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fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...
, pressure head is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column on the base of its container. It may also be called static pressure head or simply static head (but not ''static head pressure''). Mathematically this is expressed as: :\psi = \frac = \frac where :\psi is pressure head (which is actually a
length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), base unit for length is chosen, ...
, typically in units of meters or centimetres of water) :p is fluid
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
(i.e.
force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
per unit
area Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-di ...
, typically expressed in pascals) :\gamma is the
specific weight Specific may refer to: * Specificity (disambiguation) * Specific, a cure or therapy for a specific illness Law * Specific deterrence, focussed on an individual * Specific finding, intermediate verdict used by a jury in determining the fin ...
(i.e. force per unit
volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
, typically expressed in N/m3 units) :\rho is the
density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
of the fluid (i.e.
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
per unit volume, typically expressed in kg/m3) :g is acceleration due to gravity (i.e. rate of change of velocity, expressed in m/s2). Note that in this equation, the pressure term may be gauge pressure or
absolute pressure Pressure measurement is the measurement of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in unit of measurement, units of force per unit of surface area. Many techniques have been developed for the me ...
, depending on the design of the container and whether it is open to the ambient air or sealed without air.


Head equation

Pressure head is a component of
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., 410 pages. See pp. 43–44., 650 pages. See p. 22, eq.3.2a. It is usually meas ...
, in which it is combined with elevation head. When considering dynamic (flowing) systems, there is a third term needed: velocity head. Thus, the three terms of ''velocity head'', ''elevation head'', and ''pressure head'' appear in the head equation derived from the Bernoulli equation for incompressible fluids: :h_ + z_\text + \psi = C\, where :h_ is velocity head, :z_\text is elevation head, :\psi is pressure head, and :C is a constant for the system


Practical uses for pressure head

Fluid flow is measured with a wide variety of instruments. The venturi meter in the diagram on the left shows two columns of a measurement fluid at different heights. The height of each column of fluid is proportional to the pressure of the fluid. To demonstrate a classical measurement of pressure head, we could hypothetically replace the working fluid with another fluid having different physical properties. For example, if the original fluid was
water Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...
and we replaced it with mercury at the same pressure, we would expect to see a rather different value for pressure head. In fact the
specific weight Specific may refer to: * Specificity (disambiguation) * Specific, a cure or therapy for a specific illness Law * Specific deterrence, focussed on an individual * Specific finding, intermediate verdict used by a jury in determining the fin ...
of water is 9.8 kN/m3 and the specific weight of mercury is 133 kN/m3. So, for any particular measurement of pressure head, the height of a column of water will be about 33/9.8 = 13.613.6 times taller than a column of mercury would be. So if a water column meter reads "13.6 cm H2O", then an equivalent measurement is "1.00 cm Hg". This example demonstrates why there is some confusion surrounding pressure head and its relationship to pressure. Scientists frequently use columns of water (or mercury) to measure pressure (manometric
pressure measurement Pressure measurement is the measurement of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pressu ...
), since for a given fluid, pressure head is proportional to pressure. Measuring pressure in units of " mm of mercury" or " inches of water" makes sense for
instrumentation Instrumentation is a collective term for measuring instruments, used for indicating, measuring, and recording physical quantities. It is also a field of study about the art and science about making measurement instruments, involving the related ...
, but these raw measurements of head must frequently be converted to more convenient pressure units using the equations above to solve for pressure. In summary pressure head is a measurement of length, which can be converted to the units of pressure (force per unit area), as long as strict attention is paid to the density of the measurement fluid and the local value of g.


Implications for gravitational anomalies on ''ψ''

