About Seepage Flow Calculator
The seepage flow calculator estimates how much water flows through soil under a hydraulic head difference. In Darcy mode it applies Darcy's law to a soil mass of known cross-sectional area and flow length, returning the hydraulic gradient, the discharge velocity, the actual pore (seepage) velocity, and the volumetric discharge.
In flow-net mode it estimates seepage beneath or through a structure such as a dam, sheet-pile wall, or cofferdam from a graphical flow net defined by the number of flow channels Nf and the number of equipotential drops Nd. The discharge is reported per unit width along with the head loss across each equipotential drop.
How It Works
- Choose Darcy mode for flow through a soil sample or block, or flow-net mode for seepage beneath a structure.
- In Darcy mode, enter the permeability k, head difference H, flow length L, and cross-sectional area A; the gradient is i = H/L, the discharge velocity is v = k·i, and the discharge is Q = k·i·A.
- The seepage (pore) velocity is the discharge velocity divided by the porosity, vs = v/n, and represents the actual speed of water moving through the pore spaces.
- In flow-net mode, enter k, the total head H, and the counts Nf and Nd read from the net; the discharge per unit width is Q = k·H·(Nf/Nd) and the head loss per drop is H/Nd.
Worked Example
Darcy mode: a sand layer has permeability k = 1×10⁻⁴ m/s, a head difference H = 2 m over a flow length L = 4 m, and a cross-sectional area A = 10 m². The hydraulic gradient is i = H/L = 0.5, the discharge velocity is v = k·i = 1×10⁻⁴ × 0.5 = 5×10⁻⁵ m/s, and the discharge is Q = k·i·A = 5×10⁻⁴ m³/s. With a porosity n = 0.3 the seepage velocity is vs = v/n = 1.67×10⁻⁴ m/s. Flow-net mode: with the same k and H, a flow net with Nf = 4 flow channels and Nd = 8 equipotential drops gives Q = k·H·(Nf/Nd) = 1×10⁻⁴ × 2 × 4/8 = 1×10⁻⁴ m³/s per metre width, and the head loss per drop is H/Nd = 0.25 m.
Formulas
- Darcy's law - gradient, velocity, discharge
i = H / L, v = k * i, Q = k * i * A- Seepage (pore) velocity
vs = v / n- Flow-net discharge (per unit width)
Q = k * H * (Nf / Nd)- Head loss per equipotential drop
dh = H / Nd
Standards & References
- Darcy's law (Henry Darcy, 1856)
- Flow-net method (Forchheimer / Casagrande)
- Das, Principles of Geotechnical Engineering
Frequently Asked Questions
What is the difference between discharge velocity and seepage velocity?
The discharge (Darcy) velocity v = k·i is a fictitious velocity computed over the total cross-sectional area, including the solid grains. The seepage velocity vs = v/n is the actual speed of water through the pore spaces and is always larger because the flow is squeezed through only the void fraction of the area.
When should I use the flow-net method instead of Darcy directly?
Use Darcy directly for one-dimensional flow through a soil block or sample with a clear length and area. Use the flow-net method for two-dimensional seepage beneath or around a structure such as a dam, weir, sheet-pile wall, or cofferdam, where the flow paths curve and a single length and area cannot be defined.
How do I read Nf and Nd from a flow net?
Nf is the number of flow channels, the strips between adjacent flow lines, and Nd is the number of equipotential drops, the steps between adjacent equipotential lines from the upstream to the downstream boundary. A correctly drawn flow net forms approximate squares, and the discharge per unit width is k·H·Nf/Nd.
What units should I use?
Use a consistent SI set: permeability k in m/s, heads and lengths in metres, and area in square metres. Velocities then come out in m/s and discharge in m³/s (or m³/s per metre of width in flow-net mode). Permeability for soils spans a huge range, roughly 10⁻² m/s for gravel down to 10⁻⁹ m/s for clay.