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!

Rotating cone filled with water

  1. Dec 6, 2008 #1
    I have a cone filled with liqid with radius R and height H rotating with \omega. Where do we have to drill a hole that the water would spray to the maximum distance from the cone?

    I used the Bernoulli equation obtainig
    p_0+0.5 \rho {v_1}^2=p_0+0.5 \rho v^2
    v is the speed at the hole, getting

    v^2=2g(H-h-h^2-r^2\frac{\omega^2}{2g})=2g(H-h-h^2\frac{(tg{\alpha})^2}\omega^2}{2g}),
    where tg{\alpha}=R/H.
    I taught using Lagrange multiplicator, where the constraint is the water falling on the floor prom the upward cone:

    \psi=v sin{\alpha} t+gt^2/2-h=0.

    Further more:
    F=v_x t+\lambda(v sin{\alpha} t+gt^2/2-h)
    =v cos{\alpha}+\lambda(v sin{\alpha} t+gt^2/2-h)
    Solution should be obtained by
    \frac{\partial F}{partial t} and

    \frac{\partial F}{partial v}, v=v(h),
    but i can't solve it.
    Did I make the concept wrong? Any ideas would be helpfull.

    PS: The cone is standing on its tip and it is opened at the top.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 8, 2008 #2
    Two things will help to spray that water; the pressure which increases as we go down the cone, and the angular momentum which increases as we go up the cone. With a very flat cone I should imagine the best place is near the top; With a very sharp cone I guess the best place is near the bottom. There should be an angle at which it doesn't matter.
     
  4. Dec 8, 2008 #3
    Thank you. I agree. But the problem is solving the equation. Is the use of Bernoulli eq. even correct. Do I incorporate the rotation velocity in Bernoulli eq. or as a separate contribution?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Rotating cone filled with water
Loading...