Which type of flow meter counts the flow rate based on the gear shaft revolutions per unit time?

The correct choice is indeed the type of flow meter known as Positive Displacement Flow Meters. These meters operate by capturing a fixed amount of fluid in a chamber and measuring how often this chamber fills and empties in a given time frame. The heart of their operation lies in using gear or other mechanical components to track the fluid movement. As the fluid passes through, it causes the gears to rotate; the revolutions of the gear shafts are directly proportional to the volume of fluid passing through the system. This allows for an accurate and continuous measurement of flow rate, making positive displacement flow meters especially effective for measuring low to moderate flow rates with high precision.

The other types of flow meters mentioned do not operate based on gear revolutions. Mag meters use electromagnetic fields to measure the flow of conductive fluids, ultrasonic flow meters utilize sound waves to measure flow, and mass flow meters assess the mass of the fluid flowing through, instead of counting revolutions of a shaft.