## 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**

**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**

**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