Page 188 - Standard Handbook Of Petroleum & Natural Gas Engineering

Fluid Mechanics 173

(2-57)

(2-58)

= 7, + P( %) (2-59)

where T is the shear stress in force per unit area, dv/dy is the shear rate (rate of
change in velocity with respect to distance from measured perpendicular to the flow).
The behavior of all three types of fluids is illustrated in Figure 2-19. Viscosities of
common fluids that are normally Newtonian are given in Tables 2-10 and 2-11.
Viscosities for hydrocarbon gases can be estimated from Figure 2-20.
If the calculated value of the Reynolds number is below 2,000, the flow will generally
be laminar, that is, the fluid particles will follow parallel flow paths. For laminar flow
the friction factor is

f = 64/R (2-60)
If the Reynolds number is greater than 4,000, the flow will generally be turbulent
and the friction factor can be calculated from the Colebrook equation:

1
- -2 log,,,[ (2-61)
=
& + "1 R&

BINGHAM PLASTIC
TO -
t POWER LAW, DILATANT

It NEWTONIAN

POWER LAW, PSEUDOPLASTIC

-
dV
*
dY
Figure 2-19. Viscous behavior of fluids.