## 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**

**Hint**

The units for dynamic viscosity (µ) are kg/(m*s), while the units for kinematic viscosity (υ) are m^2/s.

##
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__**Hint 2**

**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:

$$$\nu =\frac{1.25\frac{kg}{m\cdot s}}{1,500\frac{kg}{m^3}}=0.00083\:m^2/s$$$

$$$0.00083\:m^2/s$$$