A simple force balance on a spherical particle reaching terminal velocity in a given fluid is given by

$v_1=\sqrt[\phantom{2}]{\frac{4\text{:}g({}_p-p)}{3C_0}{n}_p}$

$C_D$ in teims of $Vt.$

Where $v_t$ is the terminal velocity in $\frac{m}{s},g$ is the acceleration of gravity given by $g=9\mathrm{.}81\frac{m}{s^2},,$ is the parlicle's density in $k\frac{g}{m^3},$ is the fluid density in $k\frac{g}{m^3},D_p$ is the diameter of the spherical particle in $m$ and $C_D$ is a dimensionless drag coeflicient.

The drag coefficient on a sphcrical particle at terminal velocity varies with the Reynofls number $($Re$)$ as follosis:

$C_D=\frac{24}{Rc}(1+0\mathrm{.}14R{e}^{0\mathrm{.}1}),$ Where $Re=\frac{DpVtP}{}$

Please Use Newton Raphson's method to obtain the terminal velocity of the coal particles. Coal parameters given on image