How to do hydrostatic level measurement

1. Why level measurement by hydrostatic pressure?

Hydrostatic level measurement is a really simple and reliable method of measuring level. A submersible pressure transmitter or a standard pressure transmitter is lowered to or mounted at a specific depth (zero level). The transmitter then measures the pressure caused by the weight of the liquid directly on top of it. Due to the hydrostatic paradox, the pressure sensor does not measure the complete volume in the tank above it, but only the liquid column vertically above it. The hydrostatic level measurement is thus completely unaffected by the shape of reservoir or vessel, just measuring the level by the weight of the liquid column above it. If the liquid and its specific gravity are known, the pressure measurement can be calculated as the distance from the zero level, where the transmitter is located, to the surface of the liquid.

In contrary to most non-contact level measurement technologies, a hydrostatic level transmitter does not only allow to measure the current height of the surface level. It allows to monitor changes in level from any chosen reference point within the media, anywhere in between the bottom of the resource and its surface, as hydrostatic level transmitters are always installed below the surface level. Hence, hydrostatic level transmitters are unaffected by any disturbances of the liquid’s surface like overflow, flood or spill. As their installation point becomes the reference for zero meter or zero feet of level they allow to analyse and monitor the level of resources with unknown depths. Examples for such resources are underground water reservoirs, aquifers, rivers and lakes, as in all of these resources the surface level can vary heavily, especially in case of heavy rain or floods.


2. Submersible pressure transmitter vs. standard pressure transmitter?

First, you have to decide on which type of product you want to use. If you have an accessible tank and if you don’t mind to have a threaded bore in the bottom or side wall of your tank, you should use a standard pressure transmitter such as S-11, S-10 or IS-3. But if you have an underground reservoir, an in-ground basin or a tank which you don’t want to weaken by a threaded bore, you should use a submersible pressure transmitter, such as LS-10, LW-1 or LF-1, level probes that are lowered from the top of the tank or basin downwards into the media.


3. How to choose the right product for your hydrostatic level measurement?

Once you have decided whether you will use a standard pressure transmitter or a submersible one, for most applications you only need to define three to four simple things. The pressure connection (only if it is a standard transmitter for side-mounting), the measuring range, the accuracy and the electrical connection.

The pressure connection should fit to the threaded bore within your tank, while the measuring range should be chosen according to the level you want to measure in your application. If it is a stand-alone tank, you will know the level by the height of the tank, if it is an underground basin or reservoir, you need to decide how deep you want to submerse the level probe and choose a corresponding measuring range. Keep in mind, 10 metres of water column correspond to approximately 1.000 mbar (1 bar) or 14.5 psi.

The accuracy should be chosen according to the needs of your application, standard accuracy of <0.5 % will give you a possible error of max. 5 mm per metre of level, while highest accuracy variants with <0.1% will be as accurate as max. 1 mm per metre of level. Finally, you have to pick the electrical connection. If you have a standard pressure transmitter, you are free to pick a connector (such as M12 or DIN A) or cable outlet, while you have to stick with a cable anyhow when choosing a submersible pressure transmitter. If your transmitter features a cable connection, you need to choose the appropriate length to allow wiring from the transmitter to the control system and to allow for the immersion length when using a submersible pressure transmitter.


4. How to install and set up a hydrostatic level transmitter?

Having defined and ordered the pressure transmitter, you are ready to install and set up your hydrostatic level measurement system.

In case you have chosen a submersible pressure transmitter, you have to lower the unit via the cable into the media until you either reach the bottom of your tank, reservoir or underground resource, or until you have reached your desired zero level. You then run the cable from the tank or basin to your control system and connect the level probe to your PLC accordingly.

If you have a turbulent medium, you should use an additional sink weight to stabilise the level probe in the medium in order to get a stable pressure reading. To prevent any mechanical damaging of the cable, you can use cable clamps to fix the cable at the top of the tank or along the way when you run the cable to the control system.

If you have chosen a standard pressure transmitter, you simply screw the transmitter into the threaded bore at the bottom or the side of your tank. You then connect the transmitter with an appropriate cable connector to your PLC or you wire the transmitter, if a cable connection has been chosen, directly to the control system.


5. How to calculate level of liquids from hydrostatic pressure measurement?

The calculation of level is very simple if a few things are kept in mind. The hydrostatic pressure is influenced only by the distance of the measuring point from the surface, by the specific gravity and by the ambient pressure around the tank or basin, which “lies” as an additional pressure on top of the media.

If you have an open basin or a vented tank, no matter if you use a level probe or a standard transmitter, your transmitter should be a gauge pressure sensor to automatically eliminate the influence of the ambient pressure surrounding the tank. The level is then simply calculated by:

h = p / (ρ * g)

p = hydrostatic pressure [bar (gauge)]

ρ = specific gravity of the liquid [kg/m³]

g = gravitational force or gravitational acceleration [m/s²]

h = height of the liquid column [m] = level

Rule of thumb (media of density ~ 1.000 kg/m³): h = 1 bar (relative) / (1.000 kg/m³ * ~ 10 m/s²) = 10 m*

 

If you have a closed, non-vented tank, very common e.g. in the chemical industry, your measurement gets just a little bit more complicated. In a non-vented tank an amount of air is enclosed above the liquid and will cause additional pressure on the liquid. Therefore you will need one transmitter to measure the hydrostatic pressure for the actual level measurement and another one to measure the additional pressure of the enclosed gas phase, on top of the media surface within the tank. Both are best measured with standard transmitters, either both gauge sensors or both absolute pressure sensors. Then, your calculation changes slightly to the following:

h = (p2 - p1) / ((ρ * g)

p2 = hydrostatic pressure [bar]

p1= pressure of the enclosed gas in the vessel [bar]

ρ = specific gravity of the fluid [kg/m³]

g = gravitational force or gravitational acceleration [m/s²]

h = height of the liquid column [m] = level

Find further information on how to accurately calculate the level and how the mechanics behind this measurement procedure work in "Fundamentals of hydrostatic pressure measurement“.

