Finite Volume Analysis: Application of Conservation of Mass (continued)

Example 2 (continued)

Strategy for solution:

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.

Continue with steps 2 and 3.

In general, conservation of mass is: Note: The flow across surfaces is uniform.

d/dt ∫ ρ dV + ∫ ρ V● n dA = 0

cv cs

Since the river flows steadily, the first term in the above equation is zero. (steady flow)

The second term expands as follows:

∫ ρ V₁● n₁ dA ₊ ∫ ρ V₂● n₂ dA + ∫ ρ V₃● n₃ dA + ∫ ρ V₄● n₃ dA = 0

ρ ( -3)(50)(6) + ρ (-4)(80)(6) + ρ (V)(70)(6) + ρ(0.8V)(30)(6) = 0

Cancel ρ and 6 from the above equation and solve for V.

94 V = 470 or V = 5 ft/sec (result)

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