thumb|upright=1.3|Available difference in hydraulic head across a [[hydroelectric dam, before head losses due to turbines, wall friction and turbulence]]
thumb|Fluid flows from the tank at the top to the basin at the bottom under the pressure of the hydraulic head.
thumb|Measuring hydraulic head in an [[artesian aquifer, where the water level is above the ground surface]]
Hydraulic head or piezometric head is a measurement related to liquid pressure (normalized by specific weight) and the liquid elevation above a vertical datum.
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. The hydraulic head can be used to determine a hydraulic gradient between two or more points.
Definition
In fluid dynamics, the head at some point in an incompressible (constant density) flow is equal to the height of a static column of fluid whose pressure at the base is equal to the static pressure at that point. As greater energy per unit volume corresponds to a taller column, head increases with energy per unit volume and serves as an alternate measure of it.
Head has dimension of length and is expressed in units such as meters or feet, whereas energy per unit volume has dimension of energy over volume, and is expressed in units such as Pa or psi. It may therefore be questioned whether one really is a measure of the other. This discrepancy can be resolved by noting that length is dimensionally equivalent to energy over weight (the higher a mass of liquid is raised, the greater its potential energy per unit weight), and remembering the restriction to incompressible (constant density) flow so that weight ∝ volume. It follows that while these measures of energy density are not equivalent, they do at least stand in a simple proportional relationship.
To justify this definition further, it can be noted that the aforementioned proportionality is practically useful in certain energy based analyses. For example, suppose we have a raised tank containing fluid flowing out through a pipe under the influence of gravity. We wish to know whether this system will produce a particular minimum flow rate through the pipes. Consider starting with the gravitational potential energy of the fluid in the tank and subtracting the energy that will be lost to friction from the pipe walls. If the result is negative, the energy losses must exceed the initial energy in the tank, implying that the desired flow rate cannot physically be sustained, so the tank must be raised. However, note that this conclusion depends only on whether the final result is positive or negative. Because head is proportional to energy per unit volume, it can stand in for energy in such an analysis. The elevation head (see below) is practically determined by simple measurement of the height of the tank and pipe outlets.
The hydrostatic pressure at the base of a column of fluid with density <math>\rho </math>, height <math>h</math> and gravitational acceleration <math>g</math>, as well as the potential energy per unit volume of a static fluid element at height <math>h</math> above datum, is <math>\rho g h</math>. The total energy per unit volume is given by Bernoulli's equation in pressure form with static pressure <math>p</math>, velocity <math>v</math> and height <math>z</math> as <math>p + \frac{1}{2}\rho v^2 + \rho g z</math>. Equating these and dividing by <math>\rho g</math> leads to, <math display="block">h = \frac{p}{\rho g} + \frac{v^2}{2g} + z</math>.
The individual terms can be interpreted as follows:
- <math>p/\rho g</math> is the pressure head due to the static pressure, the internal random molecular motion of the fluid.
- <math>\frac{v^2}{2g}</math> is the velocity head due to the bulk motion (kinetic energy) of the fluid.
- <math>z</math> is the elevation head due to the fluid's weight, the gravitational force acting on a column of fluid.
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).
Head is useful in specifying centrifugal pumps because their pumping characteristics tend to be independent of the fluid's density.
Components
After free falling through a height <math>h</math> in a vacuum from an initial velocity of 0, a mass will have reached a speed
<math display="block">v=\sqrt</math>
where <math>g</math> is the acceleration due to gravity. Rearranged as a head:
<math display="block">h = \frac{v^2}{2 g}.</math>
The term <math>\frac{v^{2{2 g}</math> is called the velocity head, expressed as a length measurement. In a flowing fluid, it represents the energy of the fluid due to its bulk motion.
The total hydraulic head of a fluid is composed of pressure head and elevation head.
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.
See also
- Borda–Carnot equation
- Dynamic pressure
- Minor losses in pipe flow
- Total dynamic head
- Stage (hydrology)
- Head (hydrology)
- Hydraulic accumulator
- Hydrogeology#Further reading