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Colebrook-White-Banks reconciliation

Apr 12, 2017

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Engineering

  • Fluid Flow 2.9

    For fully developed laminar-viscous flow in a pipe, the loss isevaluated from Equation (8) as follows:

    (27)

    where Thus, for laminar flow, thefriction factor varies inversely with the Reynolds number.

    With turbulent flow, friction loss depends not only on flow con-ditions, as characterized by the Reynolds number, but also on thenature of the conduit wall surface. For smooth conduit walls, empir-ical correlations give

    (28a)

    (28b)

    Generally, f also depends on the wall roughness . The variationis complex and best expressed in chart form (Moody 1944) as

    shown in Figure 13. Inspection indicates that, for high Reynoldsnumbers and relative roughness, the friction factor becomes inde-pendent of the Reynolds number in a fully-rough flow regime. Then

    (29a)

    Values of f between the values for smooth tubes and those for thefully-rough regime are represented by Colebrooks natural rough-ness function:

    (29b)

    A transition region appears in Figure 13 for Reynolds numbersbetween 2000 and 10 000. Below this critical condition, for smoothwalls, Equation (27) is used to determine f ; above the critical con-dition, Equation (28b) is used. For rough walls, Figure 13 or Equa-tion (29b) must be used to assess the friction factor in turbulent flow.To do this, the roughness height , which may increase with conduituse or aging, must be evaluated from the conduit surface (Table 2).

    Fig. 13 Relation Between Friction Factor and Reynolds Number(Moody 1944)

    HL( )fL

    g------ 8V

    R2

    ---------- 32LV

    D2g

    ----------------- 64VD --------------- L

    D----

    V2

    2g------

    = = =

    Re VD and f 64 Re.==

    f0.3164

    Re0.25

    ----------------= for Re 105

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