Two streams merge to form a river.
Stream 1: width = 8.2 m, depth = 3.4 m, current speed = 2.3 m/s
Stream 2: width = 6.8 m, depth = 3.2 m, current speed = 2.6 m/s
River: width = 10.5 m, depth = ?, current speed = 2.9 m/s
What is the river's depth d(river)?
Work:
R = AV, where R = current speed
A1V1 = A3V3
(8.2 m)*(3.4 m)*(2.3 m/s) = (10.5 m)*(d3a)*(2.9 m/s)
d3a = 2.10 m
A2V2 = A3V3
(6.8 m)*(3.2 m)*(2.6 m/s) = (10.5 m)*(d3b)*(2.9 m/s)
d3b = 1.86 m
d(river) = d3a + d3b = 3.96 m
Solution
d(river) = 3.96 m