Falling Head Conductivity Calculator
Enter standpipe area, sample geometry, time and head levels to compute hydraulic conductivity via the falling-head (constant-head) test.
Input Data
Results
At a glance:The falling-head permeameter measures the hydraulic conductivity K of a saturated soil sample. Water in a narrow standpipe of area a drains through a sample of area A and length L; the head h(t) falls exponentially: dh/dt = −(a·K·h)/(A·L). Integrating from h₀ at t=0 to h_t at time t gives K = (a·L/(A·t))·ln(h₀/h_t). K (m/s) is Darcy's proportionality constant relating flow rate to hydraulic gradient. It characterizes soil permeability: gravels ~10⁻²–10⁻¹ m/s, sands ~10⁻⁴–10⁻², clays <10⁻⁷. The method suits low-permeability (fine-grained) soils better than constant-head.
Formula
K = (a·L/(A·t))·ln(h₀/h_t)
$$K = \dfrac{a\,L}{A\,t}\,\ln\!\left(\dfrac{h_1}{h_2}\right)$$How to Use
- Enter standpipe area a, sample length L and sample area A.
- Enter time t and the initial and final heads h₀, h_t.
- The calculator returns K.
Case Studies
Clay sample
a=5e-4 m², A=5e-3 m², L=0.1 m, t=600 s, h₀=0.5, h_t=0.2 m.
K = (5e-4×0.1/(5e-3×600))·ln(2.5) ≈ 1.53×10⁻⁵ m/s.
Typical of silty clay.
FAQ
When is the falling-head method used?
For relatively impermeable (fine-grained) soils where too little flow passes for a constant-head test; the falling head is sensitive over longer times.
Why the natural log of head ratio?
Head decays exponentially with time, so the integrated form gives ln(h₀/h_t) — a direct measure of how fast head fell.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.