Worked problem

Hydrostatic Level Measurement: Pressure to Tank Level

Convert a 24.5 kPa bottom gauge pressure into tank level for a 1,150 kg/m³ liquid and see how the wrong density shifts the indicated level.

Controls & Instrumentation · Last reviewed October 17, 2026

Given

An open tank holds a liquid of density 1,150 kg/m³. A gauge-pressure transmitter at the bottom of the tank, at the same height as the zero of the measured level, reads 24.5 kPa. The transmitter range corresponds to 0 to 4.0 m of level and outputs 4 to 20 mA.

Find

The liquid level, the transmitter output in mA, and the level that would be indicated if the transmitter were set up for water (998 kg/m³).

Solution

h = P(gauge) ÷ (ρ × g)

Level: h = 24,500 ÷ (1,150 × 9.81) = 2.17 m.
Pressure at the top of the range: 4.0 × 1,150 × 9.81 = 45.1 kPa.
Fraction of span = 24.5 ÷ 45.1 = 0.543, so the output = 4 + 0.543 × 16 = 12.7 mA.
Wrong density: a transmitter that assumes water would calculate 24,500 ÷ (998 × 9.81) = 2.50 m.

Answer

2.17 m (54% of span, 12.7 mA)  |  with the water density the indicated level is 2.50 m, 15% too high

The error is the density ratio

The transmitter divides the pressure by the density it was told. Using 998 instead of 1,150 makes every reading higher by the factor 1,150 ÷ 998 = 1.152. The error is proportional to the level, so it is zero at an empty tank and largest when the tank is full.

True level	Indicated with water density	Error
1.00 m	1.15 m	+0.15 m
2.17 m	2.50 m	+0.33 m
4.00 m	4.61 m	+0.61 m

Common mistakes

Using the density of water for every liquid. Liquids that vary with temperature or concentration need the density at operating conditions.
Forgetting that the transmitter must be mounted at, or corrected for, the height of the zero level. Mounting it below the tank bottom adds a constant offset.
Using absolute pressure in an open tank without removing atmospheric pressure, or a gauge transmitter on a closed tank where the vapor pressure above the liquid also acts.
Mixing units, such as kPa with g in ft/s².

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

Questions

What changes for a closed, pressurized tank?

The vapor pressure above the liquid acts on the transmitter too, so a differential-pressure transmitter compares the bottom pressure with the top pressure, and the difference is the hydrostatic part.

What if the density changes during operation?

The level reading drifts with it. Density compensation, a different measuring principle such as radar, or a density measurement fixes this.

Is this the same as an inverse of 4–20 mA scaling?

Scaling from pressure to level is one step. The 4–20 mA signal is a linear scale of the pressure span. See the scaling problem in this section.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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