the merging of two streams to form a river. One stream has a width of 8.9 m, depth of 3.5 m, and current speed of 2.1 m/s. The other stream is 6.5 m wide and 3.7 m deep, and flows at 2.2 m/s. The width of the river is 10.7 m, and the current speed is 3.1 m/s. What is its depth?
To find the depth of the river formed by merging two streams, we can first calculate the total volume of water flowing from both streams and then divide it by the width of the river.
The volume of water flowing in each stream can be calculated using the formula:
Volume = (width * depth * current speed)
For the first stream:
Volume1 = (8.9 m * 3.5 m * 2.1 m/s) = 65.415 m³/s
For the second stream:
Volume2 = (6.5 m * 3.7 m * 2.2 m/s) = 54.03 m³/s
Now we can calculate the total volume of water flowing in the river by adding the volumes from both streams:
Total Volume = Volume1 + Volume2 = 65.415 m³/s + 54.03 m³/s = 119.445 m³/s
Finally, we can find the depth of the river by dividing the total volume by the width and current speed:
Depth = Total Volume / (width * current speed)
Depth = 119.445 m³/s / (10.7 m * 3.1 m/s)
Depth = 3.47 m
So, the depth of the river formed by merging the two streams is approximately 3.47 meters.