Unit conversion check: 1 Pascal (Pa), the SI unit of pressure, equals how many newtons per square metre (N/m^2)?

Introduction / Context:Consistent SI unit handling prevents serious design and safety errors. Pressure appears in fluid mechanics, thermodynamics, and transport operations; the Pascal is the SI coherent unit.

Given Data / Assumptions:

• Definition of Pascal: 1 Pa = 1 N acting uniformly over 1 m^2.
• Derived from base SI units: kg, m, s.

Concept / Approach:By definition, pressure = force / area. The SI unit of force is the newton (N), and area is in square metres (m^2). Hence, 1 Pa = 1 N / m^2 exactly. Larger units include kPa (10^3 Pa) and MPa (10^6 Pa).

Step-by-Step Solution:

Verification / Alternative check:Dimensional analysis from base units shows Pa = kg·m^−1·s^−2, matching N/m^2.

Why Other Options Are Wrong:

• 10, 0.1, 1000, 0.01 N/m^2: incorrect scaling; these correspond to deca-, deci-, kilo-, centi- multiples not aligned with the base definition.

Common Pitfalls:Confusing Pa with bar: 1 bar = 10^5 Pa = 100 kPa.

Final Answer:1