Pressure head

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In fluid mechanics, 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:

${\displaystyle \psi ={\frac {p}{\gamma }}={\frac {p}{\rho \,g}}}$

where

${\displaystyle \psi }$ is pressure head (which is actually a

centimetres of water

)

${\displaystyle p}$ is fluid pressure (i.e. force per unit area, typically expressed in pascals)

${\displaystyle \gamma }$ is the specific weight (i.e. force per unit volume, typically expressed in N/m³ units)

${\displaystyle \rho }$ is the density of the fluid (i.e. mass per unit volume, typically expressed in kg/m³)

${\displaystyle g}$ 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

Head equation

Pressure head is a component of

${\displaystyle h_{v}+z_{\text{elevation}}+\psi =C\,}$

where

${\displaystyle h_{v}}$ is velocity head,

${\displaystyle z_{\text{elevation}}}$ is elevation head,

${\displaystyle \psi }$ is pressure head, and

${\displaystyle C}$ is a constant for the system

Practical uses for pressure head

Venturi meter

with two pressure instruments open to the ambient air. (${\displaystyle p>0}$ and ${\displaystyle g>0}$) If the meter is turned upside down, we say by convention that ${\displaystyle g<0}$ and the fluid inside the vertical columns will pour out the two holes. See discussion below.

For example, if the original fluid was

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

• 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, the pressure head approaches infinity. Fluid in the pipe may "leak out" of the top of the vertical columns (assuming ${\displaystyle p>0}$).
• 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 ${\displaystyle p>0}$).
• If ${\displaystyle p<0}$ and ${\displaystyle g>0}$, 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 partial vacuum inside the vertical columns. In many venturis, the column on the left has fluid in it (${\displaystyle \psi >0}$), while only the column on the right is a siphon (${\displaystyle \psi <0}$).
• If ${\displaystyle p<0}$ and ${\displaystyle g<0}$, 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

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

• Centimetre of water
• Pressure measurement
• velocity head
  , which includes a component of pressure head
• Venturi effect

External links

• Engineering Toolbox article on Specific Weight
• Engineering Toolbox article on Static Pressure Head