FOR 420 Exam 2 Equations

Darcy’s Law (q = -K dh/dl)

Describes groundwater flow; flow is proportional to hydraulic conductivity and hydraulic gradient, negative sign means flow goes from high to low head

q (specific discharge)

Flow rate per unit area (apparent velocity of groundwater)

K (hydraulic conductivity)

How easily water moves through soil or rock

dh/dl (hydraulic gradient)

Change in hydraulic head over distance (driving force of flow)

Average linear velocity (v = q/ϕ)

Actual velocity of water moving through pore spaces

v (average linear velocity)

Speed of water through pores (faster than q)

q (specific discharge)

Flow per unit area including solids + pores

ϕ (porosity)

Fraction of total volume that is pore space

Porosity (ϕ = Vv/Vt)

Defines how much empty space exists in soil or rock

ϕ (porosity)

Ratio of void (pore) volume to total volume

Vv (void volume)

Volume of empty pore space

Vt (total volume)

Total volume of soil/rock sample

Discharge equation (Q = q·A)

Total groundwater flow through an area

Q (discharge)

Total volume of water flowing per time

q (specific discharge)

Flow per unit area

A (area)

Cross-sectional area water flows through

Hydraulic conductivity equation (K = (Q·L)/(A·Δh))

Calculates K based on measured flow, distance, and head difference

K (hydraulic conductivity)

Ability of material to transmit water

Q (discharge)

Flow rate

L (length)

Distance water travels

A (area)

Cross-sectional area

Δh (head difference)

Change in hydraulic head

Volumetric water content (θ = Vw/Vt)

Amount of water in soil relative to total volume

θ (volumetric water content)

Fraction of soil volume that is water

Vw (water volume)

Volume of water in soil

Vt (total volume)

Total soil volume

Gravimetric to volumetric (θ = (mwet - mdry)/(ρw·Vt))

Converts mass-based water content to volumetric

mwet

Wet soil mass

mdry

Dry soil mass

ρw (water density)

Density of water

Vt

Total soil volume

Soil water balance (dθ/dt · zr = I - L - ET)

Describes change in soil moisture over time

dθ/dt

Change in soil water content over time

zr (root zone depth)

Depth of soil where roots extract water

I (infiltration)

Water entering soil

L (leakage/drainage)

Water leaving downward

ET (evapotranspiration)

Water lost to atmosphere

Total hydraulic head (h = ψm + z)

Total energy of water in soil

h (total head)

Total energy driving flow

ψm (matric potential)

Suction force (negative in unsaturated soil)

z (elevation head)

Height relative to reference

Unsaturated flow (q = K(h) dh/dl)

Water flow in unsaturated soil where conductivity depends on moisture

q (flow)

Water movement

K(h)

Hydraulic conductivity that changes with moisture

dh/dl

Gradient in hydraulic head

Wetland water balance (dV/dt = P + Ri + Gi - Ro - Go - ET)

Change in water storage in a wetland over time

dV/dt

Change in water volume over time

P (precipitation)

Water input from rainfall

Ri (surface inflow)

Water entering from streams/runoff

Gi (groundwater inflow)

Groundwater entering wetland

Ro (surface outflow)

Water leaving via streams

Go (groundwater outflow)

Groundwater leaving

ET (evapotranspiration)

Water lost to atmosphere

Paired catchment ΔQ (ΔQ = Qtreatment,obs − Qtreatment,exp)

Change in streamflow due to treatment (like deforestation)

ΔQ

Change in discharge due to treatment

Qtreatment,observed

Measured flow after treatment

Qtreatment,expected

Predicted flow without treatment