Question

Two identically sized primary settling tanks receive water for type-I settling surface overflow rate (SOR) maintained in the two tanks are $30m^3/s^{2}d$ and $15m^3/m^{2}d$. The lowest diameters of the particles, which shall be settled out completely under SORs of $30m^3/m^{2}d$ and $15m^3/m^{2}d$ are designated as $d_{30}$ and $d_{15}$ , respectively. The ratio $d_{30}/d_{15}$ (round off to two decimal places), is

• A. 1.41

Answer 1

The correct option is A 1.41
For type I settling (discrete particles in dilute suspension) under laminar flow condition, Stokes’ law can be applied.

As per Stokes’ law,
Settling velocity $\left(V_s\right)=\frac{(G_s-1){\gamma }_w{d}^2}{18\mu }$

If other parameters are assumed to be constant, then,

$V_s\propto d^2$

$\Rightarrow \left(\frac{V_{30}}{V_{15}}\right)={\left(\frac{d_{30}}{d_{15}}\right)}^2$

$\Rightarrow \left(\frac{d_{30}}{d_{15}}\right)=\sqrt{\left(\frac{V_{30}}{V_{15}}\right)}=\sqrt{\left(\frac{30}{15}\right)}=1.414$

$\Rightarrow \left(\frac{d_{30}}{d_{15}}\right)=1.414$