Problem Statement
Determine the specific gravity of a fluid having a dynamic viscosity of 0.07 poise and a kinematic viscosity of 0.042 stokes.
Given Data
- Dynamic Viscosity, \(\mu = 0.07 \, \text{poise}\)
- Kinematic Viscosity, \(\nu = 0.042 \, \text{stokes}\)
Solution
1. Identify the Relationship between Viscosities and Density
Kinematic viscosity (\(\nu\)) is defined as the ratio of dynamic viscosity (\(\mu\)) to the fluid's density (\(\rho\)). We can rearrange the formula to solve for density.
2. Calculate the Density of the Fluid (ρ)
The given units, poise and stokes, are from the CGS (Centimeter-Gram-Second) system. Poise is g/(cm·s) and stokes is cm²/s. Therefore, the resulting density will be in g/cm³.
3. Calculate the Specific Gravity (s)
Specific gravity is the ratio of the fluid's density to the density of water. In the CGS system, the density of water is 1 g/cm³.
The specific gravity of the fluid is approximately \( s = 1.667 \).
Explanation of Terms
- Dynamic Viscosity (\(\mu\)): A measure of a fluid's internal resistance to flow under an applied force (shear).
- Kinematic Viscosity (\(\nu\)): A measure of a fluid's resistive flow under the influence of gravity. It is the dynamic viscosity divided by the fluid's density.
- Specific Gravity (s): A dimensionless value that compares the density of a substance to the density of water.
Physical Meaning
A specific gravity of 1.667 indicates that the fluid is 1.667 times denser than water. If this fluid were mixed with water, it would sink because it is significantly heavier for the same volume.
This single, dimensionless number is very useful in practice as it immediately tells an engineer or scientist how the fluid will behave relative to water, which is a universal reference point in many industrial and scientific applications.
