Relationship between drainage channel basin size and length of channel?
I have been asked an essay type question for part of my homework about rivers. The question is:
Suggest reasons for the relationship between the size of drainage basin and the total length of the drainage channel.
I know that the larger the drainage basin, the longer the drainage channel. But I’m having difficulties explaining why..
Can anyone help? Any drainage experts out that who want to share their knowledge?

In my opinion, and as you have stated, the larger the drainage basin, the longer the drainage channel. For a large or long river, the number of tributaries are enormous and water flow could be traced eventually to the main river. Think of the shape of a pyramid and how the base supports the entire weight of the structure. Now, think of the pyramid as a drainage basin diagram. The bottom of the pyramid contains the various tributaries and drainage channels that eventually wind up coming together to form larger rivers, with the number of tributaries decreasing. When you reach the top, you have only one water flow, the main river. This is the reason why the drainage channel is longer when the drainage basin is larger; all the tributaries act in concert to funnel the water into a waterway that flows downhill or toward the ocean. By the time all these smaller streams can efficiently funnel the water to the exit point, it may take many square miles of land to accomplish this goal due to local topography. Each drainage basin is separated topographically from adjacent basins by a geographical barrier such as a ridge, hill or mountain, which is known as a water divide.
Drainage systems develop in such a way as to efficiently move water off the land. Each stream in a drainage system drains a certain area, called a drainage basin. In a single drainage basin, all water falling in the basin drains into the same stream.
Drainage basins can range in size from a few square miles for small streams to extremely large areas, such as the Mississippi River drainage basin which covers about 40% of the contiguous United States. Perhaps, the Mississippi River can act as an example for your question. Look at the length of the river and the amount of land it drains.
See the sources below for additional information.