Seepage Flow Calculator
Applies Darcy's law, Q = k · i · A, to estimate the seepage flow rate through soil from its permeability, the hydraulic gradient and the cross-sectional area. It reports Q in m³/s, litres per minute and m³/day, plus the Darcy discharge velocity. Used for dewatering design, seepage under dams and walls, drainage and inflow estimates.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the coefficient of permeability k (m/s), the hydraulic gradient i and the cross-sectional area A (m²) normal to flow.
- Optionally enter the porosity n to also get the true seepage (pore) velocity.
- Read Q in your preferred unit (m³/s, L/min, m³/day) and the discharge velocity v = k·i.
How it works
Darcy's law states that flow through a porous medium is proportional to the permeability, the hydraulic gradient and the flow area: Q = k · i · A. Dividing by the gross area gives the Darcy (discharge) velocity v = Q/A = k · i.
The Darcy velocity is an apparent velocity spread over the whole gross area. Because water only travels through the connected pore space, the actual seepage (pore) velocity is higher: v_seepage = v / n, where n is the porosity.
Worked example
Flow through a sand layer. For k = 1×10⁻⁵ m/s, i = 0.3 and A = 2 m², Q = 1×10⁻⁵ × 0.3 × 2 = 6×10⁻⁶ m³/s = 0.36 L/min = 0.518 m³/day. The Darcy velocity is v = k·i = 3×10⁻⁶ m/s; with porosity n = 0.4 the seepage velocity is 3×10⁻⁶ / 0.4 = 7.5×10⁻⁶ m/s.
Common mistakes
- Mixing units for k — Darcy's law here expects k in m/s; convert from m/day or cm/s first.
- Confusing the Darcy (discharge) velocity with the real seepage velocity — the seepage velocity is v/n and is always larger.
- Using the wetted or pipe area instead of the gross soil cross-section normal to the flow direction for A.
Frequently asked questions
What is Darcy's law?
Q = k · i · A: the seepage flow equals the permeability times the hydraulic gradient times the cross-sectional area. It is the basic law of groundwater flow through soil.
What is the difference between Darcy velocity and seepage velocity?
The Darcy (discharge) velocity v = k·i is spread over the whole gross area. The seepage (pore) velocity v/n is the real speed of water in the pores and is higher because flow is confined to the pore space.
What units should k be in?
This tool uses k in metres per second (m/s). Convert from cm/s (×0.01) or m/day (÷86400) before entering.
Does Darcy's law always apply?
It holds for laminar flow in most soils. In very coarse gravels or fractured rock at high gradients the flow can become turbulent and Darcy's law overestimates the velocity.
How do I turn m³/s into litres per minute?
Multiply by 60000 (1 m³ = 1000 L and there are 60 seconds in a minute). This tool does it for you.
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- Permeability from Falling Head Test Calculator
- Pore Pressure Calculator
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Tip: Enter any known values to calculate the remaining results.
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