Playfair's law

In estimating erosion, Playfair's law is an empirical relationship that relates the size of a stream to the valley it runs through.

This is because steady, heavy flow of water will tug surrounding soil and subsequently erode and deepen the valley it cuts through.

By modeling Playfair's law in the following mathematical scheme, we can find the incision rate of the stream into the valley by following: In evaluating the case specific parameters, we regard

as a parameter that is dependent on the type of land or soil that the stream is penetrating.

can be estimated by first assuming that at the junction the law holds over the distance used to determine S and taking their ratios (m/n) at different points, then substitution.