Pressure-head equivalence: 1 kg per square metre corresponds to how many millimetres of water column?

Introduction / Context:
Engineering pressure units are often interconverted between force/area (or weight/area) and a fluid head such as millimetres of water column. Being fluent with this conversion helps in calibrating manometers, specifying blower performance, and reading differential pressure indicators.

Given Data / Assumptions:

• Quantity given: 1 kg/m^2, interpreted as weight per unit area.
• Standard gravity: g ≈ 9.80665 m/s^2.
• Density of water near room temperature: rho ≈ 1000 kg/m^3.
• Definition: 1 mm H2O is the hydrostatic pressure from a 1 mm water column.

Concept / Approach:
Convert weight per area into pascals, then compare with the pressure represented by 1 mm of water head. Hydrostatic relation: P = rho * g * h. Also, 1 kg/m^2 corresponds to P = g N/m^2 because 1 kg of mass under gravity exerts g newtons of weight.

Step-by-Step Solution:
Compute pressure from 1 kg/m^2: P = 1 * g ≈ 9.80665 Pa.Pressure from 1 mm H2O: P_mm = rho * g * h = 1000 * 9.80665 * 0.001 = 9.80665 Pa.Therefore, 1 kg/m^2 equals exactly the pressure of 1 mm of water column (at standard conditions).

Verification / Alternative check:
Dimensional check confirms both are pressures in pascals and numerically identical using standard gravity and water density.

Why Other Options Are Wrong:
10, 100, and 1000 mm H2O would be 10×, 100×, and 1000× larger pressures; 0.1 is 10× too small.

Common Pitfalls:
Confusing kilogram-force with kilogram of mass; forgetting to include g; using centimetres of water instead of millimetres.

Final Answer:
1