Geol 121Hydrology
Prof. J Bret Bennington
Hydrology
Hydraulic Head
Reading assignment: Chapter 4, pg. 113 - 122
Hydraulic Head
Hydraulic head has been defined as the water level above a zero datum (mean sea level)
of water in a well tapping an aquifer that is open to the atmosphere.
We have a pretty good idea that the hydraulic head represents some kind of flow potential
- water flows from regions of high hydraulic head to regions of low hydraulic head.
Hydraulic head is actually a measure of potential energy.
Energy is the same as work, that is to say a force applied moving a mass over a distance.
Potential energy is the potential to do work - to move something over some distance.
There are three types of energy possessed by a fluid in an aquifer.
The first is the kinetic energy of the fluid. This is the energy of motion that any moving
mass has. The formula for kinetic energy is...
Ek = 21 mv 2
Notice the large contribution of velocity to kinetic energy. Because groundwater moves
very slowly, the amount of kinetic energy that it possesses in relation to the two other
types of energy it has is trivial. Thus we can safely ignore kinetic energy from here on.
The second type of energy possessed by fluids in an aquifer is gravitational potential
energy.
This is the energy that a mass has in a gravitational field sitting above a zero datum. It is
equivalent to the work that was done lifting the mass above the datum.
For example, one might imagine a car driving to the top of a hill. At the top of the hill
the car has gained in potential energy equal to the work it too to push the car from the
bottom to the top of the hill. If the car coasted to the top of the hill then its kinetic energy
was transformed into gravitational potential energy as it climbed the hill.
The equation for gravitational potential energy is...
Eg = 12 mgz
Geol 121Hydrology
Prof. J Bret Bennington
where z is the distance above the datum.
A fluid mass has another component of potential energy owing to the pressure of the
surrounding fluid acting on it. Pressure is the force per unit area acting on a body...
P=F/ A
So, the total energy of a fluid mass is...
Et = mgz + P
To cut to the chase, if we normalize this equation to express the energy per unit weight of
fluid (this process can be followed in the textbook reading), we get the total mechanical
energy per unit weight of fluid, which has units of Length and is called the hydraulic
head.
From the above equation, we would expect hydraulic head to have two components, one
based on height (z) and one based on pressure (P). Indeed, the normalized equation has
two length components...
ht = z + h p
What are these components? If we imagine a well sunk into an aquifer that is open at the
top and screened at the bottom...
The distance from the water level in the well to the zero datum (sea-level) is the total
hydraulic head.
The distance from the datum to the well screen at the base of the well is the head
produced by the gravitational potential energy of the water at the measuring point at the
well screen. This is called the elevation head (z).
The distance from the well screen to the water level inside the well is the head produced
by pressure and is called the pressure head (hp).
Geol 121Hydrology
Prof. J Bret Bennington
Piezometers
This well that we have been using to measure hydraulic head is more than just a well, it is
a piezometer. Piezometers must be impermeable throughout their length (a cased well)
and open at the end in the aquifer as well as the end in the atmosphere above the surface.
Note that because we live on the surface and drill wells downward, measurements of
head are usually given as distances down from the elevation of the top of the well. Thus,
for the following data:
top of well - 225’
water level - 30’
bottom of well - 55’
Total head = 225-30 = 195’
Elevation head = 225-55 = 170’
Pressure head = 195-170 = 25’
Remember, water will always flow from higher to lower total hydraulic head. Given a
sufficient elevation head, water will flow from a region of low pressure to a region of
high pressure. Likewise, given a sufficient pressure head, water will flow from lower to
higher elevations.
Now, hydraulic head as we understand it now is well and good as long as the fluid in all
of the wells in the region of study contain fluid of the same density.
This is not always the case. Sometimes the salinity of the groundwater changes over
distance.
For example, let’s consider two wells, one salty and one fresh. The water in the more
saline well is denser than the water in the fresh water well. This makes the hydraulic
heads of the two wells impossible to compare directly.
Why? Imagine if the total head in each well is the same. The elevation heads will be
equivalent because elevation of the fluid does not depend on density. However, the
height of the pressure head depends on the pressure of the surrounding fluid pushing the
fluid up the well. Because saltwater is more dense than freshwater, it takes more pressure
to raise a column of saltwater to the same height as a column of freshwater. So, even at
equal heads, the saltwater pressure head has more potential energy - more pressure.
Point-water pressure head: The level of water in a well that will just balance the
pressure at the base of the well = pressure head as measured in the field.
Fresh-water pressure head: The level of fresh water in a well that will just balance the
pressure at the base of the well.
Geol 121Hydrology
Prof. J Bret Bennington
If all of the wells of interest are freshwater, then the point-water head and the fresh-water
head are the same.
If, however, some of the wells are of variable salinity, then all point-water heads
measured in the field must be converted to equivalent fresh-water heads before hydraulic
gradients can be analyzed.
The equation to convert point-water pressure head to equivalent fresh-water pressure
head is...
hf =
ρp
ρf
hp
Unfortunately, this conversion into equivalent freshwater heads allows for accurate
modelling of flow only in vertically variable aquifers. In aquifers where the salinity
gradient is horizontal, the different density of the fluid affects lateral flow as well as the
hydraulic gradient, making it more difficult to model.
Pressure and pressure head
One can calculate the hydraulic pressure in the aquifer at the base of a well (if the well is
being used as a piezometer, we are measuring at the point where the well is
screened).
All we need to know is the pressure head of the well, and the following formula:
P = ρgh p
The pressure is proportional to the force that is needed to raise fluid of density (rho)
against the force of gravity (g) to a height of hp.
For Example:
If the pressure head on a well is 12 M, and the density of the water is 1001 kg/M3,
what is the pressure at the well screen?
P = 1018 kg/M3 x 9.8 M/sec2 x 12 M = 1.2 X105 kg /M sec2 = N/M2
While we are at it, why don’t we calculate the freshwater pressure head in this well?
Notice that the water is more dense than 1000 kg/M3. It must be somewhat saline.
Remembering the equation for converting point head to pressure head...
Geol 121Hydrology
Prof. J Bret Bennington
hf =
ρp
ρf
hp
hf = 1018/1000 x 12 M = 12.2 M fresh water pressure head.