A viscometer is a device for measuring viscosity. A rotating cylinder viscometer is shown in the

figure below $($not to scale$).$ An inner cylinder $(r_i=2\mathrm{.}4in)$ rotates at a constant speed of $50$ rpm

within a hollow, stationary, outer cylinder $(r_o=2\mathrm{.}52in).$ The inner cylinder is $10\mathrm{.}8$ in long. The

space between the concentric cylinders is filled with a liquid of unknown viscosity. The torque

provided by the motor that turns the inner cylinder is measured to be $0\mathrm{.}65lbf-ft.$ Ignoring the shear

forces on the bottom and top of the cylinder, determine the absolute viscosity of the liquid $($lbf$-$

$($:$\frac{s}{f}{t}^2\}.$

Hint: When the inner cylinder rotates at a

constant velocity, the torque from the

motor just balances the opposing torque

from the fluid shear force on the inner

cylinder. The velocity profile in the liquid

between the cylinders is linear $(0$ at the

outer cylinder surface; same speed as the

inner cylinder at its surface$).$ This is

called Couette flow $($see p$.46$ in your

textbook$).$ Use what you know about the

relationship between shear stress,

velocity gradient, and viscosity to find the

viscosity.

Given:

$r_i=2\mathrm{.}4in$

$r_0=2\mathrm{.}52in$

$=0\mathrm{.}651bf-f_t$

Solution: Find Absolute Viscosity of liquid $lbf-\frac{5}{P}{r}^2$