# How to calculate the hydrostatic head pressure

## Hydrostatic level measurement in closed geometries - calculation of the level

In my last blog article I presented the calculation of the fill level in open geometries and containers. In contrast to open containers, the calculation of the level in closed geometries such as encapsulated tanks or containers requires a compensation of the pressure of the gas enclosed above the liquid with the measurement result of the hydrostatic pressure measurement.

A level measurement in closed, i.e. unventilated, containers therefore requires an additional pressure measurement of the enclosed gas with a second pressure sensor. In closed containers, the pressure measurement is primarily carried out by conventional pressure sensors that are installed in the side of the container or tank.

How do you calculate the fill level of a closed, non-ventilated tank or container from the hydrostatic pressure?

The level in a closed container is calculated using the following formula:

h = (p2 - p1) / (ρ * g)
p2 = hydrostatic pressure [bar]
p1= Pressure of the enclosed gas in the container [bar]
ρ = density of the liquid [kg / m³]
g = gravity or acceleration due to gravity [m / s²]
h = height of the liquid column [m]

If you measure a volatile medium such as gasoline in an encapsulated, non-ventilated tank, an overpressure builds up above the liquid which, due to the lack of ventilation, cannot equalize with the ambient pressure. This overpressure must be measured by a further pressure sensor, since this gas trapped above the liquid causes a higher hydrostatic pressure without any real change in the fill level.

Example of an incorrect fill level calculation:
p2 (Measurement at the bottom of the tank) = 2 bar
p1 (Measurement of gas pressure) = 1.2 bar
p1-typ (typical gas pressure) = 1.3 bar
ρ = 750 kg / m³
g = 9.81 m / s²

With a compensation of the gas pressure to the measured value, the filling level can be measured very precisely by the hydrostatic pressure.

With gas pressure measurement: h = (2 bar - 1.2 bar) / (750 kg / m³ * 9.81 m / s²) = 10.9 m

However, if you decide to forego the additional pressure measurement of the enclosed gas and work with an estimate z. B. on the basis of the typically prevailing gas pressure, even small pressure fluctuations in the process can lead to large errors in the calculation of the level.

Without gas pressure measurement: h = (2 bar - 1.3 bar) / (750 kg / m³ * 9.81 m / s²) = 9.5 m

So you can see that a small fluctuation in the gas pressure of 100 mbar in this very realistic example already leads to a large measurement error of approx. 13% of the fill level. In particular, the example of under-measurement could result in a process-critical error such as the medium escaping from the tank or contamination of the other process tanks. It is therefore essential to compensate for the gas pressure in the level calculation in closed, non-ventilated containers.

Note
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