Question

Two streams merge to form a river. One stream has a width of 8.9 m, depth of 3.8 m, and current speed of 2.3 m/s. The other stream is 6.5 m wide and 3.9 m deep, and flows at 2.6 m/s. If the river has width 10.7 m and speed 3.0 m/s, what is its depth?

Answer 1

Depth of river is 4.48 m

Explanation:

Discharge = Area x Velocity

Discharge of river = Discharge of stream 1 + Discharge of stream 2

$A_rv_r=A_1v_1+A_2v_2$

Area of stream 1 = w₁ x d₁ = 8.9 x 3.8 = 33.82 m²

Area of stream 2 = w₂ x d₂ = 6.5 x 3.9 = 25.35 m²

Velocity of stream 1 = 2.3 m/s

Velocity of stream 2 = 2.6 m/s

Velocity of river = 3 m/s

$\texttt{Area of river = }w_r\times d_r=10.7\times d_r$

Substituting

             $A_rv_r=A_1v_1+A_2v_2\\\\10.7\times d_r\times 3=33.82\times 2.3+25.35\times 2.6\\\\d_r=4.48m$

Depth of river = 4.48 m