Hydraulic head
Hydraulic head or piezometric head is a measurement related to liquid pressure (normalized by specific weight) and the liquid elevation above a vertical datum.
[1][2] It is usually measured as an equivalent liquid surface elevation, expressed in units of length, at the entrance (or bottom) of a piezometer.
In an aquifer, it can be calculated from the depth to water in a piezometric well (a specialized water well), and given information of the piezometer's elevation and screen depth.
Hydraulic head can similarly be measured in a column of water using a standpipe piezometer by measuring the height of the water surface in the tube relative to a common datum.
On Earth, additional height of fresh water adds a static pressure of about 9.8 kPa per meter (0.098 bar/m) or 0.433 psi per foot of water column height.
The static head of a pump is the maximum height (pressure) it can deliver.
The capability of the pump at a certain RPM can be read from its Q-H curve (flow vs. height).
[1][2] The pressure head is the equivalent gauge pressure of a column of water at the base of the piezometer, and the elevation head is the relative potential energy in terms of an elevation.
The head equation, a simplified form of the Bernoulli principle for incompressible fluids, can be expressed as:
where In an example with a 400 m deep piezometer, with an elevation of 1000 m, and a depth to water of 100 m: z = 600 m, ψ = 300 m, and h = 900 m. The pressure head can be expressed as:
is the gauge pressure (Force per unit area, often Pa or psi), The pressure head is dependent on the density of water, which can vary depending on both the temperature and chemical composition (salinity, in particular).
This means that the hydraulic head calculation is dependent on the density of the water within the piezometer.
It also has applications in open-channel flow where it is also known as stream gradient and can be used to determine whether a reach is gaining or losing energy.
This requires a hydraulic head field, which can be practically obtained only from numerical models, such as MODFLOW for groundwater or standard step or HEC-RAS for open channels.
This vector can be used in conjunction with Darcy's law and a tensor of hydraulic conductivity to determine the flux of water in three dimensions.
The distribution of hydraulic head through an aquifer determines where groundwater will flow.
However, if there is a difference in hydraulic head from the top to bottom due to draining from the bottom (second figure), the water will flow downward, due to the difference in head, also called the hydraulic gradient.
Often detailed observations of barometric pressure are not available at each well through time, so this is often disregarded (contributing to large errors at locations where hydraulic gradients are low or the angle between wells is acute.)
The effects of changes in atmospheric pressure upon water levels observed in wells has been known for many years.
Pascal first qualitatively observed these effects in the 17th century, and they were more rigorously described by the soil physicist Edgar Buckingham (working for the United States Department of Agriculture (USDA)) using air flow models in 1907.
For relatively short pipe systems, with a relatively large number of bends and fittings, minor losses can easily exceed major losses.
In design, minor losses are usually estimated from tables using coefficients or a simpler and less accurate reduction of minor losses to equivalent length of pipe, a method often used for shortcut calculations of pneumatic conveying lines pressure drop.
