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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Simple Natural Decay Question

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