# How viscosity affects motion?

1. Sep 22, 2009

### oxnume

How does the viscosity of a fluid in a circular can affect the way the can rolls?
For example, 2 cans of similar size, volume, and mass are rolled down a ramp with the same slope. The can with a viscous liquid will take more force to begin rolling than a can with a less viscous liquid, but once it gets moving the thicker liquid will roll a longer distance. As a result, on a shallow ramp, the more viscous can will hardly begin to roll and will go a lot shorter than the other one, but on a high sloped ramp, the more viscous can will begin to roll very fast and go a lot further than the less viscous one.
I have tried looking up viscosity but couldn't really find much related.

What are some theories or concepts that can help explain why this occurs?

2. Sep 22, 2009

### mdnazmulh

High viscosity fluid can flow less than a fluid of low viscosity. High viscosity indicates high internal resistive instinct of the fluid to flow. So when the can of fluid having high viscosity starts to roll, the internal layers of fluid experiences greater fluid friction among its layers and provide greater resistivity against rolling. So this can needs more force to roll than the other can.
And for an analogy of it think of inertial mass of matter. The more mass it has, the more force it needs to accelerate. High viscosity fluids are thicker than the low viscosity fluids. May be this thickness(or, density) has something to do with its motion.
Another interesting thing hot water runs faster than cold water due to the difference of viscosity.

3. Sep 23, 2009

### jambaugh

Let me add some points. For a can to roll it needs to have forward momentum and also angular momentum. The energy you put into the can when you start it rolling will eventually be distributed among these two components.

Also recall that the energy you put in is the work = force times distance. Easy to push means not much energy but typically also means less energy to keep it rolling as well.
Now with a can full of fluid when you push it initially only the can turns and the fluid just slides along. Because during the push you don't have to roll the fluid, only get it sliding, you don't have to push as hard and so you don't inject as much energy as you would if say the fluid was frozen (infinite viscosity).

But as the can rolls, unless you have a superfluid (zero viscosity) the friction due to the viscosity will cause the fluid to turn until eventually it is also rolling with the can. This takes some of the forward sliding energy and moves it to turning fluid energy. The forward motion slows as the rotation of the fluid builds.

Now if you hit the can sharply I don't think you'd see much difference between low and high (but finite) viscosity. But since you push steadily for a short while the fluid already starts turning while you're still pushing it (and so by equal and opposite reaction you need more force to push) thus you are injecting more energy (doing more work) during a push at the same speed and distance.

Since the more viscous fluid is already rotating somewhat at the end of the initial pushing period it takes less to get the fluid rolling along with the can. It slows less after you're done pushing it.

Again the ultimate case is if the can is solid and so it is rolling already as you push and doesn't slow down at all.

There is a parallel to this with pool shots. (I just got back from shooting pool in town.) Since you're striking the cue ball instead of steadily pushing, it will start out sliding (assuming you hit it in the middle) and friction between ball and table will transfer some of the sliding motion into rolling motion. It will slow down.

You can hit it higher than middle (top English) which will put more energy into the roll to the point where it actually rolls too fast for its motion. It will actually speed up as the over-spinning transfers energy to forward motion. Or you can hit it low putting back spin on it so it slows down more dramatically.

Add to this the case where the cue ball hits an object ball and so loosing all forward motion but not its rotation (English). After impact the rotation kicks in causing the cue ball to ether follow or draw back depending on whether you hit it above or below center.

You can think of the billiard example as the fluid in a can but without the can and with viscosity replaced with table friction.

4. Sep 23, 2009

To make it a fair comparison the masses of the two different liquids(plus cans) must be the same and of course the other variables must be controlled and I don't think that all of the conclusions you made above are correct.What is the difference between a shallow ramp and a high sloped ramp?If the cans were solid then the main energy change occuring as they roll down the slope is that GPE is changed into translational and rotational KE.With liquid filled cans the analysis becomes much more complicated due to the liquid slurping around and having KE(plus there will be internal changes of GPE if the cans are not completely filled)The more energy picked up by the liquid the slower the can will go.Consider this question:What sort of liquid moves around more easily?
There are some easy experiments you can try.
1.Try spinning an uncooked egg and a hard boiled egg.
2.Viscosity can vary with temperature so try rolling identical drink filled cans at different temperatures.Just for the fun of it you may want to freeze one of your cans but remember that ice expands and it can break your can and change the shape of it.

Last edited: Sep 23, 2009
5. Sep 24, 2009

### oxnume

@mdnazmulh
I tried searching fluid friction on wikipedia but theres only a 1 line description of it on the friction page. Also, isn't resistivity for electricity and stuff?

@jambaugh
So even if I'm not pushing it and gravity is the only thing doing the work, its still the same thing right? I understand what you're saying, but I think your trying to dumb it down for me :P What are the "proper physics names" of some of the things you are saying? I want to find out more precisely what some of them mean.

The 2 different cans(+liquids) are roughly the same mass, any difference is quite negligible. We were just told what to expect in the situation and during the lab, which we designed the experiment to, we played around with the slope and got the expected result. The "steep" ramp that allowed the more viscous liquid to come in front was about 7 degrees, while the shallow one was about half that.

6. Sep 24, 2009

### oxnume

From my shallow understanding of what happens:
With the less viscous liquid (consume soup), it is constantly able to "flow" with the can with the air bubble on top. This is why no matter what kind of slope it is run on, its acceleration is kind of the same (not the magnitude, just what it appears as).

