Help with Capillary Rise Equation for Differential Equations Class

[RagincajunLA]

Hey guys, I have a problem in one of my classes where I need to make an equation of capillary rise in a strip of paper towel. I am given data points and I need to make an equation that fits the points. Can someone please help me through the physics and derivation behind this. I tried doing some research but i can't quite understand what is going on. This if for my differential equations class so i need to go about making an ODE and integrating it to the answer. I am not looking for you guys to flat out give me the answer. I would like someone to explain it to me so i can understand it

 

[Chestermiller]

Use the Poiseulle flow equation for a capillary in conjunction with the material balance and the Young-Laplace equation at the interface.