To find a solution to this problem it is necessary to apply the concepts related to the Reynolds number and its definitions on the type of fluid.
A Reynolds number less than 2000 considers the laminar fluid, while a Reynolds number greater than 4000 is considered a turbulent fluid. (The intermediate between the two values would be a transient fluid)
The mathematical equation that defines the Reynolds number is given by
[tex]Re = \frac{\rho V D}{\mu}[/tex]
Where
[tex]\rho =[/tex] Density
V= Velocity
D= Diameter
[tex]\mu =[/tex] Viscosity
Our values are given as
[tex]Q = 0.2m^3/s[/tex]
[tex]D = 203*10^{-3}m[/tex]
[tex]\rho = 680kg/m^3[/tex]
[tex]\mu = 3.1*10^{-4}Ns/m^2[/tex]
[tex]\sigma = 0.022N/m[/tex]
The velocity can be find through the Discharge equation,
Q = VA
Where
V = Velocity
A = Area
Replacing,
[tex]0.2 = V* (2\pi*(\frac{203*10^{-3}}{2})^2)[/tex]
[tex]V = 3.08m/s[/tex]
Replacing at the Reynolds equation,
[tex]Re = \frac{\rho VD}{\mu}[/tex]
[tex]Re = \frac{680*3.08*203*10^{-3}}{3.1*10^{-4}}[/tex]
[tex]Re = 1.37*10^6[/tex]
Since Reynolds' number is greater than 4000, then we consider this a turbulent fluid.
