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Simple Natural Decay Question 
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#1
Feb1613, 06:39 AM

P: 76

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 (πr^{2} 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
Mar413, 01:25 PM

P: 266




#3
Apr713, 02:12 AM

P: 76

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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