Question

The SI unit of dynamic viscosity is:

• A. Poise
• B. Centipoise
• C. $N\cdot s/m^{2}$
• D. $m^{2}/s$

Hint:

Logic Tip: Remember that $1 \text{ N}/m^2$ is $1 \text{ Pascal (Pa)}$. Therefore, the SI unit $N\cdot s/m^2$ is also frequently written as Pascal-seconds ($Pa\cdot s$).

Answer 1

The Correct Option is C

Concept:
Dynamic viscosity ($\mu$) measures a fluid's internal resistance to flow. Its unit can be derived directly from the variables in Newton's law of viscosity.

Step 1:
Starting with $\tau = \mu \frac{du}{dy}$, we isolate dynamic viscosity ($\mu$): $$ \mu = \frac{\tau}{du/dy} $$

Step 2:
Shear stress ($\tau$) is force over area, measured in Newtons per square meter ($N/m^2$ or Pascals). Velocity ($u$) is measured in meters per second ($m/s$). Distance ($y$) is measured in meters ($m$).

Step 3:
$$ \text{Unit of } \mu = \frac{N/m^2}{(m/s) / m} $$

Step 4:
The $(m/s)/m$ simplifies to $1/s$ (inverse seconds). $$ \text{Unit of } \mu = \frac{N/m^2}{1/s} = \frac{N \cdot s}{m^2} $$ This matches option (C). Note that Poise and Centipoise are CGS units, not SI units, and $m^2/s$ is the unit for kinematic viscosity.