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Finite Volume Analysis: Application of Conservation of Mass

Example 2 Two rivers merge to form a larger river as shown in the figure below.

At a location downstream from the junction (before the two streams completely merge)

the nonuniform velocity profile is as shown. The depth of the river is 6 ft. Determine

the value of V.

Strategy for solution:

Step 1

Identify (draw) the control surface and control volume for the fluid flow.

Show the unit normals at each control surface that flow crosses.

Step 2

Write the equation for conservation of mass and simplify for known

values. Check for steady flow. Identify surfaces across which flow occurs.

Step 3

Solve for desired values.

The figure below shows step 1 completed.