Diagram for Computing Particle Settling Velocity

As derived in class, the relation for terminal fall velocity $($settling velocity$)$ in quiescent

fluid $v_s$ can be presented as

$R_f=[\frac{4}{3}\frac{1}{C_D}{]}^{\frac{1}{2}}$

Here

$R_f=\frac{v_s}{\sqrt[\phantom{2}]{RgD}},R_p=\frac{v_{s}D}{v}$

and the functional relation $C_D($versus $R_p)$ denotes the drag curve for spheres. This

relation is not very useful because it is not explicit in $v_s$; one must compute fall velocity

by trial and error. Use an appropriate drag curve for spheres and the definition:

$R_{ep}=\frac{\sqrt[\phantom{2}]{RgD}D}{v}$

to obtain an explicit relation for fall velocity in the form of $R_f$ versus $R_{ep}.$

Hint: Verify relation:

$R_p=R_f*R_{ep}$

Mark off ranges for silt, sand, and gravel on your plot for $v=0\mathrm{.}01c\frac{m^2}{s}($clear water at

$20C)$ and $R=1\mathrm{.}65($quartz$).$