Viscous Density

#446 / Fluids Easy

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.

Expand 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


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