Question

Which one of the following measures of viscosity is dimensionless?

• A. Inherent viscosity
• B. Reduced viscosity
• C. Zero-shear viscosity
• D. Specific viscosity

Hint:

Whenever a property is expressed as a ratio of two identical physical quantities, the result is dimensionless (like relative density, refractive index, or specific viscosity).

Answer 1

The Correct Option is D

Step 1: Recall definitions of viscosity measures.
- Inherent viscosity: Defined as \(\eta_{inh} = \frac{\ln(\eta_r)}{c}\), where \(\eta_r\) is relative viscosity and \(c\) is concentration. Its unit depends on concentration, so it is not dimensionless.
- Reduced viscosity: Defined as \(\eta_{red} = \frac{\eta_{sp}}{c}\). Again, it has unit reciprocal concentration, so not dimensionless.
- Zero-shear viscosity: Refers to the absolute viscosity value at very low shear rate. This carries the same dimension as viscosity (\([M L^{-1} T^{-1}]\)), not dimensionless.
- Specific viscosity: Defined as \(\eta_{sp} = \frac{\eta - \eta_0}{\eta_0}\), where \(\eta\) is solution viscosity and \(\eta_0\) is solvent viscosity. Since it is a ratio of two viscosities, this is dimensionless.

Step 2: Conclusion.
Only \(\eta_{sp}\) (Specific viscosity) is dimensionless. \[ \boxed{\text{Specific viscosity is dimensionless.}} \]