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Standard XI

Economics

Fixed and Variable Factors of Production

A wastewater ...

Question

A wastewater is to be disinfected with 28 $m g / l$ of chlorine to obtain 99.9% kill of micro-organisms. The number of micro-organisms remaining at the time t is given by mathematical expression. $N_{t} = N_{0} e^{- 0.13 t}$ where $N_{0}$ is initial concentration of micro-organisms and t is time in minutes. The waste water flow rate is 0.015 $m^{3} / s e c$ If the depth of chlorination tank is 1.5 m, the diameter of chlorination tank is 1.5 m, the diameter of chlorination tank is m.
6.3

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Solution

The correct option is A 6.3
Efficiency of chlorination tank, $η = \frac{N_{0} - N_{t}}{N_{0}} = 0.999$

$N_{0} - N_{t} = 0.999 N$

$N_{t} = 0.001 N_{0}$

$N_{0} e^{- 0.13 t} = 0.001 N_{0}$

t=53.14 minutes

Volume of tank= Qt
$= 0.015 \times 53.14 \times 60 m^{3}$
$= 47.826 m^{3}$

Let diameter of chlorination tank be d
$\frac{π}{4} d^{2} \times 1.5 = 47.826$
d=6.37 m

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The correct option is A 6.3Efficiency of chlorination tank, η=N0−NtN0=0.999 N0−Nt=0.999N Nt=0.001N0 N0e−0.13t=0.001N0 t=53.14 minutes Volume of tank= Qt =0.015×53.14×60m3 =47.826m3 Let diameter of chlorination tank be d π4d2×1.5=47.826 d=6.37 m