## Viscous Density

A certain fluid has a dynamic viscosity of 1.5 kg/(m∙s), and a kinematic viscosity of 0.002 m^2/s. What is the fluid’s specific gravity? Note the standard density of water is 1,000 kg/m^3.

Hint
$$\nu =\mu/\rho$$$where $$\nu$$ is the kinematic viscosity, $$\mu$$ is the absolute dynamic viscosity, and $$\rho$$ is the fluid’s density. Hint 2 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.
The units for the absolute dynamic viscosity ( $$\mu$$ ) are $$kg/(m\cdot s)$$ . The units for the kinematic viscosity ( $$\nu$$ ) are $$m_{}^{2}/s$$ . The relationship between the the two viscosities is:
$$\nu =\mu/\rho$$$where $$\rho$$ is the fluid’s density in $$kg/m^{3}$$ . $$\rho=\frac{\mu }{\nu }=\frac{1.5\frac{kg}{m\cdot s}}{0.002\frac{m^2}{s}}=750\:kg/m^3$$$
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. $$SG=\frac{750kg/m^3}{1,000kg/m^3}=0.75$$$
0.75