Transducers and measurement principles — match each device in List I with the corresponding operation mapping in List II. List I (Transducer) A. Bourdon tube B. Hot-wire anemometer C. Hydrometer D. Pitot tube List II (Operation) 1. Fluid flow/velocity to resistance change 2. Velocity (stagnation) to pressure 3. Pressure to displacement 4. Specific gravity to displacement

Introduction / Context:
Many sensors convert a physical quantity into a more convenient intermediate signal such as displacement, resistance, or pressure. Recognizing these mappings helps in selecting appropriate transducers for flow, density, pressure, and velocity measurements in instrumentation and process control.

Given Data / Assumptions:

• Bourdon tube is a mechanical pressure sensor producing tip displacement.
• Hot-wire anemometer uses convective cooling of a heated wire to infer flow velocity from resistance changes.
• Hydrometer indicates specific gravity by floating height (displacement principle).
• Pitot tube converts dynamic pressure from velocity into measurable pressure difference.

Concept / Approach:

Map each device to its primary transduction: pressure → displacement (Bourdon), velocity/flow → resistance change (hot-wire), specific gravity → displacement (hydrometer buoyancy), and velocity → pressure (Pitot dynamic pressure to a manometer or transducer).

Step-by-Step Solution:

Verification / Alternative check:

For the Pitot tube, Bernoulli's relation gives velocity from measured differential pressure; for the hot-wire, King's law relates heat loss to velocity, which in turn changes resistance; for the Bourdon tube, elastic deformation converts pressure to tip displacement proportional to applied pressure; a hydrometer follows Archimedes’ principle.

Why Other Options Are Wrong:

• Swapping the hot-wire and pitot mappings confuses thermal and pressure-based flow measurement principles.
• Assigning Bourdon to electrical resistance ignores its mechanical nature.
• Mapping hydrometer to pressure or resistance disregards buoyancy-based operation.

Common Pitfalls:

Assuming all flow meters are pressure-based; thermal anemometry is distinct. Also, mis-spelling “Bourdon” (not “Bourden”) is common in exams.

Final Answer:

A-3, B-1, C-4, D-2