Learn: Seepage velocity
Darcy velocity spreads discharge over the whole soil cross-section, including solids. Actual average pore-water velocity is larger because water moves only through the connected pore space.
What the formula is saying
If connected pore area is represented by n times gross area, dividing Darcy velocity vd by n gives seepage velocity. The same discharge passes through a smaller flow area.
Read the symbols in plain language
- v
- Darcy velocity
Discharge divided by total cross-sectional area, including solid grains; actual pore-water speed is generally larger.
m/sUse m/s as the base unit shown here. vd and vs use m/s. n is the effective connected porosity used by the model and is a decimal fraction, not percent as a whole number and not void ratio.
- n
- Porosity as decimal
Void volume divided by total volume, strictly below one. It differs from void ratio, whose denominator is solid volume.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- vs
- Result to find
Seepage velocity. Dividing by the connected pore fraction converts bulk discharge velocity to average pore velocity.
m/s
Sort out the units first
vd and vs use m/s. n is the effective connected porosity used by the model and is a decimal fraction, not percent as a whole number and not void ratio.
Assumptions before calculating
Assume a representative saturated flow medium in which the chosen porosity represents the connected flowing pore space. Require 0 < n < 1 and a nonnegative discharge-velocity magnitude.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find vs and explain the result in the stated output unit.
- v · Darcy velocity
- 0.00001 m/s
- n · Porosity as decimal
- 0.35
Identify the Darcy discharge velocity
This velocity is defined over gross soil area rather than only water-filled connected pores.
(0.00001) = 0.00001 m/sCorrect for the flowing pore fraction
Dividing by the connected pore fraction converts bulk discharge velocity to average pore velocity.
(0.00001) ÷ (0.35) ≈ 0.00002857142857 m/s
Does this worked answer make sense?
For 0 < n < 1, vs is at least vd for nonnegative speeds. Halving effective porosity doubles the average seepage velocity for the same Darcy discharge velocity.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- v · Darcy velocity
- 0.00002 m/s
- n · Porosity as decimal
- 0.4
Identify the Darcy discharge velocity
This velocity is defined over gross soil area rather than only water-filled connected pores.
(0.00002) = 0.00002 m/sCorrect for the flowing pore fraction
Dividing by the connected pore fraction converts bulk discharge velocity to average pore velocity.
(0.00002) ÷ (0.4) = 0.00005 m/s
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- v · Darcy velocity
- 0.000015 m/s
- n · Porosity as decimal
- 0.3
Find: Learn: Seepage velocity
A hint, not the answer
If connected pore area is represented by n times gross area, dividing Darcy velocity vd by n gives seepage velocity. The same discharge passes through a smaller flow area.
vd and vs use m/s. n is the effective connected porosity used by the model and is a decimal fraction, not percent as a whole number and not void ratio.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the Darcy discharge velocity
This velocity is defined over gross soil area rather than only water-filled connected pores.
(0.000015) = 0.000015 m/sCorrect for the flowing pore fraction
Dividing by the connected pore fraction converts bulk discharge velocity to average pore velocity.
(0.000015) ÷ (0.3) = 0.00005 m/s
Avoid the common trap
Do not multiply vd by porosity; the smaller flow area makes pore velocity larger, not smaller. Do not use total porosity blindly when only connected effective porosity carries the flow.
When this method applies — and when it does not
This is an average pore velocity, not the local velocity in every pore. Dead-end pores, preferential paths, dispersion, unsaturated conditions and travel-time retardation may require a more detailed transport model.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Seepage velocity. Read the relevant soil phase, seepage, earth-pressure, settlement or foundation topic. Effective stress, drainage and idealized geometry determine whether the relationship applies.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.