Hydrostatic Level Measurement with a Pressure Transmitter: How It Works

Quick answer: a pressure transmitter placed at the bottom of a tank can measure liquid level because pressure at depth equals density × gravity × height (P = ρ g h). Water produces about 9.81 kPa for each metre of depth, so a 3 metre tank of water gives about 29.4 kPa at the bottom. It works well for clean liquids in vented tanks and wells where the density is known and steady. It does not work for powders, or tanks with changing density, foam or sticky build-up, and in closed tanks you need a differential measurement. This guide explains the principle, how to size the range, how to install the transmitter, and when load cells are the better choice.

The principle: hydrostatic pressure

The deeper you go in a liquid, the more liquid sits above you, and the higher the pressure. The formula is:

P = ρ × g × h

• P is the pressure in pascals.
• ρ (rho) is the liquid density in kilograms per cubic metre. Water is about 1,000.
• g is gravity, 9.81 metres per second squared.
• h is the depth in metres.

So for water, each metre adds 1,000 × 9.81 × 1 = 9,810 Pa, which is 9.81 kPa or about 0.098 bar. A sensor reading 19.62 kPa means 2 metres of water above it.

Different liquids, different pressures

Densities are approximate and vary with temperature and concentration. Use the real density of your product.

Converting pressure to level and volume

1. Level: h = P ÷ (ρ × g). For example, 24.5 kPa of water gives 24,500 ÷ 9,810 = 2.5 metres.
2. Volume: multiply level by the tank cross-sectional area. In a vertical cylinder of diameter 1.5 m (area 1.767 m²), 2.5 m of water holds about 4.42 m³, or 4,420 litres.
3. Mass: in a vented tank with vertical walls, mass = pressure × area ÷ gravity, which does not depend on the density. In the same tank, 24.5 kPa corresponds to 24,500 × 1.767 ÷ 9.81 = about 4,413 kg.

Most level displays are programmed with density and tank shape. If the density changes, the level reading is wrong by the same proportion, but a mass reading from pressure is still correct for a vertical-walled, vented tank.

Choosing the range

Calculate the pressure at the maximum level, then add headroom.

Example. A diesel storage tank is 3 m tall. At full, the pressure is 850 × 9.81 × 3 = 25.0 kPa. Allow headroom and choose a 0 to 40 kPa range (0.4 bar). A 0 to 10 bar sensor would be a poor choice: at 25 kPa it uses only 2.5% of its range, so resolution and accuracy are poor. Always match the range to the small pressures involved. Our range selection guide covers the method.

Types of installation

Tank-mounted transmitter

Fitted on a port at or near the bottom. It needs a clean, unblocked connection, and often a valve for isolation and calibration.

Submersible (immersion) transmitter

Lowered into a well, sump or tank on a cable, with a vent tube for atmospheric reference. Common for bores, wet wells and rainwater tanks. Choose materials and cable for the liquid.

Differential transmitter for closed tanks

Two ports measure the bottom and top pressures. The difference removes the effect of the gas above the liquid. See differential pressure explained.

Vented reference and sealed gauge

For an open tank, a gauge-pressure transmitter needs a reference to the atmosphere. Check whether the sensor is vented or sealed. Wrong choices lead to a reading that changes with the weather. For the types of pressure, see gauge vs absolute vs vacuum pressure.

Strengths and limits

When to use load cells instead

If your product is a powder, if its density changes, if the tank is pressurised or if you need to charge by weight, weigh the vessel. Load cells measure mass directly and do not touch the product. See load cell vs pressure sensor and tank, silo and hopper weighing. Some sites use both: a transmitter for pump control and load cells for stock accounting.

Wiring and signal

A level transmitter usually gives 4 to 20 mA. Map 4 mA to empty and 20 mA to the full level. Our 4 to 20 mA guide covers wiring and scaling. In the diesel example above, with a 0 to 40 kPa range, the full level of 25.0 kPa gives 4 + (25.0 ÷ 40) × 16 = 14 mA.

