Torsional flow between parallel disks

In the assumptions for flow between concentric cylinders, we ignored any end effects. It is not too difficult to estimate their importance. At the bottom of the cylinder in Figure 5.3.1 there will also be a shear flow. This can be approximated as torsional flow between parallel disks, to be discussed in Section 5.5. From that section we can use eq. 5.5.8 and the power law, eq. 2.4.12, for to calculate the extra torque contributed by the end... 

Torsional Drag Flow between Parallel Disks Solve the torsional drag flow problem between two parallel disks, one of which is stationary while the other is rotating with an angular velocity 0(s ). Note ve/r = constant.)... 

The velocity field between the cone and the plate is visualized as that of liquid cones described by 0-constant planes, rotating rigidly about the cone axis with an angular velocity that increases from zero at the stationary plate to 0 at the rotating cone surface (23). The resulting flow is a unidirectional shear flow. Moreover, because of the very small i//0 (about 1°—4°), locally (at fixed r) the flow can be considered to be like a torsional flow between parallel plates (i.e., the liquid cones become disks). Thus... 

In torsional flows between two parallel disks, the apparent shear rate, ya. (not corrected for slip effects) is a linear function of the radius, r, and is given by t Q r... 

Another type of viscometer which finds occasional use is the disk-plate viscometer (Fig. 16.8). A disk of radius R rotates with an angular velocity of CO relative to a parallel plate. The disk and plate are separated by a distance d(d R with the test fluid in between. The torque M on either the disk or plate is measured. This is known as torsional (twisting) flow, and is another example of a viscometric flow. 

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