Water Head, Hydraulic Gradient, Permeability

Water Head:

Since we are explaining subtitle of a subtitle right now, this may seem like a detailed subject in soil mechanics at first… But actually the water head is a very important concept for water resources engineering, one of the five main branches of civil engineering, which we mentioned before briefly and will introduce in more detail later… Therefore we recommend to pay special attention below, if you did not know about this before.

In water resources engineering, water head is measured in distance units, such as in meters or feet.

“Total head of water”, has three components:

Total Head = Elevation head + Velocity Head + Pressure Head (all these three components are especially organized to give distance units, which you will see later)

In other words, water head increases as the elevation of water or velocity of water  or pressure of water increases.

Again, we emphasize that this is one of the most fundamental concepts in water resources branch of civil engineering. For now, just know that head is measured in distance units, such as meters or inches, and the total head is made of water’s elevation, velocity and pressure heads by adding them. 

Hydraulic Gradient:

Hydraulic gradient, is the total head loss of water, per unit length it flows. We have just defined what “water head”means above.

So when water flows from point A to point B, the hydraulic gradient, which is shown by “i” is:

So, hydraulic gradient is equal to the head difference between point A and B, divided by the distance over which that head loss occurred. In other words, it shows how much head is lost per unit length as we defined above. The higher the gradient, the more head loss occurs per the length of soil that water travels.

We said that head is in distance units. So it means that above we just divided distance by distance. It means, hydrulic gradient has no units.

Now since we know hydraulic gradient, let’s define permeability:


According to Darcy’s Law, water flow velocity through a porous medium such as soil, is directly proportional to that soil’s hydraulic gradient.


Water velocity, V goes up, when hydraulic gradient, i, goes up.

But this increase is of course not always one to one, but can be another constant than one. this constant, which is shown as “k”, is called the coefficient of permeability, or simply, permeability.



which means, velocity of water flowing through a porous medium is found by multiplying its permeability by its hydraulic gradient.

Velocity is distance / time, such as mph or m/s.

So this shows how fast water can flow through soil. Often times however, for engineers, this is not enough. They want to find the total water volume flowing per second, not just the distance per second. In that case, we can simply multiply this velocity by area, to find the flow of water in volume, through whatever area we multiplied the velocity with. Water flow volume is expressed by Q.

Groundwater 1


Q = A.V, where A is area, and V is velocity as above


Q = A.k.i

As we mentioned above soils vary greatly in terms of their permeability.

In the next post of this series, we will discuss “Flow Net”

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