# Viscosity Troubles: Solving a Physics Dilemma

• Mystery_Man
In summary, the researcher is trying to determine the viscosity of a viscous fluid by changing the temperature and measuring the sphere's terminal velocity. They are trying to calculate the coefficient of viscosity by looking at the forces acting on the sphere and the viscosity is not consistent when varying the temperature.
Mystery_Man
Viscosity Woes :(

Hi,

I'm conducting a Physics Investigation where I'm changing the temperature of Motor Oil and seeing how the change in temperature affects viscosity of the oil. I am measuring the terminal velocity of the sphere in the oil (V). I'm Using Stokes' Law Equation: F=6piRNV. I've re-arranged this equation to: n = F/6piRV. I want to calculate the coefficient of viscosity directly, however I can't understand how to calculate the frictional force (F). Can anybody shed some light as to how I calculate this?

i have never had to work out a problem as such, but in general for drag force you have

F = -Cv or F = -Dv^2

where you use the first for very small speeds and the second for large speeds. C and D are constants that depend on the shape of the object and the viscosity of the material

Well, one way of doing this is the following:
If the sphere is falling through the oil at a uniform rate, then the OTHER forces acting upon the sphere must balance the force of friction.

Assuming hydrostatic pressure distribution (which, at the very least, ought to require that the dimensions of the falling sphere is a lot less than the fluid volume), we ,may calculate the buoyancy force $F_{b}=\rho_{fluid}V_{sphere}g$acting upon the sphere. In addition, you'll have gravity working $$F_{g}=\rho_{sphere}V_{sphere}g$$.

where the indiced V is the volume of the sphere, and the rho's the densities
Thus, the force of friction will need to balance these to forces, which
means that your viscosity should be calculable from:
$$\eta=\frac{\rho_{s}-\rho_{f})V_{s}g}{6\pi{r}V}=\frac{2}{9}\frac{(\rho_{s}-\rho_{f})r^{2}}{V}$$

Note that the assumption that we have hydrostatic pressure can only be held if the given equation gives CONSISTENT values for $\eta$ for a large variety of test spheres.

If we do not get consistent $\eta$-values, the most likely explanation is that we cannot neglect the velocity-induced changes in the pressure profile of the fluid.

Thus, if you do this experiment, you might find that using a falling sphere through a viscous fluid is not a particularly good way to determine the viscosity of the fluid..

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## 1. What is viscosity and why is it important in physics?

Viscosity is a measure of a fluid's resistance to flow. It is important in physics because it affects the behavior of fluids, such as how they move and interact with other objects.

## 2. What are some common causes of viscosity troubles?

Some common causes of viscosity troubles include changes in temperature, contamination, and the presence of impurities or air bubbles in the fluid.

## 3. How can viscosity troubles be solved?

Viscosity troubles can be solved by identifying the root cause and addressing it accordingly. For example, if the issue is due to changes in temperature, adjusting the temperature of the fluid can help. If it is due to contamination, filtering the fluid may be necessary.

## 4. What are some methods for measuring viscosity?

There are several methods for measuring viscosity, including using a viscometer, measuring flow rate through a capillary tube, and using a rotational viscometer. Each method has its own advantages and is suitable for different types of fluids.

## 5. Can the viscosity of a fluid be changed?

Yes, the viscosity of a fluid can be changed by altering the temperature, pressure, or composition of the fluid. It can also be changed by adding certain substances, such as polymers, to the fluid.

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