Answer to Question #215782 in Physics for Faithy

Question

In an experiment, the following readings were observed;

Volume of alcohol flowing per minute= 10^-5m^3

Density of alcohol = 800kg/m^3

Length of tube was 0.5m

Radius of tube is 0.05cm and the height of alcohol is 60cm. Calculate the coefficient of viscosity of alc ohol

Answer 1

According to Poiseouille equation, the volumetric flow rate of the fluid through long cylindrical pipe of constant cross section is $Q = \frac{\pi R^4}{8 \eta} \frac{\Delta p}{L}$, where $L$ is the length of the pipe, $R$ - radius of the pipe, $\eta$ - viscosity of the fluid and $\Delta p$ is the pressure drop. Here, the pressure drop is $\Delta p = \rho g L$, where $\rho$ is the density of the fluid.

Combining last two formulas, obtain:

$Q = \frac{\pi R^4}{8 \eta} \frac{\rho g L}{L} = \frac{\pi R^4}{8 \eta} \rho g$, from where the viscosity of the alcohol is $\eta = \frac{\pi R^4 \rho g}{8 Q} \approx 0.193 Pa \cdot s$.