## Newtonian Fluid

A Newtonian fluid with a dynamic viscosity of 0.4 kg/(m∙s) and a specific gravity of 0.9 flows through a 30 mm diameter pipe with a velocity of 3 m/s. Calculate the Reynolds number. Assume the standard density of water is 1,000 kg/m^3.

##
__
__**Hint**

**Hint**

The Reynolds number for a Newtonian fluid:

$$$Re=\frac{vD\rho}{\mu}$$$

where
$$v$$
is the fluid velocity,
$$D$$
is the pipe diameter or the fluid stream dimension or the characteristic length,
$$\rho$$
is the mass density, and
$$\mu$$
is the dynamic viscosity (or absolute viscosity).

##
__
__**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.

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.

$$$\rho=SG\times \rho_w=(0.9)(1,000\frac{kg}{m^3})=900\:\frac{kg}{m^3}$$$

The Reynolds number for a Newtonian fluid:

$$$Re=\frac{vD\rho}{\mu}$$$

where
$$v$$
is the fluid velocity,
$$D$$
is the pipe diameter or the fluid stream dimension or the characteristic length,
$$\rho$$
is the mass density, and
$$\mu$$
is the dynamic viscosity (or absolute viscosity).

$$$Re=\frac{(3m/s)(0.03m)(900kg/m^3)}{0.4\frac{kg}{m\cdot s}}=202.5$$$

202.5