## 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
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
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