g Two streams merge to form a river. One stream has a width of 8.7 m, depth of 3.6 m, and current speed of 2.4 m/s. The other stream is 6.8 m wide and 3.4 m deep, and flows at 2.4 m/s. If the river has width 11.9 m and speed 2.9 m/s, what is its depth?

h = 3.78 m

Explanation:

For stream 1

h₁ = 3.6 m, b₁ = 8.7 m, v₁ = 2.4 m/s

For stream 2

h₂ = 3.4 m, b₂ = 6.8 m, v₂=2.4 m/s

For river

b = 11.9 m, v = 2.9 m/s

Lets take depth of the river = h

Total discharge should be constant.

We know that discharge

Q = A v

A=Area, v=velocity

Q₁+Q₂ = Q

By putting the values

h₁b₁v₁ + h₂ b₂ v₂ = b h v

3.6 x 8.7 x 2.4 + 3.4 x 6.8 x 2.4 = 11.9 x 2.9 x h

h = 3.78 m