When there is a heavy downpour of rain, the flowing water is likely to cause soil erosion. The water is likely to form a tiny stream as it flows along. Therefore the tiny channel through which the water passes is called a rill.
There are some other words that can be used to show the same meaning as rill. They include; Rivulet, Runnel, Streamlet among others.
However the word can be easily turned into a verb; a doing word.
For example in a sentence we can say, I could feel the water from the rain rill down my face.
This means that the water was flowing down.