With the more viscous liquid (cream soup), the cream tries its best to also stay on the bottom with the air on top but it takes a long time for it to "flow" with the motion of the can. This is why on the lower slope, it bares moves because the cream is trying to stay on the bottom as it turns. But on the higher slope, it no longer has a chance to do that and instead forms a kind of centrifuge where the air is in the middle and the soup is evenly distributed around the outer layer.

The reason why one travels further than the other is because it experiences a better acceleration on the decent. After the length of the slope, it simply travels on flat ground until rest and that part shouldn't be different for any of them.

Now I don't really know how this can affect the Fnet on the can...

7. Sep 25, 2009

### jambaugh

I should have read more carefully, if you are using a ramp and gravity then eventually (neglecting rolling friction) all the cans should end up rolling at the same speed. In my exposition I was assuming more work done in the more viscous cases by assuming an initial push at the same speed. But that is just a quantitative difference in comparing different cans. The qualitative part is the same.

Here is an explanation of viscosity: Consider first the idea of a substance being "fluid" rather than "rigid" and also elastic vs inelastic. There are two concepts stress and strain. Stresses are collections of forces on an object and strains are a collection of movements (deformations) of an object. Stresses may be positive vs negative. For example when I speak of compression this includes negative compression = expansion.

There are four types of stress tensile stress which is just a force trying to enlongate an object, compressive stress which is a force trying to change the size (but not shape) of an object, bending stress which tries to bend the object and shear stress which is a force trying to skew the shape of an object. Imagine a deck of cards stacked vertically so you see a rectangle looking from the side. Apply a shear and the stack will be skewed so you see a parallelogram from the side:

_____ ---------->_____
_____ -------->_____
_____ ------>_____
_____ ---->_____

Now I'm going to ignore bending stress for various reasons it is less fundamental than the other three.

Now along with each type of stress is a corresponding type of strain (deformation of shape).

Now in addition to these forces you can apply a uniform linear force (like gravity) or a torque which is a collection of forces trying to rotate the object.

Lets start with a perfectly rigid solid. Think of a cube of glass.
We can move it around fine with a force or a torque but try to compress it (decrease the volume) and you can't, it is incompressible (actually it will compress slightly but too small to see normally). Apply a tensile stress and it won't stretch. Apply a shear stress and it won't shear. Increase stresses and eventually it will break.

Now consider a block of foam rubber. This is an elastic body which is defined by the property that strain is proportional to stress. Compress the block and it will get smaller in proportion to the pressure. But remove the pressure and it will spring back. Similarly with tensile and shear stresses.

Now consider a block of wadded up aluminum foil. You can apply any of the strains and it will deform and not spring back. Basically this is the definition of a fluid, it deforms inelastically until the stress is zero. But a wad of aluminum foil is not a fluid you say? Well it isn't a perfect fluid. It is elastic under small stresses but fluid when the stress exceeds some point. (A particular property of metals). But what you can visualize with the wad of foil you can now consider with say gas or liquid. Note ideal gases are elastic with respect to compression but otherwise act as fluids. Liquids are incompressible but otherwise fluid.

OK! Now viscosity is usually defined as resistance to shear (or more generally to any stress). But in a way it is really the tendency of shear stresses to propagate through the fluid. Consider again the deck of cards and assume the bottom card is glued to the table. With your finger slide the top card laterally. If there is no friction between the cards then the top card will slide against the next and you get:

---->_____
_____
_____
_____

This is "zero viscosity". Note also it will take very little force to move the card. But if there is some friction between each card when you push the top card the deck will shear and this is viscosity. In reality the deck of cards will not shear linearly but instead you get a curved stack (there is some bending):

--------->_____
--->_____
->_____
_____

As the viscosity goes up the shearing will be straighter. But this is just a matter of scale. Increase the viscosity but also stack the cards higher and you'll tend to get the same shape only on a larger scale. Now replace the cards with a fluid (except top and bottom which you consider as infinite surfaces) and you should be able to visualize the viscosity of the fluid in terms of the rate of motion of fluid a given distance from the top surface relative to its motion or equivalently the force transferred to it.

So that's viscosity. In the can experiments gravity tries to pull the can and its contents straight down. The ramp converts some of this force to lateral motion. The surface friction applies a torque on the can which makes it roll. If the surface friction isn't high enough or the ramp too steep the can will slide down but will get some rotation from the sliding friction. However if the fluid inside has no viscosity this rotation of the can will not be transferred to the fluid. The moment of inertia of just the can without counting the fluid is much smaller than the can plus fluid rotating together. This is like applying a linear force to a small mass. It will accelerate more quickly.

With small viscosity the rotation of the can applies shear to the fluid near it which applies shear to fluid closer to the center so the outer fluid begins rotating more than the inner but eventually all the fluid is rotating together and viscosity no longer matters.

In terms of energy you start with the potential energy h*g due to gravity where h is the height of the ramp. This is converted to kinetic energy (and a little heat due to viscous friction) in the form of linear KE 1/2 m V^2 and rotational KE 1/2 I omega^2 (I = moment of inertia for the can + fluid, omega is angular velocity in radians per time unit). I think the viscous losses will be relatively small so practically all the energy is converted to motion.

Assuming the can weighs very little relative to the fluid or assuming all the different fluids you use weigh the same then once the fluid is turning with the can all cases will be rolling at about the same speed. To see how the motion manifests between releasing the can at the top of the ramp and this final rolling motion you have to look at how long it takes for the viscosity to get the fluid turning and how much of this happens on the ramp vs later.