Level measurement by using hydrostatic pressure respectively level sensors is the most popular solution for level measurement applications by far, due to its simple way of installation and ease of use. Yet, when using a hydrostatic pressure sensor to measure changes in fill level, it is essential to calculate the filling height of a vessel correctly from the pressure measurement value to get an accurate level measurement.

So, how does one calculate, from the hydrostatic pressure, the filling height of an open vessel, an open body of water or a deep well? And what is the relation between filling level of liquids and the pressure reading? In my last post, I introduced how hydrostatic level measurement works. The hydrostatic pressure is used to determine the level through the measurement of the liquid column and is directly proportional to the filling height, as well as to the specific gravity of the medium and the force of gravity. Under the influence of gravity, the hydrostatic pressure rises with the increasing height of the liquid column, thus with the filling height of the vessel.

Hence the level is calculated from the formula: h = p / (ρ * g) p = hydrostatic pressure [bar relative] ρ = specific gravity of the fluid [kg/m³] g = gravitational force or gravitational acceleration [m/s²] h = height of the liquid column [m] For further calculation by different units, please find here a helpful “Unit converter”

Rule of thumb – Water:                h = 1 bar relative / (1000 kg/m³ * ~ 10 m/s²) = 10 m

For the medium water, one can adopt the rule of thumb that a pressure of 1 bar corresponds to a filling height of 10 m. This rule of thumb can be used for selection and specification of a suitable submersible pressure transmitter or pressure transmitter. Using the level measurement as a controlled variable, however, a more-precise calculation should be performed, which includes the influence of temperature on the density, as well as the location-dependent force of gravity in the level calculation.

As the specific gravity of a medium can significantly deviate from the specific gravity of water, this rule of thumb only applies to liquids with a density close to water. Thus, for example, with the same filling height of diesel and water, the hydrostatic pressure of diesel is much lower than that of water.

Example –  Diesel fuel:  h = 0.82 bar relative / (820 kg/m³ * ~ 10 m/s²) = 10 m

The difference in density has, in this example, led to a measuring error of around 22 %. In hydrostatic level measurement in open basins and vessels, a pressure equalisation takes place between the gas above the liquid and the ambient air, thus, the pressure of the gas / ambient air on top of the media must not be included in the calculation of the level.

By using submersible pressure transmitters, such as the WIKA model LH-20, a special cable design of the level probe, automatically compensates for the fluctuating ambient pressure outside the vented tank and always gives you a correct level measurement.

In my next blog post, I will therefore explain the calculation of the filling height in closed geometries or vessels, and clarify the effect of the enclosed gas on the level measurement. WIKA offers various solutions for the hydrostatic pressure measurement of level.

Your contact person will assist you in selecting the sensor which is most suitable for your application.

Please find further information on this topic on our information platform “Hydrostatic level measurement”