rivers

Rarely is a river a "closed pipe." However, if we treat the perimeter of the cross-section of the water in a river as an imagninary pipe, we can apply the concepts associated with fluid flow in a closed pipe to the case of a river. In particular we can define a mass flow rate and a volume flow rate (discharge) for water in a river. We can even express the volume flow rate at a particular positon along the river as Av, but, for a real river, the water flowing through the middle/upper region of the cross section has a higher velocity than that near the river bed. So the v in the expression Av for volume flow rate has to be the average velocity of the water over the entire cross section.

Because a typical riverbed acts as a leaky pipe, the continuity equation typically does not apply, not even in the case of a segment of the river which has no tributaries or distributaries. Consider two points along such a river, point 1, and, downstream from that position, point 2. The continuity equation states that the flow rate at point 2 is equal to the flow rate at point 1. In the case of a river flowing through a desert, not all of the water flows downstream, some of it soaks into the bed of the river contributing to the groundwater. (Such a river is called an influent stream because water flows into the ground.) Thus the flow rate at point 2 is less than the flow rate at point 1. In the case of rivers flowing through humid regions, groundwater flows into the river from the ground. In such a case the flow rate at point 2 is greater than the flow rate at point 1. (Such a river is referred to as an effluent stream because water flows out of the ground The Merrimack River is an example of an effluent stream.)