|Feb16-13, 06:39 AM||#1|
Simple Natural Decay Question
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?
|Mar4-13, 01:25 PM||#2|
|Apr7-13, 02:12 AM||#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!
|decay, emptying of water, water tank|
|Similar Threads for: Simple Natural Decay Question|
|Natural Log on Radioactive Decay Formula||Introductory Physics Homework||5|
|Simple Natural log graph?||Calculus & Beyond Homework||2|
|simple equation involving natural log!||Introductory Physics Homework||1|
|Simple Question on Natural Logarithms||Calculus & Beyond Homework||6|
|Natural decay of U235||High Energy, Nuclear, Particle Physics||1|