GATE 2023 IN Q.13: solution and answer

Official answer: DSource: Official answer key, GATE 2023 IN (IIT Kanpur)

1. Resistance to flow means the permanent pressure loss that a meter introduces, which comes from any obstruction it places in the flow path.

2. Orifice meter: a thin plate with a small hole narrows the flow abruptly. The jet separates and mixes downstream, so a large part of the differential pressure $\Delta p$ is lost for good. This is the highest loss of the four.

3. Venturi meter: the gradual cone and diffuser recover most of the pressure, so the permanent loss is much smaller than for an orifice. It is still a constriction in the pipe.

4. Turbine meter: the rotor, blades and hub sit in the stream and obstruct it, and bearing friction adds to the pressure drop.

5. Electromagnetic meter: the measuring section is an open, unobstructed pipe with electrodes flush to the wall. By Faraday's law, $e=BDv$ is generated in the moving conductive liquid, so there is no moving or intruding part.

6. So its pressure drop is essentially that of a plain straight pipe, the lowest resistance of the four. The answer is (D).