Problem Statement
Determine the viscosity of a liquid having kinematic viscosity 6 stokes and specific gravity 1.9.
Given Data
- Kinematic viscosity, ν = 6 stokes = 6 cm²/s
- Specific gravity of liquid = 1.9
- Density of water = 1000 kg/m³
Solution
1. Convert Kinematic Viscosity to SI Units
\( \nu = 6 \, \text{stokes} = 6 \times 10^{-4} \, \text{m}^2/\text{s} \)
2. Calculate Density of Liquid
\( 1.9 = \frac{\rho_{\text{liquid}}}{1000} \)
\( \rho_{\text{liquid}} = 1.9 \times 1000 = 1900 \, \text{kg/m}^3 \)
3. Calculate Dynamic Viscosity (μ)
\( \mu = \nu \times \rho \)
\( \mu = (6 \times 10^{-4}) \times 1900 = 1.14 \, \text{N·s/m}^2 \)
4. Convert to Poise
\( \mu = 1.14 \times 10 = 11.40 \, \text{poise} \)
- Dynamic viscosity (μ) = 1.14 N·s/m² = 11.40 poise
Explanation
1. Unit Conversion:
The kinematic viscosity was converted from stokes (CGS unit) to SI units (m²/s) for consistent calculations. This conversion factor (1 stoke = 10⁻⁴ m²/s) is standard in fluid mechanics.
2. Density Calculation:
Specific gravity is the ratio of a substance's density to that of water. By multiplying specific gravity (1.9) with the density of water (1000 kg/m³), we obtained the liquid's density as 1900 kg/m³.
3. Viscosity Relationship:
The relationship between kinematic viscosity (ν), dynamic viscosity (μ), and density (ρ) is fundamental: ν = μ/ρ. We rearranged this to solve for dynamic viscosity: μ = ν × ρ.
Physical Meaning
1. Practical Significance of Values:
A dynamic viscosity of 1.14 N·s/m² indicates this liquid is significantly more viscous than water (0.001 N·s/m²). Combined with a specific gravity of 1.9, this suggests a thick, heavy fluid like certain industrial oils or syrups.
2. Measurement Context:
This calculation demonstrates how kinematic viscosity measurements can be converted to dynamic viscosity when density is known, which is essential for various engineering applications.
3. Industrial Applications:
Fluids with these viscosity characteristics are often used in damping systems, high-pressure hydraulic systems, and specialized lubrication applications where thicker fluids are required.
