Hydraulic Gradient Calculator
The hydraulic gradient calculator helps you determine the magnitude and direction of water flow. It is a hydrogeological concept that is helpful in determining groundwater movement. You can also track the flow of contaminants using the same hydraulic gradient that causes the water to move or flow. The value of the hydraulic gradient can be reused in a hydraulic conductivity calculation to find out how much water flows through the soil.
This article briefly explains what a hydraulic gradient is and how to calculate it.
Hydraulic gradient formula
The hydraulic gradient is the ratio of the hydraulic head difference to the distance between two sample points. In simple words, it tells us how the hydraulic head changes over a certain distance. If you plot the hydraulic head vs. distance on a graph, the hydraulic gradient is the slope of the line. One can also define it as the change in water level per unit distance.
For the heads h₁ and h₂ at two points separated by a distance L, the hydraulic gradient i is:
i = (h₁ − h₂) / L
The hydraulic gradient is a vector quantity whose sign (direction) denotes the movement of water. Following the convention used by this tool, a negative hydraulic gradient means the flow is downwards, while a positive hydraulic gradient signifies that the flow is upwards.
How to calculate hydraulic gradient
Find the hydraulic gradient if the heads are 5 m and 14 m at points 1 and 2, respectively, and the distance between the two points is 9 m.
- Enter the head at point 1, h₁ = 5 m.
- Insert the head at point 2, h₂ = 14 m.
- The calculator returns the change in head, Δh = −9 m.
- Fill in the distance between points 1 and 2, L = 9 m.
The hydraulic gradient calculator returns the answer as:
i = (h₁ − h₂) / L = (5 − 14) / 9 = −1 m/m
The answer −1 m/m implies the hydraulic head decreased 1 m for every meter of distance from point 1, and the water flow is downwards.
Units
This calculator supports both the metric system (heads and distances in meters) and the American / imperial system (heads and distances in feet). Because the hydraulic gradient is a ratio of two lengths, its value is dimensionless (m/m or ft/ft) and is the same in either system — only the change in head and the distance are reported in your chosen units (and in both, for comparison).
FAQs
What do you mean by hydraulic gradient?
The hydraulic gradient is the ratio of the change in hydraulic head to the distance between two points. It is a vector: the direction of the hydraulic gradient (or head gradient) gives the direction of water movement, while the magnitude tells us its significance.
How do I calculate hydraulic gradient?
To calculate the hydraulic gradient: find the hydraulic heads h₁ and h₂, find the difference between them (Δh), and divide that difference by the distance L between the two points. Mathematically: i = (h₁ − h₂) / L.
What do you mean by a positive hydraulic gradient?
A positive hydraulic gradient denotes upward flow, whereas a negative hydraulic head gradient implies the flow is downwards. The sign tells us the movement of water in aquifers and underground. It is also helpful when drawing potentiometric surface maps for areas of interest.