44 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
h
Pointer
Retaining spring
Rotating outer
cylinder
Stationary inner
cylinder
ri
ro
Figure 3d. Partial section of concentric-cylinder viscometer
which is established with the outer rotating and the inner stationary is less disturbed by
centrifugal forces. The couple transmitted through thefluid to the suspended stationary
inner cylinder is resisted by a calibrated spring, the deflection of which allows calculation
of the torque,T, and hence the inner wall shearing stressRiis given by:
TDRiri 2 rih
This torqueToriginates from the outer cylinder which is driven at a uniform speed. On
the inner surface of the outer cylinder the shear stress isRoand:
TDRoro 2 roh
∴ RoD
T
2 r^2 oh
and: RiD
T
2 r^2 ih
For any intermediate radiusr, the local shear stress is:
RrD
T
2 r^2 h
DRo
(
r^2 o
r^2
)
DRi
(
r^2 i
r^2
)
In this example,riD 0 .015 m,r 2 D 0 .035 m,hD 0 .05 m andTD 0 .01 Nm which just
produces motion at the surface of the inner cylinder.
Using these equations:
RiDT/ 2 r^2 ihD[0. 01 / 2 ð 0. 0152 ð 0. 05 ]D 141 .5N/m^2