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Engineering ToolBox > Static Pressure and Pressure Head in Fluids
The pressure indicates the normal force per unit area at a given point acting on a given plane. Since there is no shearing stresses present in a fluid at rest - the pressure in a fluid is independent of direction.
For fluids - liquids or gases - at rest the pressure gradient in the vertical direction depends only on the specific weight of the fluid.
How pressure changes with elevation can be expressed as
dp = - γ dz (1)
where
dp = change in pressure
dz = change in height
γ = specific weight
The pressure gradient in vertical direction is negative - the pressure decrease upwards.
Specific Weight can be expressed as:
γ = ρ g (2)
where
γ = specific weight
g = acceleration of gravity
In general the specific weight - γ - is constant for fluids. For gases the specific weight - γ - varies with the elevation.
For a incompressible fluid - as a liquid - the pressure difference between two elevations can be expressed as:
p2 - p1 = - γ (z2 - z1) (3)
where
p2 = pressure at level 2
p1 = pressure at level 1
z2 = level 2
z1 = level 1
(3) can be transformed to:
p1 - p2 = γ (z2 - z1) (4)
or
p1 - p2 = γ h (5)
where
h = z2 - z1 difference in elevation - the dept down from location z2.
or
p1 = γ h + p2 (6)
(6) can be transformed to:
h = (p2 - p1) / γ (6)
h express the pressure head - the height of a column of fluid of specific weight - γ - required to give a pressure difference of (p2 - p1).
A pressure difference of 5 psi (lbf/in2) is equivalent to
5 (lbf/in2) 12 (in/ft) 12 (in/ft) / 62.4 (lb/ft3) = 11.6 ft of water
5 (lbf/in2) 12 (in/ft) 12 (in/ft) / 847 (lb/ft3) = 0.85 ft of mercury
when specific weight of water is 62.4 (lb/ft3) and specific weight of mercury is 847 (lb/ft3).
Heads at different velocities can be taken from the table below:
| Velocity (ft/sec) | Head Water (ft) |
| 0.5 | 0.004 |
| 1.0 | 0.016 |
| 1.5 | 0035 |
| 2.0 | 0.062 |
| 2.5 | 0.097 |
| 3.0 | 0.140 |
| 3.5 | 0.190 |
| 4.0 | 0.248 |
| 4.5 | 0.314 |
| 5.0 | 0.389 |
| 5.5 | 0.470 |
| 6.0 | 0.560 |
| 6.5 | 0.657 |
| 7.0 | 0.762 |
| 7.5 | 0.875 |
| 8.0 | 0.995 |
| 8.5 | 1.123 |
| 9.0 | 1.259 |
| 9.5 | 1.403 |
| 10.0 | 1.555 |
| 11.0 | 1.881 |
| 12.0 | 2.239 |
| 13.0 | 2.627 |
| 14.0 | 3.047 |
| 15.0 | 3.498 |
| 16.0 | 3.980 |
| 17.0 | 4.493 |
| 18.0 | 5.037 |
| 19.0 | 5.613 |
| 20.0 | 6.219 |
| 21.0 | 6.856 |
| 22.0 | 7.525 |