Q1GATE 2022MCQ

Henry's law constant for transferring $O_2$ from air into water, at room temperature, is 1.3 $\frac{mmol}{liter-atm}$ . Given that the partial pressure of $O_2$ in the atmosphere is 0.21 atm, the concentration of dissolved oxygen (mg/liter) in water in equilibrium with the atmosphere at room temperature is (Consider the molecular weight of $O_2$ as 32 g/mol)

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📖 Explanation

Henry's Law $C_g=KP$ $C_g=$ Concentration of dissolved gas $K=$ Henry?s law constant $P=$ Partial pressure of gas $C_g= 1.3 \;m\; mol/(lit-atm) \times 0.21 atm =0.273 \;m\; mol/lit=0.273 \times 32 \; mg/lit=8.736 \; mg/lit$

Q2GATE 2022MSQ

For wastewater coming from a wood pulping industry, Chemical Oxygen Demand $(COD)$ and 5-day Biochemical Oxygen Demand $(BOD_5)$ were determined. For this wastewater, which of the following statement(s) is/are correct?

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📖 Explanation

We know COD is the oxygen demand for both biodegradable and non-biodegradable organic matter. Hence $COD \gt BOD_5$ also $COD \neq BOD_5$

Q3GATE 2020NAT

A stream with a flow rate of 5 $m^3/s$ is having an ultimate BOD of 30 mg/litre. A wastewater discharge of 0.20 $m^3/s$ having BOD5 of 500 mg/litre joins the stream at a location and instantaneously gets mixed up completely. The cross-sectional area of the stream is 40 $m^2$ which remains constant. BOD exertion rate constant is 0.3 per day (logarithm base to e). The BOD (in mg/litre round off to two decimal places) remaining at 3 km downstream from the mixing location, is ________.

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📖 Explanation

\begin{aligned} t &=\frac{d}{v} \\ \text{where,} \;\; v&=\frac{Q_s+Q_R}{A} \\ &= \frac{0.2+5}{40}=0.13 m/sec\\ t&=\frac{3 \times 10^3}{0.13 \times 86400}=0.26 \;day \\ BOD_5&=BOD_u(1-e^{-k\times 5}) \\ BOD_u&=\frac{500}{(1-e^{-0.5 \times 5})}=643.66\; mg/l \\ DO_{mix}&=\frac{Q_RBOD_u+Q_s BOD_u}{Q_s+Q_R} \\ &=\frac{5 \times 30+0.2\times 643.66}{5+0.2} \\ &= 53.6\; mg/l\\ L_t&=L_0 e^{-k \times t} \\ &=53.6 e^{-0.3 \times 0.26}\\ &=49.57\; mg/l \end{aligned}

Q4GATE 2020MCQ

The relationship between oxygen consumption and equivalent biodegradable organic removal (i.e. BOD) in a closed container with respect to time is shown in the figure. Assume that the rate of oxygen consumption is directly proportional to the amount of degradable organic matter and is expressed as $\frac{dL_t}{dt}=-kL_t$ , where, $L_t$ (in mg/litre) is the oxygen equivalent of the organics remaining at time t and $k$ (in $d^{-1}$ ) is the degradation rate constant. $L_0$ is the oxygen of organic matter at time, t = 0. In the above context, the correct expression is

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📖 Explanation

Given,

\begin{aligned} \frac{dL_t}{dt}&=-kL_t \\ \Rightarrow \; \frac{dL_t}{L_t} &=-kdt \\ \Rightarrow \; \int_{L_o}^{L_t} \frac{dL_t}{L_t} &=-k\int_{0}^{t}dt \\ \Rightarrow \; \ln \left ( \frac{L_t}{L_o} \right ) &=-kt \\ \Rightarrow \; L_t&=L_o e^{-kt} \end{aligned}

The term $L_o$ in the above equation represents the total oxygen equivalent of the organics at time $t=0$ , while $L_t$ represents the amount remaining at time $t$ , and decays exponentially with time. The amount of oxygen used in the consumption of the organics, the ${BOD}_t$ can be found from the $L_t$ value. The difference between the value $L_o$ and $L_t$ is the oxygen equivalent consumed, or the BOD exerted. Mathematically ${BOD}_t=(L_o-L_t)=L_o-L_oe^{-kt}=L_o(1-e^{-kt})$

Q5GATE 2004MCQ

The present population of a community is 28000 with an average water consumption of 4200 $m^{3}$ /d. The existing water treatment plant has a design capacity of 6000 $m^{3}$ /d. It is expected that the population will increase to 44000 during the next 20 years. The number of years from now when the plant will reach its design capacity, assuming an arithmetic rate of population growth, will be

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📖 Explanation

Assuming arithmetic rate of growth of population. Increase in population per year $=\frac{44000-28000}{20}=800$ Discharge required to reach design capacity $=6000-4200=1800 m^{3} / d$ Present average water consumption per head per day $=\frac{4200}{28000}=0.15 \mathrm{m}^{3}$ Increase in water consumption each year $=0.15 \times 800=120 \mathrm{m}^{3} / \mathrm{day}$ $\therefore$ No. of years required to reach design capacity $=\frac{1800}{120}=15 \text { years }$

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