Unit conversion (kinematic viscosity): 1 m^2/s is equal to how many stokes (1 stoke = 1 cm^2/s)?

Introduction / Context:Kinematic viscosity is commonly reported in SI units (m^2/s) and in cgs units (Stokes, where 1 St = 1 cm^2/s). Accurate unit conversion is essential in fluid mechanics, pump sizing, and heat-and-mass-transfer calculations, especially when mixing data from different standards.

Given Data / Assumptions:

• 1 stoke (St) = 1 cm^2/s.
• 1 m = 100 cm.
• Goal: convert 1 m^2/s into St.

Concept / Approach:Use the length conversion squared. Since 1 m = 100 cm, then 1 m^2 = (100 cm)^2 = 10^4 cm^2. Therefore, 1 m^2/s corresponds to 10^4 cm^2/s, which equals 10^4 stokes.

Step-by-Step Solution:

Verification / Alternative check:Dimensional analysis confirms the squared factor: converting a squared unit always multiplies by the square of the linear conversion factor.

Why Other Options Are Wrong:

• 10, 10^2, 10^3: undercount because they fail to square the 100 cm per meter factor.
• 10^5: overcount; would correspond to 316.2 cm per meter, which is incorrect.

Common Pitfalls:Forgetting to square when converting squared units; confusing stokes with centistokes (1 cSt = 0.01 St).

Final Answer:10^4