Question

Which of the following is a unit of viscosity ?

• A. N.s/m
• B. \(\text{N.s/m}^2\)
• C. N/s
• D. N.m

Hint:

Remember the unit conversions for dynamic viscosity: \[ 1\ \text{Pa}\cdot\text{s} = 1\ \frac{\text{N}\cdot\text{s}}{\text{m}^2} = 10\ \text{Poise} \] This is a common question on engineering fluid mechanics exams.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Viscosity is a measure of a fluid's resistance to flow or gradual deformation by shear or tensile stress.
Key Formula or Approach:
According to Newton's law of viscosity, shear stress (\(\tau\)) is proportional to the velocity gradient (shear rate):
\[ \tau = \mu \frac{du}{dy} \]
Where \(\mu\) is the dynamic viscosity. Rearranging this equation gives:
\[ \mu = \frac{\tau}{\frac{du}{dy}} \]

Step 2: Detailed Explanation:
Let us substitute the SI units into this equation:
- Shear stress (\(\tau\)) has the unit of force per unit area, which is Newtons per square meter (\(\text{N/m}^2\)) or Pascals (\(\text{Pa}\)).
- The velocity gradient (\(\frac{du}{dy}\)) has the unit of velocity divided by distance:
\[ \frac{\text{m/s}}{\text{m}} = \text{s}^{-1} \]
Substituting these units into the viscosity equation:
\[ \text{Unit of } \mu = \frac{\text{N/m}^2}{\text{s}^{-1}} = \frac{\text{N}\cdot\text{s}}{\text{m}^2} \]
This unit is also equivalent to Pascal-seconds (\(\text{Pa}\cdot\text{s}\)) or Poise (\(1\text{ Pa}\cdot\text{s} = 10\text{ Poise}\)).
The other options do not represent viscosity.

Step 3: Final Answer:
The unit of dynamic viscosity is \(\text{N.s/m}^2\).