Frictional pressure drop
Generally, methods for determining the frictional pressure drop begin by using
a physical model of the two-phase system, and then applying an approach
similar to that for single phase flow. Thus, in the so-called separated flow
model, the two phases are first considered to be flowing separately and
allowance is then made for the effect of interfacial interactions. Irrespective
of the type of flow and the rheology of the liquid phase, the total pressure
gradient .??1pTP=L/ in horizontal flow consists of two components which
represent the frictional and acceleration contribution respectively, i.e.
Laminar conditions
When a gas is introduced into a shear-thinning fluid in laminar flow, the
frictional pressure drop may, in some circumstances, actually be reduced below
the value for the liquid flowing alone at the same volumetric rate. As the
gas flowrate is increased, the two-phase pressure drop decreases, then passes
through a minimum (maximum drag reduction) and finally increases again and
eventually exceeds for the flow of liquid alone. This effect which has been
observed with flocculated suspensions of fine kaolin and anthracite coal and
with shear-thinning polymer solutions occurs only where the flow of liquid
on its own would be laminar. A typical plot of drag ratio . 2L
/ as a function
of superficial air velocity is shown in Figure 4.10, for a range of values of
the liquid superficial velocity, and the corresponding values of its Reynolds
number ReMR are given. The liquid is a 24.4% (by volume) kaolin suspension
in water which exhibits power-law rheology. An analysis of a large number
of experimental results identifies the following salient features:
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 .
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