Question

Which formula is used to calculate the coefficient of viscosity of a given liquid in the laboratory (symbols have their usual meanings)?

• A. $\eta =\frac{9}{2}(\rho -\sigma )g\frac{r^2}{v}$
• B. $\frac{2}{9}(\rho -\sigma )g\frac{r^2}{v}$
• C. $\frac{2}{9}(\rho -\sigma )g\frac{r^2}{vg}$
• D. $\frac{2}{9}(\rho -\sigma )g\frac{vg}{r^2}$

Answer 1

The correct option is B $\frac{2}{9}(\rho -\sigma )g\frac{r^2}{v}$

To calculate the viscosity of a fluid we use the Stokes method.

Let's say the body resembles a perfect sphere that is travelling in the fluid at a constant velocity that is at a terminal velocity.

The weight of the sphere is, $W=\rho 1.33\pi r^{3}g$

The force of buoyancy is, $B=\sigma 1.33\pi r^{3}g$

Since, this has to be equal to the drag force experienced by the body as it is travelling at a constant velocity.

$D=6\pi \eta rV$

D = W - B

substituting the values,

$\eta =\frac{2(\rho -\sigma )g{r}^2}{9v}$