## Viscosity Variations

Determine the kinematic viscosity (m^2/s) of a fluid that has a 1.25 kg/(m∙s) dynamic viscosity, and a 1.5 specific gravity. Keep in mind that the standard density of water is 1,000 kg/m^3.

Hint
The units for dynamic viscosity (µ) are kg/(m*s), while the units for kinematic viscosity (υ) are m^2/s.
Hint 2
$$\nu =\frac{\mu}{\rho}$$$where $$\mu$$ is the dynamic viscosity, $$\nu$$ is the kinematic viscosity, and $$\rho$$ is the density. The units for dynamic viscosity (µ) are kg/(m∙s), while the units for kinematic viscosity (υ) are m^2/s. Thus, $$\nu =\frac{\mu}{\rho}$$$
where $$\mu$$ is the dynamic viscosity, $$\nu$$ is the kinematic viscosity, and $$\rho$$ is the fluid’s density in $$kg/m^3$$ .

To find the fluid’s density, recall that Specific Gravity is:
$$SG=\frac{\rho }{\rho_w}$$$where $$\rho$$ is the fluid density and $$\rho_w$$ is the density of water at standard conditions. $$\rho=SG\cdot \rho_w= (1.5)(1,000\frac{kg}{m^3})=1,500\:\frac{kg}{m^3}$$$
Solving for kinematic viscosity:
$$\nu =\frac{1.25\frac{kg}{m\cdot s}}{1,500\frac{kg}{m^3}}=0.00083\:m^2/s$$$$$0.00083\:m^2/s$$$