Physics - Fluid Question with Solution | TestHub

The nature of the flow of a fluid through a pipe is determined by the Reynolds number ($R_e$), which is given by the formula:

$R_e=\frac{\rho vD}{\eta }$

where:
$\rho =10^3{\text{ kg/m}}^3$ (density of water)
$v=12\text{ cm/s}=0.12\text{ m/s}$ (average velocity)
$D=2\times r=2\times 1.4\text{ cm}=2.8\text{ cm}=0.028\text{ m}$ (diameter of the pipe)
$\eta =10^{-3}{\text{ kg m}}^{-1}{\text{ s}}^{-1}$ (coefficient of viscosity)

Substituting the given values into the formula:

$R_e=\frac{10^3\times 0.12\times 0.028}{10^{-3}}$

$R_e=\frac{3.36}{10^{-3}}=3360$

According to the standard convention:
If $R_e<1000$, the flow is streamline (laminar).
If $1000<R_e<2000$, the flow is unsteady.
If $R_e>2000$, the flow is turbulent.

Since $R_e=3360$, which is greater than $2000$, the flow of water is turbulent.

Answer: turbulent