Sources of Error in Deadweight Tester Pressure Calibration

The deadweight tester (piston gauge) is the primary high-accuracy pressure-generation standard and the fundamental reference of calibration laboratories. However, for the system to give correct results, several physical corrections must be taken into account.

The Basic Formula

The pressure generated by a deadweight tester is calculated from local gravity, the masses and the effective area:

Air Buoyancy Correction

Weighing the masses in air gives a result that differs from their true mass in vacuum, because of Archimedes’ principle. Since air density (ρ_a) changes with ambient temperature, pressure and humidity, an up-to-date value must be used for every calibration. If ignored, an error of up to 0.015% can occur.

Local Gravitational Acceleration

Standard gravity is 9.80665 m/s², but in Turkey it varies between 9.799–9.810 m/s² depending on latitude and altitude. For Istanbul the average value is around 9.8076 m/s². Not knowing the local value can cause an error of up to 0.05% — an unacceptable deviation in high-accuracy calibration.

Temperature and Effective Area

The piston-cylinder assembly expands with temperature. Typically the sum of the thermal expansion coefficients of the piston and cylinder is about 18×10⁻⁶ /K. Each 1 °C deviation from the 20 °C reference changes the effective area by about 1.8 ppm.

Hydrostatic Pressure

If there is a height difference between the reference level and the DUT (device under test), the pressure created by the liquid (or gas) column must be corrected. A 100 mm height difference requires a correction of about 8.8 Pa for oil.

Piston Friction and Rotation

For the piston to remain balanced, it must rotate continuously inside the cylinder (typically 30–60 rpm). If rotation stops, friction increases and the reading deviates. The piston fall rate must also stay within certain limits (for example 3–5 mm/min).