Kerosene flow: smooth, rough or transition

The type of boundary is decided by the roughness Reynolds number $Re_* = \dfrac{u_* k}{\nu}$ (Nikuradse): smooth $Re_* < 4$, transition $4 \le Re_* \le 100$, rough $Re_* > 100$.

Data. $D = 0.2$ m, $V = 5$ m/s, $k = 0.5$ mm, $f = 0.02$, $\rho = 800$ kg/m³. The viscosity is not given, so it is assumed that for kerosene at about 20 °C, $\mu \approx 1.9\times10^{-3}$ Pa s, giving $\nu = \mu/\rho = 2.375\times10^{-6}$ m²/s.

Shear velocity

$$u_* = V\sqrt{\frac{f}{8}} = 5\sqrt{\frac{0.02}{8}} = 0.250\ \text{m/s}$$

Roughness Reynolds number

$$Re_* = \frac{u_*k}{\nu} = \frac{(0.250)(0.0005)}{2.375\times10^{-6}} = 52.6$$

Check: laminar sub-layer thickness $\delta' = \dfrac{11.6\nu}{u_*} = 0.110$ mm, which is smaller than $k = 0.5$ mm, but $k/\delta' \approx 4.5$ lies in the transition range (0.25 to 6).

Since $4 < Re_* < 100$ (about 53), the pipe is neither smooth nor fully rough.

Answer: The pipe behaves in the transition regime ($Re = 421053$, $k/D = 0.0025$, $Re_* \approx 53$). The conclusion is the same for any realistic kerosene viscosity ($\nu$ between 1.9 and 2.8 $\times10^{-6}$ m²/s).