A servo gauge operates based on the principle of buoyancy and weight displacement to measure the level of liquid in a tank. Here's a breakdown of its working principle:

1. Displacer and Measuring Wire: A small, lightweight object called a displacer is suspended by a strong measuring wire inside the tank. As the liquid level changes, the displacer experiences a varying buoyant force due to Archimedes' principle.
2. Servo Motor and Drum: The measuring wire is wound around a precisely machined drum housed within the instrument. This drum is connected to a servo motor, which can raise and lower the displacer as needed.
3. Buoyancy Detection and Control: The weight of the displacer on the wire creates a torque. This torque is detected by a mechanism within the instrument, often involving magnets and a transducer.
4. Servo Mechanism Adjustment: The control system continuously monitors the torque. If the torque changes due to a varying liquid level, the servo motor adjusts its position to maintain a constant tension on the measuring wire. This effectively keeps the displacer at a constant weight relative to the fluid.
5. Level Measurement Conversion: As the liquid level in the tank changes, the amount of measuring wire reeled onto the drum changes as well. This movement of the drum is precisely correlated with the liquid level and is converted into an electrical signal or digital output.

Here are some additional points to note:

• Servo gauges offer high accuracy and precision compared to traditional float-based systems.
• They can be used for various applications beyond just level measurement, such as interface level between two liquids (e.g., oil and water) or even density measurement.
• The design can be modified for different tank shapes and environments.

Overall, servo gauges provide a reliable and accurate method for measuring liquid level in tanks through a clever combination of mechanical and electronic components.