How do you calculate pressure level?

You can calculate the liquid level (height) in a closed vessel using the following formula, which utilizes pressure measurements:

h = (p₂ – p₁) / (ρ * g)

Where:

h = height of the liquid column (liquid level) [meters (m)]
p₂ = hydrostatic pressure [Pascals (Pa) or bars. Must be converted to Pascals for use with SI units] at depth h, this is the total pressure at the sensor location.
p₁ = pressure of the enclosed gas in the vessel [Pascals (Pa) or bars. Must be converted to Pascals for use with SI units], also known as the head space pressure.
ρ = density of the liquid [kilograms per cubic meter (kg/m³)]
g = gravitational acceleration [approximately 9.81 meters per second squared (m/s²)]

Explanation of the Formula and its Components

This formula works by relating the difference between two pressure readings to the height of the liquid column. Let's break down each component:

Hydrostatic Pressure (p₂): This is the total pressure measured at a specific depth within the liquid. It's the sum of the pressure exerted by the enclosed gas above the liquid (p₁) and the pressure exerted by the weight of the liquid column above the sensor.
Enclosed Gas Pressure (p₁): This is the pressure of the gas trapped above the liquid in the closed vessel. It's important to account for this pressure because it contributes to the total pressure measured at depth h.
Density (ρ): The density of the liquid is a crucial factor. Denser liquids exert more pressure per unit height. It must be expressed in kg/m³.
Gravitational Acceleration (g): This constant represents the acceleration due to gravity, which affects the weight of the liquid column and, consequently, the pressure it exerts. We are assuming the measurement is on Earth (or similar environment with gravitational acceleration near 9.81 m/s²).

Here's how to use the formula to calculate the liquid level:

Measure p₂: Determine the hydrostatic pressure at a known depth using a pressure sensor.
Measure p₁: Determine the pressure of the gas enclosed above the liquid.
Determine ρ: Find the density of the liquid at its current temperature. Liquid density can vary significantly with temperature.
Look up g: Use the standard value for gravitational acceleration (approximately 9.81 m/s²).
Calculate h: Plug the values into the formula: h = (p₂ – p₁) / (ρ * g)
Ensure Consistent Units: Make sure all units are consistent. If pressure is measured in bar, it needs to be converted to Pascals (1 bar = 100,000 Pascals) before using the formula. Use meters for height, kg/m³ for density, and m/s² for gravity.

Let's say you have the following measurements:

Then, the liquid level (h) would be:

h = (150,000 Pa – 100,000 Pa) / (1000 kg/m³ * 9.81 m/s²)
h = 50,000 Pa / 9810 kg/(m²s²)
h ≈ 5.097 meters

Therefore, the liquid level is approximately 5.097 meters.

Accuracy of Sensors: The accuracy of your pressure sensors directly impacts the accuracy of the liquid level calculation.
Liquid Density Variations: Changes in temperature or liquid composition can affect the density, so accurate density measurements are essential. Some installations use a temperature sensor to compensate for temperature-related density changes.
Vessel Shape: This formula assumes a uniform cross-sectional area. For irregularly shaped vessels, further calculations or calibration might be needed to relate the calculated height to the actual volume.