What term describes small ditches in a field that direct the flow of water?

The term that describes small ditches in a field that direct the flow of water is "furrow." Furrows are specifically designed for agricultural applications, where they are created to manage water distribution, prevent erosion, and improve crop irrigation efficiency. They are typically formed by plowing and are a common practice in row cropping, allowing water to flow through them and reach the plant roots effectively.

In contrast, a channel is often a broader term that refers to any conduit designed to carry water but might not be as specifically related to agricultural practices. Drainage refers to the removal of excess water and does not necessarily imply the presence of ditches in the same way that furrows do. A trench is generally deeper and wider than a furrow and is often used for different purposes, such as for the installation of utilities.