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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

[itex]\frac{dP}{dt}[/itex]=c-g

[itex]\frac{dG}{dt}[/itex]=p

[itex]\frac{dP}{dt}[/itex] is the rate of change of water on the pavement.

[itex]\frac{dG}{dt}[/itex] 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:

[itex]\frac{dP}{dt}[/itex]=c-g

[itex]\frac{dG}{dt}[/itex]=g

Does this look right? Thanks

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# Modeling Rain Hitting Surface

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