# Flow Rate of Merging Streams

1. Dec 19, 2006

### mbrmbrg

1. The problem statement, all variables and given/known data

Figure 14-43 shows the merging of two streams to form a river. One stream has a width of 9.3 m, depth of 4.3 m, and current speed of 2.5 m/s. The other stream is 6.8 m wide and 4.0 m deep, and flows at 2.7 m/s. The width of the river is 10.2 m, and the current speed is 2.7 m/s. What is its depth?

2. Relevant equations

$$R_v=Av=constant$$

$$A_1v_1=A_2v_2$$

3. The attempt at a solution

Sure, the rate flow should be constant for an ideal river of varying cross-sectional area, but I don't understand what to do when more fluid is added. Since two streams are merging, do I say that $$(A_{stream 1})(v_{stream1})+(A_{stream2})(v_{stream2})=(A_{river})(v_{river})$$?

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Last edited: Dec 19, 2006
2. Dec 19, 2006

### Staff: Mentor

Looks good to me. That's conservation of mass (the continuity equation) in action.

3. Dec 19, 2006

Thank you!