Chemical, sludge and wet well levels are often measured as pressure and then shown as a level or volume. The first tool turns a level into gallons for common tank shapes. The second turns a pressure reading into a level, corrected for specific gravity and the sensor mounting height.
Tank Level to Volume
Formula
Rectangular: V, ft³ = L x W x level
Vertical cylinder: V, ft³ = 3.1416 x D² / 4 x level
Horizontal cylinder: V, ft³ = L x [R² x acos((R - h) / R) - (R - h) x square root of (2Rh - h²)]
(R = D / 2, h = level, acos in radians)
Gallons = ft³ x 7.48
Inputs used
- Tank shape
- Liquid level (from the tank bottom) (ft)
- Length (rectangular or horizontal cylinder) (ft)
- Width (rectangular) (ft)
- Diameter (cylinders) (ft)
- Full height (optional, rectangular or vertical cylinder) (ft)
Worked example (fictional plant data)
- Horizontal ferric chloride tank, 8 ft diameter, 20 ft long, level 3 ft
- Segment area = 4² x acos(1 / 4) - 1 x square root of (2 x 4 x 3 - 3²) = 21.090 - 3.873 = 17.217 ft²
- Volume = 17.217 x 20 x 7.48 = 2,576 gal
- Full = 3.1416 x 8² / 4 x 20 x 7.48 = 7,520 gal, so 34.3% full
Hydrostatic Pressure to Level
Formula
Water column, ft = Pressure x (Pa per unit) / 2,988.98 (1 psi = 2.307 ft = 27.68 in of water at 39.2 °F) Liquid above sensor, ft = Water column, ft / Specific gravity Level = Liquid above sensor + Sensor height above bottom
Inputs used
- Pressure at the sensor (gauge)
- Pressure unit
- Specific gravity of the liquid
- Sensor height above the tank bottom (optional) (ft)
Worked example (fictional plant data)
- Digester level sensor reads 5.2 psi, sludge SG 1.02, sensor 0.5 ft above the floor
- Water column = 5.2 x 2.3067 = 11.995 ft
- Sludge above sensor = 11.995 / 1.02 = 11.760 ft
- Level = 11.760 + 0.5 = 12.26 ft
Cautions
- Horizontal tanks with dished or hemispherical heads hold more than flat ends. Use the manufacturer strapping chart when you have one.
- Specific gravity changes with chemical strength and temperature, and sludge SG with solids. Update the SG in the transmitter when the product changes.
- A pressure sensor in a vented tank reads gauge pressure. In a closed or pressurized tank, use a DP transmitter to cancel the head space pressure.
- Never enter a tank or wet well to service a sensor without following your confined space program.
References
- NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B (pressure and water column factors).
Results are estimates for operator and technician use. Equations follow the references above; always check against the instrument manual, your calibration procedure and plant data.