Help with Capillary Rise Equation for Differential Equations Class

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To derive the capillary rise equation for a paper towel, start by applying the Poiseuille flow equation, which describes fluid movement through a narrow space. Combine this with a material balance to account for the fluid volume and the Young-Laplace equation, which relates pressure differences to surface tension and curvature. This approach will help formulate a differential equation (ODE) that can be integrated to find the solution. Understanding these principles will clarify the physics behind capillary action and aid in fitting the equation to the provided data points. A thorough grasp of these concepts is essential for successfully completing the assignment.
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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
 
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Use the Poiseulle flow equation for a capillary in conjunction with the material balance and the Young-Laplace equation at the interface.
 

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