1. Limited time only! Sign up for a free 30min personal 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!

Water bell; got answer but shape's weird?

  1. Aug 3, 2012 #1
    1. The problem statement, all variables and given/known data

    This question is about finding the smallest bowl to contain all the water being spurt out of a water spray head.


    They used the lagrange multipliers to solve it which I understand, but the the envelope doesn't look like a parabola to me??

    Isn't the envelope supposed to be a curve that is parallel to a certain point on every member of a family curve?



    3. The attempt at a solution

    I dont even see how it's possible to draw a curve that's tangential to all water-jet curves..
     

    Attached Files:

  2. jcsd
  3. Aug 3, 2012 #2
    They did not use Lagrange multipliers. An envelope of a family of curves F(x, y, p) = 0, where p is parameter, is obtained by [itex]\frac {\partial F} {\partial p} = 0[/itex], which is what they do.
     
  4. Aug 3, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Your picture is very strange. You seem to have water coming from a head that is convex downward and raised above the surface of the water. The situation described in the post has a hemispherical (convex upward) head at the level of the surface of the water.
     
  5. Aug 4, 2012 #4
    LOL i thought it was the bottom hemisphere. That was the first picture that came to my mind when i thought of a tap and a basin (come on, who builts a tap that spurts upwars? :P)


    I finally see it, thank you!


    I seem to lack the imagination.
     
  6. Aug 4, 2012 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Well, who builds a water feature with a spray head at water level, pointing down?

    RGV
     
  7. Aug 4, 2012 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Think of it not as a "tap" but as a fountain in an outdoor pool.

    (But they are making some very peculiar bathroom fixtures now. I recently had my bathroom remodeled. I looked at some bathroom sinks that are acryic hemispheres sitting on top the counter. I stared at them for a while, shook my head, and walked on.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook