How hydrostatic level measurement works
A liquid column presses on the bottom of a tank with a pressure that depends only on its height and density, not on the tank’s shape or volume. A pressure transmitter at the bottom, or a submersible probe hanging in the liquid, therefore measures level:
p = ρ × g × h
where ρ is the density in kg/m³, g the gravitational acceleration and h the height of liquid above the diaphragm. With standard gravity, one metre of water at 20 °C gives 9.789 kPa, or 97.89 mbar.
Choosing the transmitter range
The transmitter is calibrated so that 4 mA corresponds to the lowest level you want to measure and 20 mA to the highest:
LRV = ρ × g × (hmin + h0) URV = ρ × g × (hmax + h0)
h0 is the height of the zero level above the transmitter. A transmitter mounted on a nozzle 0.3 m below the tank floor always sees 0.3 m of extra liquid; the LRV is then above zero (“elevated zero”). The span stays the same.
Choose a transmitter whose upper range limit is at or somewhat above the URV, so that the calibrated span uses a good part of the sensor’s range. A sensor with a much larger range turns down further and its errors, usually stated as a percentage of the upper range limit, become large compared with the span; check this with the transmitter accuracy calculator.
Worked example
A water tank at about 20 °C, level 0 to 5 m, transmitter at the tank floor:
- Density 998.21 kg/m³, pressure per metre 9.789 kPa
- LRV 0 bar, URV 0.48945 bar (489.45 mbar)
- A level of 3 m gives 0.29367 bar, 60 % of span, 13.6 mA
If the same transmitter sits 0.5 m below the floor, the range becomes 0.04895 to 0.53840 bar; the span is unchanged.
Density and temperature
Density is the largest source of error in hydrostatic level. Water is 999.97 kg/m³ at 4 °C, 998.21 kg/m³ at 20 °C and 983.20 kg/m³ at 60 °C: a tank calibrated cold reads 1.5 % low when the water is at 60 °C. Brines, oils, acids and slurries differ much more, and their density can change with concentration. Use the density at the operating temperature from the process data sheet, or measure it.
Open, closed and pressurised tanks
Open or vented tanks. A gauge pressure transmitter or a vented submersible probe measures the liquid head directly; the vent tube in the probe cable must stay open and dry.
Closed tanks with gas or vapour above the liquid. The gas pressure adds to the reading. Use a differential pressure transmitter with the low side connected to the gas space: the gas pressure acts on both sides and cancels. With a dry reference leg, the calculation here applies unchanged.
Wet reference legs. If the low-side line fills with condensate or a fill fluid, it adds a constant head to the low side. The range then shifts to negative values (zero suppression) and has to be calculated with the leg height and its own density.
Common mistakes
Calibrating in metres of water for another liquid. A transmitter ranged 0–5 mH₂O on a liquid with a density of 850 kg/m³ reads 15 % low.
Forgetting the mounting offset. A transmitter below the tank floor reads the nozzle height even when the tank is empty.
Measuring a pressurised tank with a gauge transmitter. Every change in blanket pressure looks like a level change.
Turning down too far. A 0–10 bar transmitter set to 0–0.5 bar works, but its URL-based temperature effect and stability are twenty times larger relative to the span.
Frequently asked questions
Which units can I use?
Lengths in m, cm, mm, ft and in; pressure in bar, mbar, kPa, psi, mH₂O and inH₂O. Water columns are referred to 4 °C, as in the pressure unit converter.
How do I convert the level reading to volume?
Level to volume depends on the tank geometry: linear for vertical cylinders, non-linear for horizontal cylinders and spheres. The transmitter measures height; apply the tank table in the control system.
Does the 4–20 mA output scale with level?
Yes, linearly. The current for any level is shown under “At”; the 4–20 mA converter converts readings in the field.