- Pressure head
**Pressure head**is a term used influid mechanics to represent theinternal energy of afluid due to thepressure exerted on its container. It may also be called**static pressure head**or simply**static head**(but not**static head pressure**). It is mathematically expressed as::$psi\; =\; frac\{p\}\{gamma\}\; =\; frac\{p\}\{\; ho\; ,\; g\}$where:$psi$ is pressure head (Length , typically in units of m);:$p$ is fluidpressure (Force per unitArea , often as Pa units); and:$gamma$ is thespecific weight (Weight per unitvolume , typically N·m^{−3}units):$ho$ is thedensity of the fluid (Mass per unitvolume , typically kg·m^{−3}):$g$ is acceleration due to gravity (rate of change of velocity, given in m·s^{−2})**Practical uses for pressure head**Fluid flow is measured with a wide variety of instruments. The

venturi meter in the diagram on the right 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 theworking fluid with another fluid having differentphysical properties .For example, if the original fluid was

water and we replaced it with mercury at the same pressure, we would expect to see a rather different value for pressure head. In fact, thespecific weight of water is 9.8 kN/m^{3}and the specific weight of mercury is 133 kN/m^{3}. So, for any particular measurement of pressure head, the height of the column of water will be about 13.6 times taller than the column of mercury would be (133/9.8 = 13.6). So if a water column meter reads "13.6 cm H_{2}O," then a coinciding measurement is "1.00 cm Hg."This example demonstrates why there is a bit of confusion surrounding pressure head and its relationship to pressure. Scientists frequently use columns of water (or mercury) to measure pressure, 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 forinstrumentation , 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, 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 $psi,$**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 happens as 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 zero gravity, the pressure head approaches "infinity ". 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 ", and is caused by a partialvacuum 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 doesn't leak out because the ambient pressure is greater than the pressure in the pipe.

* The above situations imply that theBernoulli equation , from which we obtain static pressure head, is extremely versatile.**ee also***Derivations of Bernoulli equation

*Hydraulic head , which includes a component of pressure head**References**See [

*http://www.engineeringtoolbox.com/density-specific-weight-gravity-d_290.html Engineering Toolbox article on Specific Weight*] See [*http://www.engineeringtoolbox.com/static-pressure-head-d_610.html Engineering Toolbox article on Static Pressure Head*]

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