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Simple Natural Decay Question

  1. Feb 16, 2013 #1
    Okay, this is a really simple question, so to anyone looking for some extraordinarily complex differential equation question turn away now, or be blinded by boredom.

    My query is rooted in a question I had about building a water clock... so seemingly relevant to Differentials, I know. Anyways, I realized that the rate of dripping (though probably much more complex than a proportionality) was at simplest proportional to the height, or at least related to it.

    Anyway, I was thinking that if the rate of change of the height is proportional to the pressure on the hole at the bottom out of which water drips (or pours) then I could create the differential dy/dt = -k (πr2 pg y(t), where p is equal to the density and g is the acceleration due to gravity, this equation translates to y = y(0) e-kπr2pgt.

    But this function seems to decline too steeply for this application, am I doing this right?
  2. jcsd
  3. Mar 4, 2013 #2
    Is you're equation dy/dt=-k(...pg)y(t) where "y(t)" is y as a function of t. or the variable y times the variable t?
  4. Apr 7, 2013 #3
    Oh, no y is a function of t!

    Not the height!

    I actually think that I found the correct function simply by playing around with the constant k. Let me revisit this!
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