Water Level Measurements with a Pressure Transducer
By Adam Hobson
Pressure transducers make it possible to collect continuous or nearly continuous water level or pressure data from wells, pipes, surface water gages, and other devices. These autonomous and rapid measurements have led to an improved understanding of hydraulic processes, better management of water resources, and protection of life and property. Pressure transducers are simple to setup and use, reliable, accurate, and low cost, and the digital data output facilitates data management and analysis. Despite these advantages, water level measurements with pressure transducers are often misunderstood which can lead to data errors, faulty conclusions, and poor decisions. While the calculation of water level from pressure is often perceived as a simple equation, the concepts and components are often overlooked or forgotten. This tech note describes the basic principles of water level measurements with a pressure transducer and is intended to be an introduction or refresher to the topic.
Pressure Transducers
A pressure transducer is a sensor that converts an applied pressure into an electrical signal. Pressure transducers are often combined with other components: a battery and data logger, a printed circuit board assembly, weights, housing, and waterproof connector for data communications. Together, the complete package is often referred to as a submersible pressure transducer, water level logger, water level sensor, or by a manufacturer’s model name (e.g., Level TROLL or Rugged TROLL).
Pressure and Depth
Pressure and depth are fundamental physical measurements in water monitoring. In fluid mechanics, static pressure (p) at any point in a water column is determined by the weight and the height of the water above the measuring point. The weight of the water is the product of the water density (ρ) and local acceleration of gravity (g). The height of the water above the measuring point (h) is the depth of the measuring point below the water surface. The relationship is expressed as:
By rearranging the above equation, depth at a point in the water column can be determined from a measurement of the static pressure at that point and knowing its density and the local acceleration of gravity such that:
Density and Specific Gravity
Water density is a critical component in the calculation of depth of water from pressure. Water density can vary based on concentration of total dissolved solids and especially salinity. Saltwater is more dense than fresh water and is therefore heavier, which affects the calculation of depth from pressure. Water density is often measured directly with a hydrometer, a simple device based on the concept of buoyancy. Hydrometers measure specific gravity (SG), or relative density, which is the ratio of the density relative to pure water at 4 °C (ρwater):
Density is calculated from specific gravity as:
Applying this to the equation for depth results in:
In-Situ pressure transducers measure pressure in pounds per square inch (psi). All derived parameter equations use this internal unit of measure. The default unit of measure for depth is meters (m). Conversion of pressure expressed in pounds per square inch to meters of water requires that the pressure be converted to the SI unit Pascal (Pa).
1psi = 6.894757kPa = 6894.757Pa
By definition, a Pa = N / m2 and a Newton (N) = kg·m/s2.
Assuming standard values for ρwater of 1000 kg/m3 and g of 9.80665 m/s2, the equation for depth with pressure in units of pounds per square inch becomes,
Where:
h = “depth of water in meters (m)”
p = “pressure in pounds per square inch ” ( psi )
SG = “specific gravity”
To calculate depth in units of feet, a conversion factor of 2.30667 ftH2O/psi is used.
Water Level
Water level is the vertical length between the water surface and a reference point or datum. When using a pressure transducer, the pressure at a point below the water surface is converted to a depth measurement. However, the water level measurement may need to be made relative to a reference point that is either above or below the water surface. In these cases, an offset or level reference can be either added to or subtracted from the depth measurement. Water level from pressure can be calculated as:
Where:
- h = water level (m)
- Lref = level reference or offset (m)
- pmeas = measured pressure (psi)
- pref = measured pressure when level reference was set (psi)
- SG = specific gravity
Pressure transducers have revolutionized how we measure water level, and their use has transformed how we interpret hydraulic changes. Yet, they are often misused, and the data misinterpreted. By understanding the fundamentals of how to derive water level from measurements of pressure, users can better understand their data and improve their data interpretation.