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Unformatted text preview: P k u ∇ − = µ ~ (where k is a constant, ~ u is the fluid velocity and P is pressure). a ) Use Darcy’s law to obtain expressions for conservation of mass (continuity) for the porous flow. b ) Show that for an incompressible fluid, the differential equation from part ( a ) reduces to 2 = ∇ P 6. (10 points) You are setting up an experiment, where a balloon initially contains some water, and through a plunger (look at figure) you introduce additional amounts of water, expanding the balloon a bit. A friend of yours makes the observation that the balloon is defining essentially a material volume. Do you agree? Please justify your answer. If you don’t agree, try to imagine what the material volume really is, and briefly describe it (a sketch will do). plunger balloon...
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- Spring '08
- Fluid Dynamics, ρ, 1.5 hours, fluid velocity, material volume, velocity gradient tensor