Parallel-disc viscometer ($\tau =\pi \eta \omega a^4/(2d)$)

In the thin-gap, laminar approximation, a rotating disc of radius $a$ separated by $d$ from a stationary disc shears a Newtonian fluid. The resisting torque is $\pi \eta \omega a^4/(2d)$, neglecting edge effects and secondary flows. This gives a way of inferring dynamic viscosity from a measured torque.