1.1Relate Density, Specific Weight, and Viscosity
A fluid has density $1000\ \text{kg/m}^3$ and dynamic viscosity $1.0\times 10^{-3}\ \text{Pa}\cdot\text{s}$.
Find:
its specific weight $\gamma$
its specific volume $v$
its kinematic viscosity $\nu$
Also state whether this fluid is usually modeled as incompressible and Newtonian in ordinary pipe flow.
Solution
Use the definitions:
$$
\gamma = \rho g = 1000(9.81) = 9810\ \text{N/m}^3
$$
$$
v = \frac{1}{\rho} = \frac{1}{1000} = 1.0\times 10^{-3}\ \text{m}^3/\text{kg}
$$
$$
\nu = \frac{\mu}{\rho} = \frac{1.0\times 10^{-3}}{1000} = 1.0\times 10^{-6}\ \text{m}^2/\text{s}
$$
This fluid is commonly modeled as incompressible and Newtonian in ordinary pipe flow.