 Solution

ID: past-exam-of-the-topics-in-fluid-mechanics-course-of-the-university-of-oxford/2023/2/a/i/solution

Take

z

vertically upward and the porous skeleton stationary. Darcy's law and incompressibility are

u = - \frac{k}{μ} (\nabla p + ρ g e_{z}), \nabla \cdot u = 0.

Here

u

v

is the liquid pore velocity and all the pore space is saturated and connected, then

u = ϕ v .

ϕ

therefore enters storage and the conversion to pore velocity; it does not multiply the Darcy velocity again when calculating discharge.

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