# Viscosity and temperature, density is changing...

#### MPZ

1. Homework Statement
Hi, I am doing physics lab on finding coefficient viscosity of fluids and how it changes by temperature by dropping a marble into fluids, finding terminal velocity, then using stoke's law to find viscosity. (using density of fluid, sphere, sphere diameter etc). The equation is found here https://en.wikipedia.org/wiki/Stokes'_law under Terminal Velocity.... I have just realized something and encountered a problem. For this experiment to work, the fluid at all temperatures should have the same density, however changing the temperature will change the density!!! How can I keep the density constant? Does what I am saying make sense?

2. Homework Equations
The equation of stoke's law is found here https://en.wikipedia.org/wiki/Stokes'_law under Terminal Velocity. It is derived when the viscous drag force plus the buoyant force equal the weight of the ball at terminal speed

3. The Attempt at a Solution
Trying to find a way to keep density constant but no success yet!

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#### mjc123

You can't keep density constant if the temperature is changing. For most common fluids, there should be tables of density vs. temperature that you could find. Failing that, you can just assume the density is constant - there will be some inaccuracy in your result, but it should not be huge. Generally viscosity varies with temperature much more than density. For example, between 10 and 80°C, the density of water decreases by about 3%, but its viscosity decreases by about 70%. (http://www.viscopedia.com/viscosity-tables/substances/water/) The density of the marble will also change, but much less than that of the fluid.

#### MPZ

You can't keep density constant if the temperature is changing. For most common fluids, there should be tables of density vs. temperature that you could find. Failing that, you can just assume the density is constant - there will be some inaccuracy in your result, but it should not be huge. Generally viscosity varies with temperature much more than density. For example, between 10 and 80°C, the density of water decreases by about 3%, but its viscosity decreases by about 70%. (http://www.viscopedia.com/viscosity-tables/substances/water/) The density of the marble will also change, but much less than that of the fluid.
will this be ok for my lab. do you think I should calculate the density for every temperature of the fluid and substitute it into stoke's equation? thanks

#### mjc123

If you have reliable density-temperature data, yes.

#### MPZ

If you have reliable density-temperature data, yes.
what if i calculate the density myself?

#### mjc123

Again, if you have a reliable density vs. temperature equation. How were you going to calculate the density?

#### MPZ

Again, if you have a reliable density vs. temperature equation. How were you going to calculate the density?
finding mass of fluid and using density=mass/volume for every temperature
Do you have an idea of a procedure that will show the relation between viscosity and temperature??

#### mjc123

Ah, you're going to measure it. (To be really accurate, you'd have to account for the thermal expansion of your volume-measuring container, but this is likely to be small compared to that of the fluid.)
Do you have an idea of a procedure that will show the relation between viscosity and temperature??
Measure it. Isn't that what you were going to do?

#### MPZ

Ah, you're going to measure it. (To be really accurate, you'd have to account for the thermal expansion of your volume-measuring container, but this is likely to be small compared to that of the fluid.)

Measure it. Isn't that what you were going to do?
Will it be ok to assume that the density of the marble and fluid is constant since the decrease will be 2 to 3% and use the value of the density at room temperature? Or will that make my lab report stupid?
also, will this assumption still make me observe the relation between viscosity and temperature?

#### mjc123

I think that's OK for a lab, unless your lab instructions specify that higher accuracy is required. You should state the assumption you have made and the justification for it. Then your lab report will certainly not be stupid. (You might get the supplementary question: if you know the density varies by 3%, that implies you know how the density varies with temperature - as indeed it is tabulated for water - so why not use these accurate values?) You should also be aware that if your fluid is not water, the density change may be greater - the coefficients of thermal expansion are typically higher for organic liquids than water - but still much less than the change in viscosity.

#### MPZ

I think that's OK for a lab, unless your lab instructions specify that higher accuracy is required. You should state the assumption you have made and the justification for it. Then your lab report will certainly not be stupid. (You might get the supplementary question: if you know the density varies by 3%, that implies you know how the density varies with temperature - as indeed it is tabulated for water - so why not use these accurate values?) You should also be aware that if your fluid is not water, the density change may be greater - the coefficients of thermal expansion are typically higher for organic liquids than water - but still much less than the change in viscosity.
The fluid I will use is Honey, here is its table (http://www.viscopedia.com/viscosity-tables/substances/flower-honey-blended/) I don't want to calculate the density or use the accurate values because i need to have one independent/dependent variable while others should be controlled.
Independent: Temperature (40°C, 50°C, 60°C, 70°C, 80°C).
Dependent: Viscosity
BTW, I am a high school person who is doing this for the IB internal assessment

#### MPZ

I think that's OK for a lab, unless your lab instructions specify that higher accuracy is required. You should state the assumption you have made and the justification for it. Then your lab report will certainly not be stupid. (You might get the supplementary question: if you know the density varies by 3%, that implies you know how the density varies with temperature - as indeed it is tabulated for water - so why not use these accurate values?) You should also be aware that if your fluid is not water, the density change may be greater - the coefficients of thermal expansion are typically higher for organic liquids than water - but still much less than the change in viscosity.
does what I said make any sense?

