Lecture 16
Steady-flow Equations
Fetter 5.11
Flow equations are partial differential equations in which head, h, is
described in terms of x, y, z, and t.
Use
| Applicable equations | |
| Steady flow - Laplace Equation - Confined Aquifer | |
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| *Saturated thickness does not change! |
Unconfined Aquifers
| Gravity drainage of water in pores. Therefore, the position of the water table declines with respect to time and saturated thickness may change. | |
| h = thickness (saturated) from the base of aquifer. |
Boussinesq Equation (Boussinesq, 1904)
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| Sy = Specific yield | |
| Nonlinear equation |
If we assume drawdown is small compared to saturated thickness -
| Replace h with b |
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*same as two dimensional non steady equation |
Potential Energy (force
potential f)
| mechanical energy / unit mass | ||
| f = gh | ||
| The force potential is a physical quantity | ||
| i.e. 15.1m x 9.81m/s2 = f = 148.1m2/s2 | ||
| because g is generally constant, f usually described by h | |
| Contouring h - contouring equal force potential or equipotentials. |
If the potential is the same everywhere, then no change in f or h - flat water table
If an Aquifer is Isotropic, K is the same in all directions.
Then flow is parallel to grad h and is perpendicular to equipotentials.
If Anisotropic, K varies with direction, flow not parallel to grad h, and flow not perpendicular
Steady flow - no change in head with time. If there is a gradient to potentiometric surface
then water moving opposite of grad h.
Use Darcy's Law directly to measure flow - linear gradient
| K = Hydraulic conductivity (L/T) | |
| b = aquifer thickness (L) | |
| dh/dl = slope of the potentiometric surface (L/L) | |
| q' = flow per unit width (L2/T) |
K = 1.2 m/d
What is total daily flow through aquifer?
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ENV 302 - Lectures