Viscous Flow in Pipes.pdf

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The Butterfly EffectThe phrase refers to the idea that a butterfly’s wings mightcreate tiny changes in the atmosphere that may ultimatelyalter the path of a tornado or delay, accelerate or even preventthe occurrence of a tornado in a certain location. The flappingwing represents a small change in the initial condition of thesystem, which causes a chain of events leading to large-scalealterations of events. Had the butterfly not flapped its wings,the trajectory of the system might have been vastly different.Of course the butterfly cannot literally cause a tornado. Thekinetic energy in a tornado is enormously larger than theenergy in the turbulence of a butterfly. The kinetic energy of atornado is ultimately provided by the sun and the butterfly canonly influence certain details of weather events in a chaoticmanner. (from Wikipedia)
About the difficulty to understand turbulenceOn his death bed, Heisenberg is reported to havesaid, "When I meet God, I am going to ask him twoquestions: Why relativity? And why turbulence? Ireally believe he will have an answer for the first."A similar witticism has been attributed to Horace Lamb(who had published a noted text book onHydrodynamics)—his choice being quantum mechanics(instead of relativity) and turbulence. Lamb was quoted assaying in a speech to the British Association for theAdvancement of Science in 1932, "I am an old man now,and when I die and go to heaven there are two matters onwhich I hope for enlightenment. One is quantumelectrodynamics, and the other is the turbulent motionof fluids. And about the former I am rather optimistic."
Page 1 and 2: Chapter 8Viscous Flow in Pipes
Page 3 and 4: 8.1.1 Laminar or Turbulent Flow•
Page 5 and 6: 8.1.2 Entrance Region and FullyDeve
Page 7 and 8: 8.1.3 Pressure and Shear Stress•
Page 9 and 10: 2. Increased Wall Shear Stress:⎡
Page 11 and 12: Nature of flow• The nature of the
Page 13 and 14: 8.2.1 From F=ma Applied Directly to
Page 15 and 16: • The above analysis is valid for
Page 17 and 18: • Average velocityVQ2 2π RVcVcΔ
Page 19 and 20: 8.2.2 From the Navier-Stokes Equati
Page 21 and 22: • It is advantageous to describe
Page 23 and 24: 8.3 Fully developed turbulent flow
Page 25 and 26: 8.3.2 Turbulent shear stress• Tur
Page 27 and 28: Time-averaged Navier-Stokes Equatio
Page 29 and 30: Total stress• Total stressduτ =
Page 31 and 32: 8.3.3 Turbulent Velocity Profile•
Page 33 and 34: Turbulent Velocity Profile• Empir
Page 35: 8.3.5 Chaos and TurbulenceChaos the
Page 39 and 40: Pressure drop• For turbulent flow
Page 41 and 42: Friction coefficient• For laminar
Page 43 and 44: • Energy Equation2 2p1 V1 p2 V2+
Page 45 and 46: 8.4.2 Minor Losses• Major losses
Page 47 and 48: Loss coefficients for minor lossFor
Page 49 and 50: Pressure loss• Flow patter and pr
Page 51 and 52: Loss coefficient• Loss coefficien
Page 53 and 54: Loss coefficient• Loss coefficien
Page 55 and 56: Loss coefficient
Page 57 and 58: 8.4.3 Noncircular Conduits• For n

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