#### mjc123

This should be OK because the change in viscosity is very large over a relatively small temperature range, over which the change in density is only about 1%. I think the uncertainty in your viscosity measurements is likely to swamp any effect due to change in density.
I don't want to calculate the density or use the accurate values because i need to have one independent/dependent variable while others should be controlled.
I'm not sure about this as a general principle, though. The density is controlled in the sense that it is determined by the temperature: if you set the temperature, you set the density. It cannot be "controlled" in the sense of being kept constant as you change the temperature, because that is physically impossible. As you are not measuring viscosity directly, but deriving it from the measured terminal velocity using a formula involving density, you will always get more accurate results using true density values than by assuming a constant value.

#### MPZ

This should be OK because the change in viscosity is very large over a relatively small temperature range, over which the change in density is only about 1%. I think the uncertainty in your viscosity measurements is likely to swamp any effect due to change in density.

I'm not sure about this as a general principle, though. The density is controlled in the sense that it is determined by the temperature: if you set the temperature, you set the density. It cannot be "controlled" in the sense of being kept constant as you change the temperature, because that is physically impossible. As you are not measuring viscosity directly, but deriving it from the measured terminal velocity using a formula involving density, you will always get more accurate results using true density values than by assuming a constant value.
thank you so much for answering my concerns. I have to ask my supervisor for this, I think I will end up using a constant value but then write about it in the "Sources of error" section and how I should have used the true density values in the "Improvements" section. Thank you again legend! If I have more concerns can I just ask you? ;) <3

#### mjc123

You should also bear in mind that "honey" is not a pure substance; there will be inevitable variations in composition between batches, even of the same type of honey, so you should not be surprised if your density and viscosity values are different from those tabulated. In a case like this it would be better to make one accurate measurement of density and use it throughout, than to rely on tabulated values.

#### MPZ

You should also bear in mind that "honey" is not a pure substance; there will be inevitable variations in composition between batches, even of the same type of honey, so you should not be surprised if your density and viscosity values are different from those tabulated. In a case like this it would be better to make one accurate measurement of density and use it throughout, than to rely on tabulated values.
That is what I thought too. I will use the same type of honey/from same company. I will measure the density at room temperature and use it throughout, right?

#### DrClaude

Mentor
That is what I thought too. I will use the same type of honey/from same company. I will measure the density at room temperature and use it throughout, right?
Not only is honey not a pure substance, it is a natural substance with enormous variation. You should only use a single jar or, if that is not possible, a set of jars with the same batch number.

#### MPZ

Not only is honey not a pure substance, it is a natural substance with enormous variation. You should only use a single jar or, if that is not possible, a set of jars with the same batch number.
Ok, I will try to do that, thanks

#### MPZ

My supervisor said that I can assume it is constant but I should explain that well. What do you suggest I do?

#### mjc123

At some point you're going to have to use your initiative. We've had quite a thorough discussion about this; what do you think you can put together from that?
Here's an idea: you have some viscosity and density data for honey (not necessarily accurate for your sample, but you can use it to illustrate the principle). Using the Stokes equation, work out the expected terminal velocity as a function of temperature. Do this (i) using the density vs. temperature data given, (ii) assuming the density is constant at the 20°C value. Plot these two curves on the same graph. Do you think the constant-density assumption gives you a good idea of how the terminal velocity varies with temperature?

#### MPZ

At some point you're going to have to use your initiative. We've had quite a thorough discussion about this; what do you think you can put together from that?
Here's an idea: you have some viscosity and density data for honey (not necessarily accurate for your sample, but you can use it to illustrate the principle). Using the Stokes equation, work out the expected terminal velocity as a function of temperature. Do this (i) using the density vs. temperature data given, (ii) assuming the density is constant at the 20°C value. Plot these two curves on the same graph. Do you think the constant-density assumption gives you a good idea of how the terminal velocity varies with temperature?
I will do this idea now. I will inform you of the results.

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#### MPZ

At some point you're going to have to use your initiative. We've had quite a thorough discussion about this; what do you think you can put together from that?
Here's an idea: you have some viscosity and density data for honey (not necessarily accurate for your sample, but you can use it to illustrate the principle). Using the Stokes equation, work out the expected terminal velocity as a function of temperature. Do this (i) using the density vs. temperature data given, (ii) assuming the density is constant at the 20°C value. Plot these two curves on the same graph. Do you think the constant-density assumption gives you a good idea of how the terminal velocity varies with temperature?
I just did what you suggested. I found the terminal speed for every temperature value. I assumed that the density is constant with the value of 1.41 g/cm^3. I assumed that the radius of the marble is 1.5cm and that it is made from steel with density 8.05g/cm^3. and g=980cm/s^2. After that I found the coeff of viscosity of every temp assuming that the density is constant, I plotted temp on x-axis vs coeff on y-axis to obtain this graph (https://gyazo.com/628c7017905b6b18217af312bb7175b1). Is this a good inversely proportional graph. I think it is, so it worked right?

#### mjc123

What are the data you have plotted? I suggested plotting two curves - terminal velocity calculated using real density values, and terminal velocity calculated assuming constant density - and comparing them. You haven't done that.

"Viscosity and temperature, density is changing..."

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