Question

Consider a primary sedimentation tank (PST) in a water treatment plant with Surface Overflow Rate (SOR) of $40m^3/m^2/d$. The diameter of the spherical particle which will have $90$ percent theoretical removal efficiency in this tank is ________µm.
Assume that settling velocity of the particles in water is described by Stoke's Law.

Given : Density of water $=1000kg/m^3$,
Density of particle = $2650Kg/m^3$,$g=9.81m/s^2$.
Kinematic viscosity of water $\left(v\right)=1.10\times {10}^{-6}{m}^2/s$.

• A. 22.576

Answer 1

The correct option is A 22.576
$\%removal=\frac{V_s^{\prime }}{V_s}\times 100$

$V_s^{\prime }=0.9\times V_s$

$=0.9\times \text{overflow rate}$

$V_s^{\prime }=\frac{0.9\times 40}{86400}m/s$

$\frac{({\gamma }_s-{\gamma }_w)d^2}{18\mu }=\frac{0.9\times 40}{86400}m/s$

$d=\sqrt{\frac{0.9\times 40\times 18{\rho }_{w}v}{86400\times (G_s-1)\times {\rho }_w\times g}}$

$d\left(m\right)=\sqrt{\frac{0.9\times 40\times 18\times 1.\times {10}^{-6}}{86400\times 1.64\times 9.81}}$

$=2.2576\times {10}^{-5}m$

$=22.576\mu m$