Viscous Flow in Pipes.pdf

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Integral Analysis for Increased Pressure Drop in theEntrance Region(From S.R. Turns, Thermal-Fluid Sciences, Cambridge Univ. Press, 2006)The increased pressure drop in the entrance region result from tworeasons: 1. flow acceleration, 2. increased wall shear stress.1. Flow accelerationIntegral momentum balance for the control volume below leads to4P0A x-sec −P2A x-sec − ∫ τAwdAw = mv &avg−mv&avgw 3Increased momentum flowor flow acceleration
2. Increased Wall Shear Stress:⎡ τ dA ⎤ > ⎡ τ dA⎢∫⎥ ⎢∫⎤⎥⎣ Aw w w ww ⎦developing⎣ Aw⎦regionfullydevelopedIncreased wall shear stress
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: 8.1.3 Pressure and 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 and 36: 8.3.5 Chaos and TurbulenceChaos the
Page 37 and 38: About the difficulty to understand
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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