In Groundwater and Aquifers you learned that most groundwater sits in the pore spaces of sand, gravel and cracked rock. It is not still: it flows, slowly, from where the water table is high toward where it is low. In 1856 Henry Darcy measured that flow through sand filters in Dijon, France, and found a simple law, a formula still used for every well and aquifer.
Why it works
Water flows from high hydraulic head to low head; head is the height the water would rise to in a well. The steeper the head drops along the flow path, the faster it flows, just as a ball rolls faster down a steeper ramp. The steepness is the hydraulic gradient, $i = \dfrac{\Delta h}{L}$. How easily water passes through depends on the material: its hydraulic conductivity $K$ is large for gravel, small for clay. Darcy's law: $Q = K A \dfrac{\Delta h}{L}$, the volume per time through area $A$. The water itself squeezes through pores that are only a fraction $n$ (the porosity) of the rock, so it actually moves at $v = \dfrac{K i}{n}$.
Key idea
Groundwater flows from high head to low head. Darcy's law: $Q = K A \dfrac{\Delta h}{L}$. Its actual speed, $\dfrac{K i}{n}$, is often less than a meter a day.
Worked examples
Worked example: Darcy's law
A sand aquifer has $K = 10\,\text{m/day}$. Across a section of $500\,\text{m}^2$, the head drops 4 m over 400 m. How much water flows through each day?
- Gradient: $4 \div 400 = 0.01$.
- $Q = 10 \times 500 \times 0.01 = 50\,\text{m}^3/\text{day}$.
Answer: $50\,\text{m}^3$ per day.
Worked example: How long to reach a well?
A spill reaches the water table 200 m up-gradient of a well. $K = 5\,\text{m/day}$, $i = 0.005$, porosity $0.25$. How long until it arrives?
- Speed: $v = \dfrac{5 \times 0.005}{0.25} = 0.1\,\text{m/day}$.
- Time: $200 \div 0.1 = 2,000$ days, about 5.5 years.
Answer: About 5.5 years.
Common mistake
It is natural to imagine groundwater flowing in underground rivers as fast as a stream. Except in limestone caves, it creeps through tiny pores, often less than a meter a day. Check with the numbers: that is why a pollutant can take years to reach a well, and years more to flush out.