| Scenario | K (m/s) | A (m²) | Δh (m) | L (m) | Computed Q (m³/s) |
|---|---|---|---|---|---|
| Fine sand column | 1.0e-4 | 0.020 | 1.5 | 3.0 | 1.0e-6 |
| Clay liner check | 1.0e-9 | 1.000 | 0.8 | 0.5 | 1.6e-9 |
| Gravel drainage layer | 5.0e-3 | 0.150 | 0.3 | 2.0 | 1.125e-4 |
Note: Example results use Q = K·A·Δh/L and assume 1D laminar flow.
Conductivity form: Q = K · A · (Δh / L)
- Q is volumetric flow rate.
- K is hydraulic conductivity.
- A is cross-sectional area normal to flow.
- Δh/L is the hydraulic gradient.
Permeability form: Q = (k · A / μ) · (ΔP / L)
- k is intrinsic permeability.
- μ is dynamic viscosity.
- ΔP/L is the pressure gradient driving flow.
- Select a calculation mode based on your available data.
- Choose the variable you want to solve for.
- Enter values for all other fields and select units.
- Click Calculate to see results above the form.
- Use the CSV and PDF buttons to export your results.
1) Why Darcy’s law matters
Darcy’s law links a driving force to seepage through porous materials. Engineers use it to estimate drainage, liner leakage, groundwater flow, and filter performance. It is a reliable first-pass method when flow is steady and laminar.
2) Conductivity and permeability are different
Hydraulic conductivity K depends on the medium and the fluid. Intrinsic permeability k depends mainly on pore structure. For the same soil, higher viscosity lowers flow. Use pressure mode when you know k and μ, and head mode when K is available.
3) Typical ranges you can sanity-check
Order-of-magnitude checks reduce mistakes. Coarse gravel can have K around 10-2 to 10-1 m/s, clean sands around 10-5 to 10-3 m/s, silts around 10-8 to 10-6 m/s, and clays often 10-12 to 10-9 m/s. Permeability k commonly spans about 10-15 to 10-10 m². Compare your inputs with lab tests, field slug tests, or published tables before finalizing designs.
4) Hydraulic gradient drives head-based flow
The hydraulic gradient i = Δh/L is dimensionless. A small head drop across a short distance can still create a large i. Many natural gradients are below 1, while engineered systems may be higher.
5) Pressure gradient drives permeability-based flow
In packed beds, cores, or filtration tests, you may measure ΔP instead of head. The pressure gradient ΔP/L is reported in Pa/m. Combined with k/μ, it yields Darcy velocity v. Water near 20°C has μ ≈ 0.001 Pa·s (1 cP).
6) What “Darcy velocity” means
Specific discharge is flow per total cross-sectional area, not just pore area. Actual pore water velocity is higher and depends on effective porosity. For transport studies, treat Darcy velocity as a bulk indicator, not a particle speed.
7) Data quality and sensitivity
Darcy calculations are linear. Doubling K, k, A, Δh, or ΔP doubles Q, while doubling L halves Q. Run sensitivity checks by varying one input at a time. Prioritize better measurements for the parameter that dominates uncertainty. When results feed safety or compliance decisions, document data sources, test methods, and unit conversions used.
8) Assumptions and safe use
Darcy’s law is best for saturated, one-dimensional flow in a homogeneous medium. Strong anisotropy, partial saturation, or inertial effects in very coarse media can reduce accuracy. Use this tool for design screening and document assumptions in your report.
1) Can I solve for any variable?
Yes. Choose “Solve for” and leave that field empty while entering all other values. The calculator uses the same Darcy relationship and returns the missing variable with your selected units.
2) What if my flow is upward or negative?
Use the sign of Δh or ΔP to represent direction. A negative gradient will produce a negative flow rate. Magnitude still reflects how strongly the gradient drives seepage.
3) Why does the calculator show hydraulic gradient?
Hydraulic gradient i = Δh/L is a compact way to describe driving force in head-based flow. Seeing i helps you spot unrealistic combinations, such as large head losses over very short distances.
4) Should I use K or k for groundwater problems?
If you have hydraulic conductivity from tests or references, use the head-gradient mode. If you have intrinsic permeability and fluid viscosity, use the pressure-gradient mode for a physics-based approach.
5) How do I pick viscosity μ?
For water near 20°C, μ is about 0.001 Pa·s (1 cP). Warmer water has lower viscosity, which increases predicted flow. Oils or brines can be much more viscous.
6) Does Darcy’s law apply to very coarse gravel?
Sometimes not. Coarse media can develop non-Darcy behavior when inertial effects rise. If measured head loss increases faster than linearly with flow, consider a non-linear model and treat Darcy as an estimate.
7) What is the difference between Q and Darcy velocity?
Q is total volumetric flow through the section. Darcy velocity is flow per total area. It is useful for comparing different geometries, while Q is the actual discharge for your specific cross-section.