1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Pressure in Tornadoes

  1. Mar 25, 2016 #1
    1. The problem statement, all variables and given/known data
    A tornado rotates with constant angular velocity ##\omega## (i.e. like a solid object would rotate) and has
    a uniform temperature T. Find an expression for the outward pressure distribution in terms of the central pressure ##p_0##. Use this to calculate ##p_0## given that T = 300 K and that at 0.1 km from the centre the atmospheric pressure p = 100 kPa and wind speed V = 100 m s-1.


    2. The attempt at a solution
    Pressure gradient force =## -\frac{1}{\rho} \nabla p##
    PV=NRT
     
  2. jcsd
  3. Mar 25, 2016 #2

    Nathanael

    User Avatar
    Homework Helper

    In my incomplete understanding, an 'equation of state' (such as PV=NRT) describes the properties of a system near equilibrium. I don't believe it can be (at least not naively) applied to more dynamic systems (such as a tornado). If anyone has more to say on this, please do; I like to learn as well.

    Perhaps you mean "acceleration due to pressure gradient force" (check dimensions).
    Anyway you want to model the tornado as having uniform angular velocity, so can you figure what the acceleration field (i.e. the left side of this quoted equation) is? (Use symmetry when choosing coordinates.)
     
  4. Mar 31, 2016 #3
    Pressure gradient (PG) = rate of change of pressure with distance which is from low to high pressure.PGF is from high to low pressure. But still don't see how you get the pressure distribution?
     
  5. Mar 31, 2016 #4
    If a body is rotating with radial acceleration ##\omega^2r##, it is analogous to a gravitational force acting in the negative radial direction. So, from the hydrostatic equation,

    $$\frac{dp}{dr}=\rho (\omega ^2r)$$

    Of course the air density ##\rho## is a function of the pressure, so you need to take that into consideration using the ideal gas law. What is the equation for the density of an ideal gas in terms of the pressure, molecular weight, and temperature?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted