# Density of dry vs. humid air

1. Aug 31, 2004

### bobbykilkenny

How do I explain to my Engineer friends that a ball will actually travel further in humid conditions b/c humid air has less density than drier air? Please help us come to a conclusion. Thanks

2. Aug 31, 2004

### arildno

Why do you believe this?
Because a ball in less dense air experience less air resistance?
Note that a ball in denser air will experience a stronger buouyancy force, and hence "float" for a longer time.

Anyways, these concerns are really about measuring unmeasurable negligibilities..

3. Aug 31, 2004

### bobbykilkenny

My assumption is an object will travel further with less resistance. I'm not so sure about your bouyancy theory though. Everyone knows baseballs fly further in the less dense air of high elevation ball parks. I am more concerned with the density (and related resistance) of dry vs. humid air

4. Aug 31, 2004

### arildno

You're probably right; but the important issue is whether the density difference is large enough to matter.
I don't think so, but then I don't know the usual, relevant density values.
possibly someone else knows, or have a reference table nearby

5. Aug 31, 2004

### Cyrus

Your logic seems to make sense to me. Humid air weighs less than dry air becuase water vapor is less dense. The thing that will cause your ball to slow down the most soonest will be air resistance. Which is primarily a function of density.
$$f ~= Dv^2$$ where f is the fluid resistance v is the object velocity and D is a proportionality constant that depends on the shape and size of the body and the properties of the fluid. The shape and size of the ball never change, so the only variable there would be the properties of the fluid. If you decrease the density, then I would likely think that D should increase in value. Because the fluid resistance should decrease with decreasing density. But for your situation you are going so slow, and the effective change in density is so small, that you would not detect it. You would need a major change in density to have noticable effects on the hight the ball obtains. The bouyancy part of what he says would probably mean that on the way down, the ball would take longer for more dense air, than it would for less dense air, since the air cushions the ball as it falls down. Again, this would be a very small undetectable difference though.

Last edited: Aug 31, 2004
6. Sep 1, 2004

### BobG

USA Today explains this very well:
http://www.usatoday.com/weather/wdensity.htm

This is going to make a very small difference, though. Pressure and temperature will have a much greater impact.

Ideal would be hot, humid day, with a storm front moving in.

7. Sep 2, 2004

### bobbykilkenny

air density

How would you respond to someone who says:

That all of the computations that shows humid air is less than dry air rely on the ideal gas law, which fails to account for the polar nature of water molecules (and therefore the REAL nature of the gas). If an alternative equation that accounts for the non-ideal (REAL) effect of water vapor were applied (such as the Van der Waal) equation, it would become evident that, in fact, there was a higher molecular density associated with air having high humidity. It is not disputed that the mass/volume nature of dry air is greater than humid air – it is. The point Camp B is trying to make is that there is actually a higher moles/volume number associated with humid air compared to dry air. Therefore, because the ball has to flow through more molecules (even if they are lighter molecules) the frictional resistance is higher with wet air. RESULT: the ball will fly further when levels of humidity are low.

Again, all of the analysis we have been able to find apply the ideal gas law (which is incorrect). Additionally, all practical inspections into the frictional resistances rely on simple Newtonian Mechanics associated with dry air having a greater mass/volume density than wet air. Because one side believes the effect to be on a quantum level (i.e. frictional resistances with individual atoms because wet air has a greater moles/volume number), Newtonian Mechanics arguments are invalid.

8. Sep 2, 2004

### krab

Ideal gas law incorrect??

It seems to me that your difficulties are related to your approach. Laws in physics like the ideal gas law are not meant to be incorrect/correct. They have their range of validity. That gases of hugely different particle mass obey such a simple law to within a few percent, is for me astounding (or was when I learned it). Vanderwaals by turn made great progress in understanding gasses, by investigating deviations. But that does not mean that we now throw out the Ideal gas law! By that reasoning, Ohm's Law is incorrect (think of semiconductors), Hooke's law is incorrect (take any spring past its elastic limit), etc.

Anyway, back to gasses. Apply the vanderwaals law to pure water vapor, we find it deviates from the ideal law by 1%. Air deviates by 0.3%. The difference between these can be attributed to the polar nature of water. Mass-wise, (18 vs. 28 to 32) the deviation is 40%. So you can see the mass argument from usatoday is around 60 times more important than the polar-molecule effect.

Also, see here.

9. Sep 2, 2004

### Chronos

The density of a mixture of dry air molecules and water vapor molecules is:

$$D =\frac{P_d}{R_dT} + \frac{P_v}{R_vT}$$

D = density, kg/m3
Pd = pressure of dry air, Pascals
Pv = pressure of water vapor, Pascals
Rd = gas constant for dry air, J/(kg*degK) = 287.05
Rv = gas constant for water vapor, J/(kg*degK) = 461.495
T = temperature, degK = deg C + 273.15

As you can see, the largest value for D will result when Pv is zero.

10. Sep 7, 2004

### bobbykilkenny

I'd like to thank all who responded, I found a lot of the same info you have posted in doing my own research. I am dealing with some very stubborn GA Tech grads who still refuse to admit a marketing guy from a rival school just might be right. So i have dropped the discussion for now, but I am still looking for info from a GA Tech source to help open their eyes. Thanks again.