Colebrook-White and Darcy Weisbach combined

Calculate Velocity in pipe
Based on uniform flow, friction loss only. Suitable for turbulent and laminar flow.
$latex \fn_cm \color{red} \LARGE V=-2\cdot \sqrt[2]{2g\cdot D\cdot S_{f}}\cdot log\left ( \frac{k_{s}}{3,70\cdot D}+\frac{2,51\cdot \nu }{D\sqrt[2]{2g\cdot D\cdot S_{f}}} \right )$

with $latex \fn_cm \color{red} \LARGE S_{f}=\frac{h_{f}}{L} $

V  = Velocity                                    [m/s]
g  = Earths gravity= 9,81                        [m/s²]
D  = Hydraulic Diameter = 4·R                    [m]
S_f = Slope hydraulic gradient caused by friction [1]
h_f = Frictional head loss                        [m]
L  = Length                                      [m]
k_s = surface roughness                           [m]

u     = Kinematic viscosity                         [m²/s]

u  water 20°C       = 1,00·10^-6 [m²/s]