Input Data
Formula Used
Darcy’s law for saturated flow is:
Q = K · A · (Δh / ΔL)
Solving for hydraulic conductivity:
K = (Q · ΔL) / (A · Δh)
Additional metrics:
i = Δh/ΔL,
q = Q/A,
v = q/ne,
T = K·b.
Temperature option estimates K(20°C) using a viscosity ratio correction.
How to Use This Calculator
- Enter discharge Q measured through the cross-section.
- Provide flow area A perpendicular to groundwater flow.
- Enter head loss Δh between two piezometric points.
- Enter spacing ΔL between those head measurements.
- Optional: add ne for seepage velocity, and b for transmissivity.
- Press Calculate to view results above the form.
Example Data Table
| Scenario | Q (m³/s) | A (m²) | Δh (m) | ΔL (m) | ne | b (m) |
|---|---|---|---|---|---|---|
| Lab column test | 0.00012 | 0.010 | 0.18 | 0.60 | 0.30 | — |
| Shallow sand aquifer | 0.00200 | 0.50 | 0.25 | 5.00 | 0.25 | 12 |
| Fine silt zone | 0.00005 | 0.20 | 0.40 | 8.00 | 0.35 | 6 |
Technical Article
1) Why hydraulic conductivity matters
Hydraulic conductivity (K) controls how easily water moves through a saturated porous medium. It governs seepage beneath foundations, well yield, contaminant migration, and dewatering performance. Because K spans many orders of magnitude, using consistent units and careful measurements is essential for defensible groundwater decisions.
2) Darcy framework used in this tool
The calculator applies Darcy’s law, Q = K·A·(Δh/ΔL). Field or laboratory tests provide discharge (Q), flow area (A), head loss (Δh), and measurement spacing (ΔL). The hydraulic gradient i = Δh/ΔL is computed first, then K is obtained from K = (Q·ΔL)/(A·Δh).
3) Typical K ranges for common materials
Reported values vary by sorting, packing, and fines content. As a practical guide: clean gravel may range from about 10−2 to 10−1 m/s; coarse sand often 10−4 to 10−3 m/s; fine sand 10−6 to 10−5 m/s; silt commonly 10−9 to 10−7 m/s; and clays may be below 10−10 m/s. Site-specific testing remains the best evidence.
4) Unit discipline and result interpretation
K is reported in m/s and m/day to match groundwater and construction workflows. When comparing sources, convert consistently: 1 m/day ≈ 1.157×10−5 m/s. A small change in K can produce large changes in travel time, especially over long flow paths or in layered systems.
5) Field and laboratory measurement notes
Laboratory permeameters are controlled and repeatable, but may miss fractures and heterogeneity at the field scale. Field methods (slug tests, pumping tests, infiltration tests) capture larger volumes, often yielding higher effective K. Always document test type, screened interval, and aquifer conditions (confined/unconfined).
6) Temperature correction and viscosity
Water viscosity decreases as temperature rises, which can increase measured conductivity. The optional correction converts K at temperature T to an equivalent K at 20°C using a viscosity ratio. This helps compare tests performed during different seasons or in laboratories with different water temperatures.
7) From Darcy flux to seepage velocity
The Darcy flux q = Q/A represents flow per bulk area. Actual pore-water velocity is higher because flow occurs through connected pore space. If effective porosity ne is provided, the tool estimates seepage velocity v = q/ne, useful for first-pass contaminant transport screening.
8) Transmissivity and reporting quality
For an aquifer thickness b, transmissivity is T = K·b (m²/s), a key parameter in well performance and regional groundwater modeling. Quality checks include confirming steady flow, verifying head readings, and repeating calculations with independent measurements. Report K with units, method, temperature, and uncertainty notes.
FAQs
1) What is the difference between K and permeability?
K depends on both the porous medium and the fluid. Intrinsic permeability reflects only the medium structure. K changes with fluid viscosity and density, so it can vary with temperature or different fluids.
2) Why does my calculated K look extremely high?
Check units first, especially Q and area A. Confirm Δh is not too small, and verify ΔL is correct. Field heterogeneity or preferential pathways can also raise effective K relative to lab samples.
3) When should I use the 20°C correction?
Use it when comparing tests done at different water temperatures or when reporting standardized results. If your project specifications already define a reference temperature, apply the correction for consistency.
4) What effective porosity value should I enter?
Use ne from site characterization when available. Typical ranges: sands ~0.20–0.35, silts ~0.10–0.25, clays ~0.01–0.10. Choose values aligned with your lithology and data source.
5) Does Darcy’s law always apply?
Darcy’s law assumes laminar flow through porous media. In very coarse gravels, high gradients, or near wells, non-Darcian effects may appear. Use caution and consider field testing or advanced models when needed.
6) How is transmissivity used in practice?
Transmissivity summarizes how much water an aquifer can transmit across its saturated thickness. It is commonly used in pumping test analysis, drawdown prediction, and screening well design and productivity.
7) What outputs should I include in a report?
Include Q, A, Δh, ΔL, computed i, q, K with units, temperature, correction status, and the test method. If you estimate v or T, state ne and b and their sources.
Accurate inputs produce reliable conductivity values for better decisions.