3.5Laminar flow between two infinite parallel plates
The steady flow of an incompressible power-law fluid between two parallel plates
extending to infinity in x- and z-directions, as shown schematically in Figure 3.15
will now be considered. The mid-plane between the plates will be taken as the
origin with the flow domain extending from y D ??b to y D Cb. The force
balance on the fluid element ABCD situated at distance y from the mid-plane,
.can be set up in a similar manner to that for flow through pipes
The shear stress is thus seen to vary linearly, from zero at the mid-plane to a
maximum value at the plate surface, as in the case of pipe flow. The system
is symmetrical about the mid-plane .y D 0/ and equation (3.62) needs to be
solved only for 0 < y < b. Because dVz=dy is negative in this region, the
shear stress for a power-law fluid is given by:
Example 3.9
Calculate the volumetric flow rate per unit width at which a 0.5% polyacrylamide
solution will flow down a wide inclined surface (30° from horizontal) as a 3mm thick
film. The shear stress–shear rate behaviour of this polymer solution may be approximated
by the Ellis fluid model, with the following values of the model parameters:
0 D 9Pas; 1=2 D 1:32 Pa; D 3:22 and the solution has a density of 1000 kg/m3.
Assume the flow to be laminar.
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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