Register to reply 
Simple Natural Decay Question 
Share this thread: 
#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: 267




#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! 


Register to reply 
Related Discussions  
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 