## Flow Characterization

A Newtonian fluid with a dynamic viscosity of 0.01 kg/(m∙s) and a specific gravity of 0.7 flows through a 100 mm diameter pipe with a velocity of 5 m/s. Is the flow through the pipe characterized as laminar, turbulent, or transitional?

##
__
__**Hint**

**Hint**

Flow through a pipe is generally characterized as laminar for Re < 2,100, fully turbulent for Re > 10,000, and transitional flow for 2,100 < Re < 10,000.

##
__
__**Hint 2**

**Hint 2**

The Reynolds number for a Newtonian fluid:

$$$Re=\frac{vD}{\nu }$$$

where
$$v$$
is the fluid velocity,
$$D$$
is the pipe diameter or the fluid stream dimension or the characteristic length, and
$$\nu $$
is the kinematic viscosity.

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.

$$$\rho=SG\times \rho_w=(0.7)(1,000\frac{kg}{m^3})=700\:\frac{kg}{m^3}$$$

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).

$$$Re=\frac{(5m/s)(0.1m)(700kg/m^3)}{0.01\frac{kg}{m\cdot s}}=35,000$$$

Flow through a pipe is generally characterized as laminar for Re < 2,100, fully turbulent for Re > 10,000, and transitional flow for 2,100 < Re < 10,000.

Since
$$Re=35,000>10,000$$
, the flow is characterized as turbulent.

Turbulent