What is the depth of a merged river with given stream dimensions and speeds?

[mbrmbrg]

Homework Statement

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?

Homework Equations

$$R_v=Av=constant$$

$$A_1v_1=A_2v_2$$

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 $$(A_{stream 1})(v_{stream1})+(A_{stream2})(v_{stream2})=(A_{river})(v_{river})$$?

 

[Doc Al]

Since two streams are merging, do I say that $$(A_{stream 1})(v_{stream1})+(A_{stream2})(v_{stream2})=(A_{river})(v_{river})$$?

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

 

[mbrmbrg]

Thank you!