We would normally use pressure head calculations in areas in which g is constant. However, if the gravitational field fluctuates, we can prove that pressure head fluctuates with it. * If we consider what would happen if gravity ''decreases'', we would expect the fluid in the venturi meter shown above to withdraw from the pipe ''up'' into the vertical columns. ''Pressure head is increased''. * In the case of
weightlessness Weightlessness is the complete or near-complete absence of the sensation of weight, i.e., zero apparent weight. It is also termed zero g-force, or zero-g (named after the g-force) or, incorrectly, zero gravity. Weight is a measurement of the fo ...
, the pressure head approaches ''
infinity Infinity is something which is boundless, endless, or larger than any natural number. It is denoted by \infty, called the infinity symbol. From the time of the Ancient Greek mathematics, ancient Greeks, the Infinity (philosophy), philosophic ...
''. Fluid in the pipe may "leak out" of the top of the vertical columns (assuming p>0). * To simulate negative gravity, we could turn the venturi meter shown above upside down. In this case gravity is negative, and we would expect the fluid in the pipe to "pour out" the vertical columns. Pressure head is negative (assuming p>0). * If p<0 and g>0, we observe that the ''pressure head is also negative'', and the ambient air is sucked into the columns shown in the venturi meter above. This is called a ''
siphon A siphon (; also spelled syphon) is any of a wide variety of devices that involve the flow of liquids through tubes. In a narrower sense, the word refers particularly to a tube in an inverted "U" shape, which causes a liquid to flow upward, abo ...
'', and is caused by a partial
vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
inside the vertical columns. In many venturis, the column on the left has fluid in it (\psi>0), while only the column on the right is a siphon (\psi<0). * If p<0 and g<0, we observe that the pressure head is again positive, predicting that the venturi meter shown above would look the same, only upside down. In this situation, gravity causes the working fluid to plug the siphon holes, but the fluid does not leak out because the ambient pressure is greater than the pressure in the pipe. * The above situations imply that the Bernoulli equation, from which we obtain static pressure head, is extremely versatile.


Applications


Static

A mercury barometer is one of the classic uses of
static pressure In fluid mechanics the term static pressure refers to a term in Bernoulli's equation written words as ''static pressure + dynamic pressure = total pressure''. Since pressure measurements at any single point in a fluid always give the static pres ...
head. Such barometers are an enclosed column of mercury standing vertically with gradations on the tube. The lower end of the tube is bathed in a pool of mercury open to the ambient to measure the local
atmospheric pressure Atmospheric pressure, also known as air pressure or barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1,013. ...
. The reading of a mercury barometer (in mm of Hg, for example) can be converted into an
absolute pressure Pressure measurement is the measurement of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in unit of measurement, units of force per unit of surface area. Many techniques have been developed for the me ...
using the above equations. If we had a column of mercury 767 mm high, we could calculate the atmospheric pressure as (767 mm)•(133 kN/m3) = 102 kPa. See the
torr The torr (symbol: Torr) is a Pressure#Units, unit of pressure based on an absolute scale, defined as exactly of a standard atmosphere (unit), atmosphere (101325 Pa). Thus one torr is exactly (≈ ). Historically, one torr was intended to be ...
, millimeter of mercury, and
pascal (unit) The pascal (symbol: Pa) is the unit of pressure in the International System of Units (SI). It is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is an ...
articles for barometric pressure measurements at standard conditions.


Differential

The venturi meter and
manometer Pressure measurement is the measurement of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pressu ...
is a common type of flow meter which can be used in many
fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...
applications to convert differential pressure heads into
volumetric flow rate In physics and engineering, in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, or volume velocity) is the volume of fluid which passes per unit time; usually it is represented by the symbol (sometimes \do ...
, linear fluid
speed In kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a non-negative scalar quantity. Intro ...
, or mass flow rate using
Bernoulli's principle Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally Bernoulli's principle states that an increase in the speed occurs simultaneously with a decrease i ...
. The reading of these meters (in inches of water, for example) can be converted into a differential, or gauge pressure, using the above equations.


Velocity head

The pressure of a fluid is different when it flows than when it is not flowing. This is why
static pressure In fluid mechanics the term static pressure refers to a term in Bernoulli's equation written words as ''static pressure + dynamic pressure = total pressure''. Since pressure measurements at any single point in a fluid always give the static pres ...
and dynamic pressure are never the same in a system in which the fluid is in motion. This pressure difference arises from a change in fluid velocity that produces velocity head, which is a term of the Bernoulli equation that is zero when there is no bulk motion of the fluid. In the picture on the right, the pressure differential is entirely due to the change in velocity head of the fluid, but it can be measured as a pressure head because of the Bernoulli principle. If, on the other hand, we could measure the velocity of the fluid, the pressure head could be calculated from the velocity head. See the Derivations of Bernoulli equation.


See also

*
Centimetre of water A centimetre or millimetre of water (US spelling ''centimeter'' or ''millimeter of water'') are less commonly used measures of pressure based on the pressure head of water. Centimetre of water A ''centimetre of water''NOTE: A centimetre of wate ...
*
Pressure measurement Pressure measurement is the measurement of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pressu ...
*
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., 410 pages. See pp. 43–44., 650 pages. See p. 22, eq.3.2a. It is usually meas ...
or velocity head, which includes a component of pressure head * Venturi effect


External links


Engineering Toolbox article on Specific Weight
{{DEFAULTSORT:Pressure Head Fluid dynamics Pressure