# Falling sphere method to find fluid's viscosity

• omicgavp
In summary: You are performing an experiment to determine the viscosity of water using the falling sphere method. I understand that the ratio of the radius of the sphere to the radius of the container has to be within a certain range in order to avoid a false high viscosity value. And a correction factor is needed in the analysis so that the effects of the container walls and ends will be accounted [ref. G.E. Leblanc,et.al., "The Measurement, Instrumentation and Sensors Handbook", Chapter 30:Viscosity Measurement].You would like to vary the mass and radius of the sphere and calculate the average viscosity. So you would be needing different spheres. Is it ok to have

#### omicgavp

We are performing an experiment to determine the viscosity of water using the falling sphere method. I understand that the ratio of the radius of the sphere to the radius of the container has to be within a certain range in order to avoid a false high viscosity value. And a correction factor is needed in the analysis so that the effects of the container walls and ends will be accounted [ref. G.E. Leblanc,et.al., "The Measurement, Instrumentation and Sensors Handbook", Chapter 30:Viscosity Measurement].
We would like to vary the mass and radius of the sphere and calculate the average viscosity. So we would be needing different spheres. Is it ok to have a modelling toy clay as a sphere? We found out that the mass of the clay, which was molded to a sphere, does not change even after it is put into water. Is it also ok to have water as the medium for the sphere? It is observed that the sphere falls through the water quickly. In our experiment, we used a container similar to a beaker but a few inches taller. We also used a camera and the LabVIEW program to record the motion of the sphere. The sphere experiences g (this can be seen by a slight parabolic curve from the y vs. t plot) at a very short time and then abruptly attains terminal velocity (this can be seen from the slope of the the positive straight line from y vs. t also).
I would like to reiterate my questions:
-Is it ok to have a modelling toy clay as a sphere?
-Is it also ok to have water as the medium for the sphere?

The dynamic viscosity we measured has a discrepancy of about 10^-3 from the accepted value. Do we need to increase our number of measurements to obtain an accurate value? Your thoughts about this would be greatly appreciated.

Repeating the experiment without changing anything will reduce the random errors (for example inaccurate velocity measurements, the ball is not perfectly spherical, etc) but it will not affect any systematic errors, for example if the conditions in the experiment don't match the assumptions in the equations you used to calculate the viscosity.

The most important assumption is that the velocity is small enough. Check what your textbook says about Reynolds number, how to calculate it, and what range it should be to make the experiment valid.

Most likely, your clay sphere is too big and falls too fast. To measure the viscosity of water accurately this way, you need a small light sphere, for example a small plastic bead.

@AlephZero:
What textbook can you recommend because the reference stated doesn't mention about Reynolds number?

Almost any text on fluid dynamics should cover this. I'm surprised your measurement handbook doesn't state the required conditions for the method to be accurate, even if it didn't explain the theory behind them.

Try this:
http://www.mech.northwestern.edu/ME224/ME224_Lab_6.pdf

Here is a different way to correct the results for fairly small Reynolds numbers:
http://www-users.aston.ac.uk/~norriswt/WTNPapers/Sphere%20Viscous%20Fluid.pdf [Broken]

Last edited by a moderator:
We used glycerin instead of water so that our reynolds number would be much less than unity. Then corrected the results using the empirical formulas from the handbook; still conforming with the range 0.16</=(radius of sphere/radius of container)</=0.32 [Leblanc, et. al.]. The dynamic viscosity that we obtained is equal to 1.603kg/m.s @ 24 deg. C. It's near from the accepted value. We also obtained the value of the density of glycerin to be 1602kg/m^3 still @ 24 deg. C. Our density is too far from the accepted value of 1261kg/m^3 @ 25 deg. C [ref. J. Cimbala, Y. Cengel, "Essentials of Fluid Mechanics", Appendix 1]. What could be wrong?

## What is the falling sphere method to find fluid's viscosity?

The falling sphere method is a technique used in fluid mechanics to measure the viscosity of a fluid. It involves dropping a small spherical object into the fluid and measuring its terminal velocity as it falls through the fluid. The terminal velocity is then used to calculate the fluid's viscosity using the Stokes' law equation.

## How does the falling sphere method work?

The falling sphere method works by measuring the terminal velocity of a small spherical object as it falls through the fluid. The terminal velocity is the maximum velocity that the object reaches as the drag force from the fluid balances out the object's weight. This velocity is directly proportional to the viscosity of the fluid, allowing for the calculation of the fluid's viscosity using the Stokes' law equation.

## What are the advantages of using the falling sphere method?

The falling sphere method has several advantages. It is a relatively simple and inexpensive technique that can be used to measure the viscosity of a wide range of fluids. It also does not require any specialized equipment and can be performed in a laboratory setting. Additionally, the results obtained from this method are accurate and reliable when performed correctly.

## What are the limitations of the falling sphere method?

While the falling sphere method is a useful technique, it does have some limitations. It is most accurate when used to measure the viscosity of Newtonian fluids, meaning that the viscosity remains constant regardless of the applied force. It may not be as accurate for non-Newtonian fluids, as their viscosity can change with the applied force. Additionally, the size and shape of the spherical object used can also affect the accuracy of the results.

## Are there any safety considerations when using the falling sphere method?

As with any laboratory experiment, safety should always be a top priority. When performing the falling sphere method, it is important to handle the fluids and objects with care to avoid spills or accidents. Additionally, follow all safety protocols and guidelines set by your institution or organization for handling and disposing of any hazardous materials used in the experiment.