## 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
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 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