Installation checklist

1. Choose gauge, absolute or differential to match the tank.
2. Calculate the pressure at maximum level and pick a suitable range.
3. Check the wetted materials for the liquid. 316L stainless steel suits many liquids.
4. Mount on a clean port with a valve, away from inlets and agitators.
5. Set the zero with the tank empty or at a known level.
6. Program density and tank shape in the controller.
7. Check against a dipstick or another reference, and recheck periodically.

Submersible sensors in bores, wells and rainwater tanks

For a deep well or a buried tank, a submersible level transmitter hangs on its own cable. The cable contains a thin vent tube that connects the back of the sensor to the atmosphere, so that the sensor reads only the liquid depth and ignores the weather. Good practice includes:

• Keep the vent tube end dry. A desiccant cartridge at the cable end stops moist air condensing in the tube.
• Use a cable and sensor body material suited to the liquid, such as stainless steel for water and many chemicals.
• Secure the cable so that the sensor does not swing or rest on the bottom, which can bury it in silt.
• Protect the cable at the entry point against abrasion and lightning-induced surges.

What does accuracy mean in millimetres?

Accuracy figures look abstract until you convert them to depth. A transmitter on a 0 to 40 kPa range with an accuracy of 0.25% of span has a possible error of 0.1 kPa. For water, 0.1 kPa corresponds to 100 ÷ 9,810 = 0.0102 metres, which is about 10 mm of depth. For a 3 metre tank, that is a very small error. If the liquid is lighter, such as diesel at 850 kg per cubic metre, the same 0.1 kPa error is about 12 mm. Remember that the sensor accuracy is only one part of the total: density errors, installation and temperature add more.

Calibration and zero checks

• Check the zero with the sensor out of the liquid and open to the atmosphere (for a gauge type).
• Check a second point against a dipstick or a reference level.
• Recheck after cleaning, moving or any suspected damage.
• Record the checks. See pressure gauge calibration.

Worked example: a rainwater tank on a farm

A 2.4 metre tall tank holds rainwater. At full, the pressure at the bottom is 1,000 × 9.81 × 2.4 = 23.5 kPa. A 0 to 40 kPa submersible transmitter fits, and a 4 to 20 mA output runs 60 metres to a house controller. The controller maps 4 mA to 0 m and 20 mA to 4.08 m, which is the sensor’s full range, and the tank is full at 2.4 m. Full tank gives 4 + (23.5 ÷ 40) × 16 = 13.4 mA. A low-level alarm at 0.3 metres protects the pump from running dry.

Foam, build-up and sludge

A pressure transmitter at the bottom of a tank sees the weight of the liquid above it, not the foam. That is an advantage in foaming liquids, where an ultrasonic sensor would be confused. The disadvantage is build-up on the diaphragm: sludge, fat or crystallised product can coat the sensing face and change the reading. In dirty services, use a flush-mounted diaphragm that is easy to clean, and schedule cleaning and zero checks. In heavily fouled tanks, load cells can be a better choice because they never touch the product.

How it compares with other level methods

• Float switches: simple and low cost, but give only point levels.
• Ultrasonic and radar: non-contact from above; can be affected by foam, steam and obstructions.
• Hydrostatic pressure: continuous level; depends on density; wetted.
• Load cells: mass of everything in the vessel; independent of density; no contact.

Frequently asked questions

How do you measure water level with a pressure sensor?

Place it at the bottom, measure the pressure and divide by 9.81 kPa per metre for water.

Does density matter?

For level, yes. A denser liquid gives a higher pressure at the same depth. For mass in a vertical-walled vented tank, no.

Can I use one in a pressurised tank?

Only with a differential arrangement that cancels the gas pressure.

Which output should I use?

4 to 20 mA is the standard for level transmitters, especially over long cables.

Do you supply level sensors?

Our WIKA Model A-10 measures pressure with 4 to 20 mA and 0 to 10 V outputs. For tank-specific needs, tell us your liquid, depth and connection through the contact page.

Next steps

Read the sensor guide and the complete load cell guide.