3.2.2Bingham plastic and yield-pseudoplastic fluids
A fluid with a yield stress will flow only if the applied stress (proportional to
pressure gradient) exceeds the yield stress. There will be a solid plug-likecore flowing in the middle of the pipe where j rzj is less than the yield stress,
as shown schematically in Figure 3.4. Its radius, Rp, will depend upon the
magnitude of the yield stress and on the wall shear stress. From equation (3.2),
In the annular area Rp < r < R, the velocity will gradually decrease from
the constant plug velocity to zero at the pipe wall. The expression for this
velocity distribution will now be derived.
For the region Rp < r < R, the value of shear stress will be greater than the
yield stress of the fluid, and the Bingham fluid model for pipe flow is given
by (equation (1.16) in Chapter 1):
Now combining equations (3.2) and (3.10) followed by integration yields the
following expression for the velocity distribution
Example 3.2
The rheological properties of a china clay suspension can be approximated by either a
power-law or a Bingham plastic model over the shear rate range 10 to 100 s??1. If the
yield stress is 15 Pa and the plastic viscosity is 150 mPas, what will be the approximate
values of the power-law consistency coefficient and flow behaviour index?
Estimate the pressure drop when this suspension is flowing under laminar conditions
in a pipe of 40mm diameter and 200m long, when the centre-line velocity is 0.6m/s,
according to the Bingham plastic model? Calculate the centre-line velocity for this
pressure drop for the power-law model
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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