How to find the speed of a river

Talking with old acquaintances, we often say: "a lot of water has flowed since...". But can we answer simple questions, how to find the speed of the current of the river and how much water flows, for example, per day even in a small river. All this is fully measurable and represents a relatively easy geometric problem.

So how do you find the speed of the river? To solve this problem, several people must perform measurements. For this, a straight section of the river is selected and two milestones A and B are placed along the coast, at a distance of, for example, 100 meters from one another. On the lines perpendicular to AB, two more milestones C and D are placed. One of the participants of the measurement is behind the milestone C, the other behind the milestone D, and both look along the directions CA and DB on the surface of the water. The third participant throws in the water above the point A some well-marked float, for example, a sealed half-empty bottle with a flag. Observers standing at the milestones with well-verified clocks in their hands mark the moments when the float intersects the continuation of the lines CA and DB. If the time difference, for example, 40 seconds, then the rate of water flow in the river:

This method of finding the velocity of the river flow and the result obtained refer only to surface jets. The deeper layers of the river flow more slowly, and the average speed of the river current is approximately 5/6 of this surface velocity, in our case about 2 meters per second.

Find the surface speed of the river can be and other, however, less reliable way. To do this, the boat needs to swim 1 kilometer (measured along the shore) upstream and then back downstream, trying to row all the time with the same force. Let you swim these 1000 meters against the current in 18 minutes, and after the flow - for 6 minutes. Denoting the required flow velocity of the river through x, and the speed of your movement in standing water through y, you make the equations:

Whence x = 55,5. The speed of the river on the surface is 55,5 meters per minute, and, consequently, the average speed is about 5/6 meters per second.