# Modeling Rain Hitting Surface

1. Apr 20, 2014

### analysis001

I would like to model rain hitting a surface and then running off of the surface. The surface would be a square, such as a slab of concrete, and the concrete would not be at any angle, so the rain would run off of all sides equally. This is a starting point for a small research project I am doing, and I'm not sure if my differential equations are right. Any help would be great.

Further information: The rain is falling at a constant rate. The ground surrounding the concrete has an unlimited capacity for rain. I am assuming that the concrete is initially fully saturated, so none of the rain will be absorbed into the concrete. I am also assuming that the rain is only falling on the concrete, not the surrounding ground.

$\frac{dP}{dt}$=c-g

$\frac{dG}{dt}$=p

$\frac{dP}{dt}$ is the rate of change of water on the pavement.

$\frac{dG}{dt}$ is the rate of change of water on the ground

c is the constant rate of rainfall.
g is the constant flow of water from the pavement onto the ground.
p is the rate at which water is flowing onto the ground.

Now that I think about it, g must equal p. So my new differential equations would be:

$\frac{dP}{dt}$=c-g

$\frac{dG}{dt}$=g

Does this look right? Thanks

2. Apr 21, 2014

### HallsofIvy

Staff Emeritus
Either you are using "P" and "p" and "G" and "g" interchangeably or you have not defined "P" and "G". Either is bad.