# B Relationship between speed and density of a medium

1. Sep 12, 2016

### louthinator

So my question is, is there a relationship between the density of a medium you are traveling through and the maximum speed achieved for an object of constant mass and shape traveling with constant thrust in both mediums?

for example if i knew that an object traveled 8 times faster in 1 medium than it did in another could i work out the difference in density between the 2 mediums?

2. Sep 12, 2016

### Staff: Mentor

Hi louthinator.

Density would be a factor, but only if all other factors were equal. Or in other words: no.

Viscosity is the most relevant factor: how sticky the medium is. Imagine trying to stir a spoon through cold honey, and compare this to the much-reduced viscosity of warm honey: practically the same density, but vastly different viscosities. And what about whether the medium is solid, liquid, or gas? There are plenty of examples of a solid plastic that is less dense than some heavy liquids; or you could just imagine trying to push an arrow through a solid block of water ice, compared with penetrating the liquid form of water, and remember that the liquid form is actually more dense!

3. Sep 12, 2016

### louthinator

what about if it was between 2 different gasses one of which is more dense than the other?

4. Sep 12, 2016

### Staff: Mentor

What if one is moving, and the other is standing still? Or, better yet, what if they were both standing still? Would you expect this to tell you anything about the densities of the two gases that the objects are immersed within.

5. Sep 12, 2016

### louthinator

i mean im looking to see if theres some ratio here. 2 identical objects with the same ammount of force pushing them through 2 gasses of different density, if one object is found to be traveling say 1/2 the speed of the other one despite the fact that the force pushing them is the same could you then detemine how much more dense the second gas is as compared to the first one. not specific numbers but a comparison? like is the second gas 2x denser or 3x or 4x etc.

6. Sep 12, 2016

### Staff: Mentor

Perhaps we could rephrase your question as: if a ball falls under gravity, would it be seen to fall faster if the atmosphere were pure helium compared with it being mainly nitrogen? Let's keep the pressure fixed as it is.

Sorry, I don't know enough about gases to be able to say.

7. Sep 12, 2016

### louthinator

exactly, i would assume they would reach different maximum speeds considering one is having more particles constantly smashing into it and therefore reaching the equilibrium of a constant falling speed faster, however is there a comparison that can be made here? like is the equilibrium speed proportional to the density of the gas it has to fall through? and can this be extrapolated to the point where you can predict the density of a gas by measuring how fast that object falls through it?

8. Sep 12, 2016

### Staff: Mentor

The method you're suggesting is not going to be very accurate. Why not just calculate the density from the ideal gas law, knowing the pressure, the temperature, and the molecular weight?

9. Sep 12, 2016

### Khashishi

You could work it out using the drag equation (c.f. https://en.wikipedia.org/wiki/Drag_equation). But as Chet mentioned, it might not be that accurate, especially if you are using very different gases, since the drag coefficient does depend on the fluid viscosity and density, among other things. But, to zeroth order, you could perhaps treat it as constant. This will work better for fairly sparse, low viscosity fluids.