Respuesta :
Explanation:
The volumetric flow rate of water will be as follows.
q = [tex]600 gpm \times \frac{0.000063 m^{3} s^{-1}}{1 gpm}[/tex]
= 0.0378 [tex]m^{3}/s [/tex]
Diameter = [tex]8 in \times \frac{0.0254 m}{1 in}[/tex]
= 0.2032 m
Relation between area and diameter is as follows.
A = [tex]\frac{\pi}{4} \times D^{2}[/tex]
= [tex]\frac{3.14}{4} \times (0.2032 m)^{2}[/tex]
= 0.785 x 0.2032 x 0.2032
= 0.0324 [tex]m^{2}[/tex]
Also, q = A × V
or, V = [tex]\frac{q}{A}[/tex]
= [tex]\frac{0.0378 m^{3}/s}{0.0324 m^{2}}[/tex]
= 1.166 m/s
As, viscosity of water = 1 cP = [tex]10^{-3}[/tex] Pa-s
Density of water = 1000 [tex]kg/m^{3}[/tex]
Therefore, we will calculate Reynolds number as follows.
Reynolds number = [tex]\frac{D \times V \times density}{viscosity}[/tex]
= [tex]\frac{0.2032 m \times 1.166 m/s \times 1000}{10^{-3}}[/tex]
= 236931.2
Hence, the flow will be turbulent in nature.
Thus, we can conclude that the Reynolds number is 236931.2 and flow is turbulent.
