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Apr 12, 2017

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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