Pipes and tank in a factory

Hydrostatic pressure

We answer basic questions about hydrostatic pressure, e.g. how it is defined, how it works and what effects this has on the measurement. Of course, we also address applications of hydrostatic pressure measurement.

Hydrostatic pressure is the pressure that is generated by gravity, i.e. by weight force, in a non-flowing liquid. The hydrostatic pressure ph is a measurand that results from the density ρ of the medium, the gravitational constant g, and the height h of the liquid column.

What factors influence hydrostatic pressure?

As mentioned above, the physical quantities that affect the hydrostatic pressure ph:

  • is the gravitational acceleration constant g [m/s²],
  • is the height of the liquid column h [m],
  • the density of the liquid to be tested ρ [kg/m³] and
  • the external pressure p[Pa].

What is the formula underlying hydrostatic pressure?

In the previous section, all physical quantities that influence the hydrostatic pressure of a liquid on the bottom of a vessel were listed. This results in the following formula for the hydrostatic pressure:

ph = ρ × g× h

What is the unit of hydrostatic pressure?

The unit of pressure is Pascal [Pa], the basic SI unit of pressure. It is defined as the pressure of gravity F of 1N on a surface of 1 m2. Here, the value of 1N corresponds to the force defined as the unit of mass of 1 kilogram multiplied by the acceleration due to gravity g = 10m/s2.

Sample calculation:

Density of the liquid (water at 4 °C):             ρ = 1000 kg/m³
Height of the liquid level:                                h = 15 m
Gravitational constant:                                    g = 9.81 m/s²
p(h) = 1000 kg/m³ × 9.81 m/s² × 15 m
p(h) = 1471.5 hPa = 1.47 bar

➔ A meter water column produces a hydrostatic pressure of approx. 0.1 bar.

What is the Hydrostatic Paradox?

The hydrostatic paradox describes the apparent phenomenon that the pressure prevailing at the bottom of a container filled with liquid does not depend on the shape of the container, and therefore does not depend on its capacity. Instead it depends solely on the level height.

Fig. 1: Hydrostatic paradox

What must be considered when mounting the sensor?

The mounting position of the sensor membrane also does not play a role when it comes to hydrostatic measurements. The pressure acts in all directions at any altitude. A pressure transmitter can be mounted on the side of the tank or suspended inside the tank as a level probe. The only decisive factor for the measurement result is the mounting height – the measurement is only performed once the membrane is fully covered.

Fig. 2: Hydrostatic probe JUMO MAERA S25 for level measurement