Solution Exercise 6
- The items and their dimensions are defined in the table of Exercise 5. Their SI units are as follows.
| [latex]Q = k\frac{\rho_{fluid}g}{\mu_{fluid}}A\frac{dh}{dl}[/latex] | |||
|---|---|---|---|
| [latex]Q[/latex] | = | volumetric discharge (m3 sec-1) | |
| [latex]k[/latex] | = | intrinsic permeability (m2) | |
| [latex]\rho_{fluid}[/latex] | = | density of the fluid (kg m-3) | |
| [latex]g[/latex] | = | gravitational acceleration (m sec-2) | |
| A | = | cross‑sectional area perpendicular to flow (m2) | |
| dh/dl | = | hydraulic gradient ([latex]:[/latex]) | |
| [latex]\mu_{fluid}[/latex] | = | viscosity of the fluid (kg m-1 sec-1) | |
- Variables are [latex]Q,\ A,\frac{dh}{dl},\ k,\ \rho_{fluid},\ \mu_{fluid}[/latex]. Constants are [latex]g[/latex].
3. Discharge is directly proportional to permeability, fluid density, gravitational acceleration, area, and hydraulic gradient. Discharge is inversely proportional to viscosity.
4. There are no exponents or logarithms in the equation; therefore, all proportionality relationships are linear.
Thought Question 19: Explain why discharge is directly proportional to density but inversely proportional to viscosity.