4 Basic concepts Table 1.2 Basic SI
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6 Basic concepts pascal (Pa) and si
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8 Basic concepts all the relevant d
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10 Basic concepts relating them by
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2 Force The dimensions of force are
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14 Force The ratio of the Moon's ac
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16 Force Figure 2.1 The sum of the
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18 Force When a motorcycle takes a
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20 Force Figure 2.3 Torque is the p
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22 Force How does momentum differ f
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24 Force the weights - that is, the
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26 Force Figure 2.6 Wall-sticking i
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3 Gravity Universal gravity When di
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30 Gravity are significant to geolo
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32 Gravity Figure 3.2 The tractive,
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34 Gravity Mean sea level It might
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36 Gravity The benefits of space fl
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38 Gravity Figure 3.6 Profile of th
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40 Gravity Figure 3.8 The siphon at
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4 Optics Light is an electromagneti
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44 Optics Figure 4.2 Refraction. (a
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46 Optics The coeficient of reflect
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48 Optics only the light oscillatin
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50 Optics called Iceland Spar. Two
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52 Optics Diffraction If you shine
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54 Optics Figure 4.7 Geometrical op
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56 Optics Figure 4.9 The mirrors in
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5 Atomic structure and age-dating P
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60 Atomic structure and age-dating
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66 Electromagnetic radiation radiat
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68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103 and 104: Stress and strain 87 than some natu
Page 105 and 106: These three elastic constants are r
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
Page 115 and 116: Stress and strain 99 from which we
Page 117 and 118: 10 Sea waves The nature of water wa
Page 119 and 120: Sea waves 103 Figure 10.1 Wave moti
Page 121 and 122: Sea waves 105 refraction by islands
Page 123 and 124: Acoustics: sound and other waves 10
Page 125 and 126: Acoustics: sound and other waves 10
Page 127 and 128: 12 Fluids and fluid flow Introducti
Page 129 and 130: Fluids and fluid flow 1 13 Figure 1
Page 131 and 132: Fluids and fluid flow 115 Figure 22
Page 133 and 134: Fluids and fluid flow 117 and the f
Page 135 and 136: water above a vertical thickness h
Page 137: Fluids and fluid flow 121 where V i
Page 141 and 142: Fluids and fluid flow 125 Figure 12
Page 143 and 144: - 14 $ 12 E 10 K .- 3 8 r cll + 6 0
Page 145 and 146: Fluids and fluid flow 129 the liqui
Page 147 and 148: Some dangers of mathematical statis
Page 155 and 156: Appendix 139 What would happen if y
Page 157 and 158: Notes 141 and since x is very large
Page 159 and 160: References Allum, J. A. E. (1966) P
Page 161 and 162: References 145 -(1950) 'Mechanism o
Page 163: Further reading 147 Trigg, G. L. an
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