CHEMICAL ENGINEERING

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