Question

In Poiseuilli's method of determination of the coefficient of viscosity, the physical quantity that requires greater accuracy in measurement is
A. Pressure difference
B. Volume of the liquid collected
C. Length of the capillary tube
D. Inner radius of the capillary tube

Answer 1

Hint: The Poiseuilli’s method of determining the coefficient of viscosity is analogous to finding the viscosity value offered during the flow of liquid in a similar way in which resistance is offered by the flow of electric current when the electric potential is applied across the ends of the resistor.

Formula used:
Hagen-Poiseuille equation is,
\[V = \dfrac{{\pi p{r^4}}}{{8\eta l}}\]
where V is the rate of flow of fluid whose coefficient of viscosity \[\eta \], p is the pressure difference across the end of the tube with radius r and length l.

Complete step by step solution:
Hagen-Poiseuille equation gives the relation between the fluid resistance to the flow through the tube, the flow rate, the length of the flow and the pressure between the ends of the tube which is analogous to the flow of electric current in the resistance when electric potential is applied across the ends of the resistor as,
\[V = \dfrac{{\pi p{r^4}}}{{8\eta l}}\]

So, the coefficient of viscosity of the fluid flowing in the capillary of radius r and length is,
\[\eta = \dfrac{{\pi p{r^4}}}{{8lV}}\]
As the radius of the capillary is of degree 4, so the precision in the radius of the capillary is the major requirement while determining the coefficient of the viscosity of the fluid because the error in the measurement will get accumulated largely.

Therefore, the correct option is D.

Note: The viscometer is used to measure the coefficient of viscosity of the fluid. It is done using Poiseuille flow theorem as well as Stokes flow theorem. The accuracy is more influenced by the measuring method and instrument design than by the specific flow regime. As long as the presumptions underlying either estimate are still true, both might be very correct.