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Finite Volume Analysis

General Strategy for Finite Volume Analysis in Fluid Mechanics

Step 1 Identify (draw) the control surface and control volume for the fluid flow.

You may need more than one control surface and control volume.

control surface of control surfaces.

Step 2 Write the equation for conservation of mass if needed.

Step 3 Write the equation for conservation of linear momentum if needed.

Step 4 Write one or more Bernoulli equations along streamlines to identify

differences in fluid pressure forces acting on the control surface.

Construct a few streamlines as needed.

i.e. For inviscid, steady, incompressible flow along a streamline:

P₁/ρ + (1/2)V₁² + g Z₁ = P₂/ρ + (1/2)V₂² + gZ₂

Step 5 Write the equation for conservation of angular momentum if needed.

Step 6 Write the equation for conservation of energy if needed.

Step 7 Combine equations and solve for the desired unknown or unknowns.