Hydrogeology Midterm Definitions, Equations, and Units

$\it Q=-K\left(\frac{dh}{dl}\right)A$

$\it \frac{Q}{W}=-T\left(\frac{dh}{dl}\right)$

$\it q=-K\left(\frac{dh}{dl}\right)$

$\it T=K_{h}b$

horizontal transmission capacity over an aquifer's thickness

water primarily flows horizontally in an unconfined aquifer (vertical flow is negligible)

volume of water an aquifer releases from storage per unit area (viewed from above) per unit decline in hydraulic head

$\it S=\frac{V_{\mathrm{released}}}{A\cdot \Delta h}$

$\it \frac{V_{\mathrm{released}}}{A}= S\cdot \Delta h$

hydraulic conductivity doesn't change with location

hydraulic conductivity changes with location

K is the same in every direction at a certain location in a medium

K varies by direction at a certain location in a medium

fraction of void space in a medium (not occupied by grains or rock)

$\it n=\frac{V_{\mathrm{void space}}}{V_{\mathrm{bulk}}}$

$\it n=\mathrm{1}-\frac{\rho_{\mathrm{particles}}}{\rho_{\mathrm{bulk}}}$

$\displaystyle \it K_{\mathrm{eq}}=\sum_{j}K_j\left(\frac{b_j}{B}\right)$

$\it K_{\mathrm{eq}}=\dfrac{\mathrm{1}}{\displaystyle{\sum_{j}}\left(\dfrac{1}{K_j}\right)\left(\dfrac{b_j}{B}\right)}$

$\it h=z+\psi$

gravitational potential energy per unit weight (elevation about a datum)

static pressure energy per unit weight

Constant head (recharge), Zero gradient (no flow; impermeable barrier or line of symmetry), Water table (hydraulic head is known, may or may not be an equipotential line)

imaginary surface representing the elevations to which water would rise at atmospheric pressure; using many piezometers tapping an aquifer at different locations, we can plot and contour an approximate potentiometric surface

$\it \Phi=\frac{\mathrm{ME}_{\mathrm{total}}}{m}=hg$

$\it h=\dfrac{\mathrm{ME}_{\mathrm{total}}}{mg}=\Phi/g$