criteria for transition from laminar to turbulent flow
for all fluids, the nature of the flow is governed by the relative importance of
the viscous and the inertial forces. for newtonian fluids, the balance between
these forces is characterised by the value of the reynolds number. the generally
accepted value of the reynolds number above which stable laminar flow
no longer occurs is 2100 for newtonian fluids. for time-independent fluids, the
critical value of the reynolds number depends upon the type and the degree of
non-newtonian behaviour. for power-law fluids .n d n0/, the criterion of
,ryan and johnson [1959] can be used
while for newtonian fluids equation (3.31) predicts the critical reynolds
number of 2100, the corresponding limiting values increase with decreasing
values of the power-law index, reaching a maximum of about 2400 at n d 0:4
and then dropingping to 1600 at n d 0:1. the latter behaviour is not in line with
the experimental results of dodge and metzner [1959] who observed laminar
flow conditions up to remr 3100 for a fluid with n0 d 0:38. despite the
complex dependence of the limiting reynolds number on the flow behaviour
index embodied in equation (3.31) and the conflicting experimental evidence,
it is probably an acceptable approximation to assume that the laminar flow
conditions cease to prevail at reynolds numbers above ca. 2000–2500 and, for
the purposes of process calculations, the widely accepted figure of 2100 can be
used for time-independent fluids characterised in terms of n0. it is appropriate
to add here that though the friction factor for visco-elastic fluids in the laminar
regime is given by equation (3.28a), the limited experimental results available
suggest much higher values for the critical reynolds number. for instance,
metzner and park [1964] reported that their friction factor data for viscoelastic
polymer solutions were consistent with equation (3.28a) up to about
remr d 10 000. however, it is not yet possible to put forward a quantitative
criterion for calculating the limiting value of remr for visco-elastic fluids.
several other criteria, depending upon the use of a specific fluid model, are
also available in the literature [hanks, 1963 govier and aziz, 1982 wilson,
1996 malin, 1997]. for instance, hanks [1963] proposed the following criterion
for bingham plastic fluids:
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
|