Question

Determination of viscosity:
A falling sphere test must be conducted on an unknown liquid. A table with some liquids' densities is given. This table must be used to identify the liquid.
Only one spherical metal ball is given. The mass and radius of the ball is known.
The density and viscosity of the liquid is unknown.

The time it takes for the ball to sink 60 cm is known.

How do I tackle this problem?

All the equations I came across has the density if the fluid AS WELL AS its viscosity in, so there are too many variables.

Some help please?

Answer 1

\[\large F_g=mg; \large F_{boyancy}=F_b=\large \frac{4\rho_{fluid}\pi r^3 g}{3}; \large F_{drag}=6\pi r \mu_{fluid} v \]
\[F_g=F_b+F_r\\\small \text{Which gives } \large \mu=\frac{g}{v}\left[ \frac{m}{6\pi r}-\frac{2\rho_{liquid}r^2}{9} \right]\small \text{, which is still a function of }\rho\]

Answer 2

fluid=liquid

Answer 3

This experiment relies on Stokes Law, and requires that the density of the liquid be known.

If the table provided listed both viscosity and density, we could just solve the problem with brute force, i.e. solving the equation for every combination to see which one fits. Since density is the only value given in the table, we don't have a case to check against. We could just solve the equation for every value in the table and see which value of viscosity made sense, but that's arbitrary.

Answer 4

I have attached the included table.
Thing is, some densities are so close to each other. And solving for each density feels like just guessing (which we could have done from the start).

Is there really no other way, or should I email the lecturer and tell him that there isn't enough information available?

Answer 5

I don't know of another way.

The wiki article on falling sphere viscometers includes the verbiage, "the density of the liquid is known."

http://en.wikipedia.org/wiki/Viscometer#Falling_sphere_viscometers

Answer 6

@eashmore, I got my hands on students' who had this subject last year's assignment. The made use of Reynold's numbers. I will message your the file.