Gtwo 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

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