Viscous Flow in Pipes.pdf

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8.2.3 From Dimensional Analysis• Consider pressure drop in the horizontal pipe( , l, , μ )Δ p=F V Dk− r = 5− 3=2D⋅Δp⎛ l ⎞= φ ⎜ ⎟μ ⋅V⎝D⎠dimensionless groups• If we assume that the pressure drop is directly proportionalto the pipe length.2D ⋅Δp ClΔp CμV Δp D= , = ⇒ V =2μ ⋅V D l D l CμorQ( π 4 )4 4C Δp⋅D π D p= AV = =μl⋅Δ128μlThe value of C must be determined by theory or experiment.C = 32 for round pipe.
• It is advantageous to describe in terms ifdimensionless quantities.32μlVΔ p =2DΔpμlV D μ l ⎛ l ⎞= = = ⎜ ⎟V V VD D ⎝ D⎠232 64641 2 1 22ρ2ρ ρ Re2i.e.,l ρVΔ p= f ⋅ ⋅D 2( ) ( )where f =Δp D l ρV 2 2 friction factor or Darcy friction factorFor laminar fully developed pipe flow• Alternatively, sincef =64Re4⋅lτwΔ p =DΔp⋅( D l)4⋅lτD 1 8τwf = = =ρV D ρV ρV 2w1 2 1 22l2(8.19)(8.20)
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: 8.2.2 From the Navier-Stokes Equati
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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