1. Jun 12, 2013

### vmedica

1. The problem statement, all variables and given/known data
I am currently stuck on parts 2b,c and d of this problem.

2. Relevant equations

3. The attempt at a solution
For part 2b, I use the the equation from part 2a and just integrate. I know that as we exit the tornado, the pressure should be atmospheric pressure so I can solve for the constant. but the problem that I have is the ln(r) term. I can choose a sufficiently small r such that the pressure is negative which does not make sense.

2c) I'm assuming it related to part 2b) so I have left that out for now.

For part 2d) I think that the solution would involve something about the dew point in air but when I type for information regarding the dew point into Google, I just get complicated formulae. Could someone perhaps suggest a website where I can get more information about this.

Any help would be appreciated.

2. Jun 12, 2013

### haruspex

Since v = v(r), I don't understand how you can "just integrate" that equation. Seems to me you need another equation from somewhere. E.g. if we assume irrotational flow except at the centre, v ~ 1/r; or if we treat it as rigid body, v ~ r. Either way, the DE gives you a formula for P=P(r), and doesn't seem to contradict any given info. Maybe I'm missing something.

3. Jun 13, 2013

### vmedica

For my working, P=∫ρairv2/r dr and then I got a ln(r) term which I can now see is wrong. For a later part (3b inside the tornado) they assume that it is a rigid body so so v~r. Would it be sensible to assume irrotational flow and what other things exhibit this kind of flow? Also, would the method then become:

v=k/r
dP=ρairk2/r3dr
Now I integrate and use the contidion that when r=rc, v=vc to solve for k. Then I use that as P=Patm as r→∞ to eliminate the constant of integration.

4. Jun 13, 2013

### haruspex

The standard treatment of a vortex is that it is irrotational flow, except in a core region, where it is more like rigid body. See http://en.wikipedia.org/wiki/Vortex. I was not at all sure which you were expected to use, or maybe some fancier relationship that encompasses both.
Looks right.

5. Jun 18, 2013

### vmedica

Thanks for your help. I have been researching the tornado and wikipedia says the water condense due to adiabatic cooling. I know that means P1-γTγ=constant and they also give γ suggesting this is perhaps the correct approach to part d). I understand that with the equation for pressure, i need to equate this to the pressure at which water condenses but how can I do this?