Water Extraction Volume Calculator
Calculate the extractable water volume from an aquifer based on hydraulic conductivity, aquifer dimensions, hydraulic gradient, and time using Darcy's Law combined with storativity principles.
Typical values: Clay 0.0001–0.01, Sand 1–100, Gravel 100–1000 m/day
Head difference divided by flow path length (typically 0.001–0.05)
Width × saturated thickness of the aquifer perpendicular to flow
Confined aquifer: 0.00005–0.005 | Unconfined (specific yield): 0.05–0.35
Horizontal surface area of the aquifer being depleted
Maximum permissible drawdown in the aquifer
Time period over which extraction occurs
Ratio of actual to theoretical yield (typically 70–95%)
Results will appear here.
Formulas Used
1. Darcy's Law — Flow Rate:
Q = K × i × A
- Q = volumetric flow rate [m³/day]
- K = hydraulic conductivity [m/day]
- i = hydraulic gradient = Δh / L [dimensionless]
- A = cross-sectional area perpendicular to flow [m²]
2. Darcy Volume over Time:
V_darcy = Q × t
3. Aquifer Storage Volume:
V_storage = S × A_aq × Δh
- S = storativity (confined) or specific yield (unconfined) [dimensionless]
- A_aq = plan area of aquifer [m²]
- Δh = allowable head decline [m]
4. Theoretical Extractable Volume (conservative):
V_theoretical = min(V_darcy, V_storage)
5. Practical Extractable Volume:
V_extractable = V_theoretical × η
- η = well efficiency [fraction]
Assumptions & References
- Darcy's Law is valid (laminar flow, homogeneous isotropic aquifer, fully saturated conditions).
- The aquifer is assumed to be in steady-state flow for the Darcy component; transient effects (e.g., cone of depression expansion) are not modelled.
- Storage volume calculation assumes uniform head decline across the entire aquifer plan area — a simplification; actual drawdown is spatially variable.
- The conservative minimum of Darcy volume and storage volume is used to avoid over-estimating yield.
- Well efficiency accounts for head losses in the well screen, gravel pack, and pump intake but does not model pump curves.
- No recharge from precipitation, rivers, or adjacent aquifers is included — results represent a conservative lower bound.
- References: Freeze & Cherry (1979) Groundwater; Todd & Mays (2005) Groundwater Hydrology; Darcy, H. (1856) Les Fontaines Publiques de la Ville de Dijon; Bear, J. (1972) Dynamics of Fluids in Porous Media.