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Simple Natural Decay Question

by That Neuron
Tags: decay, emptying of water, water tank
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That Neuron
#1
Feb16-13, 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 (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?
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MostlyHarmless
#2
Mar4-13, 01:25 PM
MostlyHarmless's Avatar
P: 266
Quote Quote by That Neuron View Post
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?
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?
That Neuron
#3
Apr7-13, 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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