- #1
analysis001
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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
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