*h = 1 bar (relative) / (1.000 kg/m³ * ~ 10 m/s²) = 1*10^5 N/m² / (1.000 kg/m³ *10m/s²) = 1*10^5 kg*m/s²*m²/(1.000 kg/m³ *10m/s²) = 10 m


6. How to increase the accuracy of your hydrostatic level measurement?

When you set up a hydrostatic level measurement system, you have to be aware that the level measurement is influenced by the specific gravity of the medium and the medium temperature, which is also affecting the specific gravity of the medium.

The specific gravity of the medium may not be stable, if the medium changes in its specific composition. If you take e.g. waste water or brine, a higher load of contamination or salt may increase the specific gravity of the medium. Therefore your hydrostatic pressure will show a higher reading, thus you will calculate an increase in level, while the real level may actually be lower than your calculation. If you do not see changes in the composition of the medium, e.g. you are always measuring the same specific medium, such as diesel, you can ignore this cause of change in the specific gravity by a varying medium.

Yet, the specific gravity can also change due to varying medium temperature. If the temperature increases, the specific gravity of the medium will reduce and the level will increase. But the hydrostatic pressure measurement may not reflect this change in level accurately.  Depending on the shape of the tank or basin the pressure could behave much differently than the increase in level caused by the temperature change. It could either indicate a decrease of level (if the tank widens towards the top), show a correct level (by chance the shape of the tank balances out the decrease of density) or even show an over-proportional increase of level (if tank shape narrows towards the top). These effects occur vice versa when the density increases due to a decrease of the ambient temperature.

To increase the accuracy of your hydrostatic level measurement you have to compensate for the temperature effects and for the change of specific gravity of the medium.


7. How to compensate for temperature effects in hydrostatic level measurement?

We know that the specific gravity changes due to changes in the medium temperature. Yet, it is easy to compensate for the temperature effects on the medium, if we know how the density changes due to increasing or decreasing temperature, e.g. by using a standard table for the medium, indicating the specific gravity for each degree of temperature.

A simple and economic additional sensor, such as a Pt100 temperature probe, or even an integrated temperature sensor within the pressure transmitter, can provide you with the needed temperature measurement. If you know the temperature behavior of the medium and how it changes its specific gravity, you can easily compensate for these effects in your control system and correct the level calculation by using the proper specific gravity according to the standard table.


8. How to compensate for specific gravity effects within the media in hydrostatic level measurement?

Changes in the specific gravity can be caused by temperature effects. But, if your mediumis changing its composition, a temperature measurement cannot provide you with a sufficient compensation for the change in specific gravity of the medium.

Still, it is also very easy to compensate for how the medium changes in its specific gravity due to variations of its composition, like e.g. in wastewater or brine. A second hydrostatic pressure sensor, thus a second level probe or a second side-mounted pressure transmitter, should be positioned a little bit above the first level sensor, in a known distance between each other. You will now have two pressure readings and as you know the difference in the position of your two sensors, you can calculate first the specific gravity and second correct your level calculation by the specific gravity. Thus, you will now be able to calculate level accurately.

The specific gravity is calculated as follows:

ρ = (p1 – p2) /  g * (h1 – h2)

ρ = density of the fluid [kg/m³]

p1 = hydrostatic pressure of the lower sensor [bar]

p2 = hydrostatic pressure of the upper sensor [bar]

g = gravitational force or gravitational acceleration [m/s²]

h1 – h2 = distance between the two sensors


Now, you have very accurately calculated the specific gravity of the medium. It is now possible to calculate your current level precisely by this standard formula:

h = p / (ρ * g)

p = hydrostatic pressure of the lower or upper sensor [bar (gauge)]

ρ = specific gravity of the liquid [kg/m³]

g = gravitational force or gravitational acceleration [m/s²]

h = height of the liquid column [m] = level


9. How to cope with steam, foam, dust, spider webs, build-up and other disturbances?

The answer to this question is very simple. Different to many non-contact level measurement technologies, the hydrostatic level measurement is extremely tolerant to disturbances.

Submersible or standard pressure transmitters are positioned in direct contact with the medium at a measuring point below the surface level. Therefore they are not affected by any disturbance above the surface level such as foam, dust, water splashes or spider webs which would impede an accurate measurement by ultrasonic or radar devices.

Even as this technology is in direct contact to the medium, build-up, contamination, particles, etc. do not disturb the sensor. As long as these disturbances are not allowed to dry up on the sensor, thus the sensor is always wetted with medium, the medium and any build-up will transfer the hydrostatic pressure to the pressure sensor. If the tank or basin is emptied and build-up is allowed to dry on the pressure sensor, it can easily be cleaned by using a cloth or rinsing it with water as part of the scheduled maintenance.

For these reasons, hydrostatic level measurement is one of the most reliable technologies you can find in the market.


10. How to monitor the volume by hydrostatic level measurement?

Very often, level is measured by hydrostatic pressure measurement, while the real target is to monitor the volume of the medium within the tank or basin. As the hydrostatic pressure is not influenced by the shape of the vessel and therefore also not by its volume, the volume has to be calculated within the control system based on the current level measured.

To calculate the volume of a vessel, the shape of it has to be programmed into the control system by using a so-called tank linearisation table, basically a simple table containing a corresponding set of volumes to different fill levels of the tank. The control system usually uses linear functions to calculate a volume for any measured hydrostatic pressure.


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