Exercise 6
Apply the procedure described in Section 4.3 to Darcy’s law with intrinsic permeability rather than hydraulic conductivity; refer to the following Equation.
| [latex]Q = k\frac{\rho_{fluid}g}{\mu_{fluid}}A\frac{dh}{dl}[/latex] |
|---|
where (parameter dimensions are dark green font with mass as M, length as L, time as T):
| [latex]Q[/latex] | = | volumetric discharge (L3T-1) |
|---|---|---|
| [latex]k[/latex] | = | intrinsic permeability (L2) |
| [latex]\rho_{fluid}[/latex] | = | density of the fluid (ML-3) |
| [latex]g[/latex] | = | gravitational acceleration (LT-2) |
| A | = | cross‑sectional area perpendicular to flow (L2) |
| dh/dl | = | hydraulic gradient ([latex]:[/latex]) |
| [latex]\mu_{fluid}[/latex] | = | viscosity of the fluid (ML-1T-1) |