From liquid height to pressure, and pressure to level

Hydrostatic pressure is the increase in pressure with depth caused by the weight of a stationary liquid. As the measurement point moves down, the vertical liquid column above it becomes taller. This relationship connects pressure and level in tanks, reservoirs, wells and water systems. Within the broader concept of pressure, the focus here is specifically on the contribution of liquid weight.

The basic calculation: Δp = ρgh

For a stationary liquid with approximately constant density, use Δp = ρ × g × h. Δp is the pressure difference between the surface and the measurement point; ρ is liquid density; g is gravitational acceleration; and h is the vertical depth below the free surface. Neither the length of an inclined pipe nor the overall tank height can automatically be used as h.

When calculating pressure, use density in kg/m³, g in m/s² and h in metres to obtain Pascals (Pa). Taking water density as 1000 kg/m³ and g as 9.81 m/s², 1 m of water produces 9.81 kPa = 0.0981 bar; 2 m produces 19.62 kPa. Keep pressure units consistent: 1 bar = 100,000 Pa.

10 m of water produces approximately 0.981 bar; exactly 1 bar requires about 10.19 m under these assumptions. Doubling depth in the same liquid doubles the pressure added by the liquid column. It does not double absolute pressure, which also includes the surface pressure.

What do density and vessel shape change?

At equal surface pressure, density and depth, vessel width or shape does not change the pressure. A narrow pipe and a wide tank can have the same pressure increase at a depth of 2 m. Their liquid volumes and bottom areas differ, however: equal pressure does not mean equal total force on the bottom.

If liquid density changes, pressure changes even at the same level. For example, a 2 m column of liquid with a density of 800 kg/m³ produces 15.70 kPa. A calculation configured for water would interpret this as approximately 1.60 m. Temperature effects and product composition can change density, so the value used for level calculation must suit the process conditions.

Gauge and absolute pressure in an open tank

For a tank open to the atmosphere, p_absolute = p_atmospheric + ρgh. A gauge-pressure sensor referenced to local atmospheric pressure ideally measures only p_gauge = ρgh. Establish the pressure reference before interpreting the reading from a pressure gauge or electronic instrument.

Removing the gas-pressure contribution in a closed tank

In a closed tank under pressure or vacuum, p_bottom = p_top + ρgh. A bottom-pressure reading alone cannot determine level when the gas pressure above the liquid varies. Differential pressure measurement gives Δp = p_bottom − p_top, allowing h = Δp / (ρg) under suitable installation conditions.

For example, 3 m of water adds 0.2943 bar. With a headspace pressure of 2 bar gauge, bottom pressure is approximately 2.2943 bar gauge; the difference remains 0.2943 bar. A differential pressure sensor needs both a suitable measurement range and an adequate static tank-pressure rating. Condensation in the gas-side line, a liquid-filled reference leg and diaphragm-seal elevations can introduce additional pressure contributions that must be included in zero and span settings.

Sensor elevation and measurement conditions

A pressure sensor can be fitted to a lower side connection, while a submersible level probe is lowered into the liquid. In both cases, calculated h is the liquid height above the sensor's sensing plane. If the sensor is 0.30 m above the tank bottom and total level is 3.00 m, it has 2.70 m of water above it and measures approximately 26.49 kPa. Include the 0.30 m offset when reporting bottom-referenced level within the applicable operating range.

Some submersible gauge-pressure probes obtain their atmospheric reference through a vent tube inside the cable. Keep its termination open to the atmosphere, dry and protected, following the manufacturer's instructions. Blockage or moisture ingress can impair measurement. If an absolute sensor has no such atmospheric reference, a separate atmospheric-pressure correction may be needed for open-tank level calculation.

Choose the measurement location away from the direct influence of a filling jet or strong mixer flow. Dynamic effects and vibration make the reading harder to explain using ρgh alone. In applications with sediment or product buildup, the pressure-port opening and diaphragm design also matter.

Range, accuracy and connection to automation

Select a sensor by considering maximum level, density, overpressure resistance, temperature, wetted materials and pressure reference together. A 5 m water column requires a hydrostatic range of approximately 49.05 kPa, or 0.4905 bar. In water-pressure measurement, an unnecessarily wide range can increase level uncertainty when accuracy is specified as a percentage of full scale.

For example, if a 0–1 bar instrument specifies an accuracy component of ±0.25% of full scale, that corresponds to ±250 Pa, or approximately ±25.5 mm of water level. Temperature, density, installation and other errors may add to this; the figure is not the total system accuracy.

A pressure transmitter can send measurements to a PLC or pressure indicator. If its 4–20 mA output is calibrated for 0–5 m of water and density remains constant, 12 mA represents 2.5 m. Although pressure-to-level conversion is linear, level-to-volume conversion depends on tank geometry. In a horizontal cylindrical tank, height percentages other than 50% cannot generally be treated directly as volume percentages.

Ocean depth and the connection with hydraulics

Deep-ocean pressure rises with the water column; seawater density varies with salinity, temperature and pressure. When explaining pressure underwater, an increase of roughly one atmosphere per 10 m is a useful approximation. At very great depths, account for density variation with depth rather than assuming constant density.

Pressure in hydraulic systems is not limited to the weight of a liquid column: loads, pumps and valves can produce much higher pressures. Pascal's principle describes the transmission of additional pressure. Hydrostatic pressure is the contribution associated with elevation differences, and this contribution can also exist in hydraulic systems.

Related measurement topics

Pressure sensors / Water-pressure measurement / Pressure FAQs