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Question 1
ప్రశ్న 1
Which combination best describes natural stream self-purification after a biodegradable wastewater discharge?
Explanation:
Stream self-purification involves several interacting physical, chemical and biological processes. Dilution reduces some contaminant concentrations without destroying pollutant mass. Sedimentation can remove settleable particles from the water column. Microbial oxidation transforms biodegradable matter while consuming dissolved oxygen, and reaeration can replenish that oxygen. These processes do not guarantee that the water becomes safe or meets discharge standards.
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Question 2
ప్రశ్న 2
In the simple Streeter–Phelps model with natural-base constants, which pairing correctly identifies the instantaneous rates of deoxygenation and atmospheric reaeration?
Explanation:
In the model, L(t) is the ultimate carbonaceous oxygen demand remaining at time t. The biological deoxygenation rate is kd multiplied by L(t). The atmospheric reaeration rate is kr multiplied by the oxygen deficit D. Both rates can be expressed in mg/L per day when the coefficients use day inverse units. They compete to determine whether dissolved oxygen decreases or increases.
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Question 3
ప్రశ్న 3
At a given stream temperature and pressure, saturation DO is 9.2 mg/L and actual DO is 5.6 mg/L. What is the oxygen deficit?
Explanation:
Oxygen deficit is defined as saturation DO minus actual DO. The given saturation concentration is 9.2 mg/L. The observed DO concentration is 5.6 mg/L. Subtraction gives D = 9.2 - 5.6 = 3.6 mg/L. A positive deficit represents oxygen below the stated saturation concentration.
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Question 4
ప్రశ్న 4
Which statement correctly describes the effect of increasing water temperature on stream dissolved-oxygen conditions, without assuming particular kinetic coefficients?
Explanation:
The equilibrium solubility of oxygen in freshwater generally declines as temperature rises under comparable pressure and salinity. Microbial reaction rates and oxygen-transfer processes may also change with temperature. Their combined effect on the sag depends on stream and wastewater conditions. A numerical prediction requires appropriate rate constants and a saturation concentration at the relevant temperature. Therefore temperature should be considered explicitly rather than assigned a universal fixed change in minimum DO.
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Question 5
ప్రశ్న 5
At the critical point of a conventional dissolved-oxygen sag curve, which condition is correct?
Explanation:
A dissolved-oxygen sag is produced by the competition between oxygen consumption and oxygen replenishment. The critical point is where the stream attains its lowest modeled DO concentration. Since deficit equals saturation DO minus actual DO, this corresponds to the largest modeled deficit when saturation is constant. At an interior critical point the deficit's time derivative becomes zero. Oxygen demand may remain positive at that point and gradually decline farther downstream.
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Question 6
ప్రశ్న 6
Starting immediately downstream of an appreciable organic-waste discharge and moving toward restored water quality, what is the conventional sequence of the four principal stream zones?
Explanation:
The zone of degradation begins where the waste causes increasing organic loading and falling DO. It is followed by the zone of active decomposition, where oxygen depletion and biological breakdown can be most intense. Farther downstream, the recovery zone develops as demand declines and oxygen replenishment becomes more effective. The clear-water zone represents substantial restoration of stream conditions. The exact extent of each zone depends on loading, stream hydraulics and environmental factors.
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Question 7
ప్రశ్న 7
Which observation is most characteristic of the conventional zone of active decomposition in a stream receiving heavy biodegradable pollution?
Explanation:
The active-decomposition zone develops where oxygen-consuming degradation is particularly intense. Dissolved oxygen may fall to very low values and can approach zero in severe cases. Anaerobic processes may develop where oxygen is exhausted. Sensitive aerobic organisms can be adversely affected in this reach. The occurrence and severity of these conditions depend on the organic load and stream oxygen supply.
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Question 8
ప్రశ్న 8
After the most oxygen-depleted reach, which condition most directly explains the increase in DO in the recovery portion of a simplified oxygen-sag model?
Explanation:
The rate of change of deficit is the deoxygenation rate minus the reaeration rate. During recovery, the oxygen-transfer contribution becomes greater than the oxygen-consumption contribution. The deficit then decreases with travel time. Since DO equals saturation DO minus deficit, DO increases when saturation is constant. Further recovery may be influenced by additional oxygen sources and sinks not included in the simple model.
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Question 9
ప్రశ్న 9
A stream-water mixture has initial ultimate carbonaceous BOD L0 = 20 mg/L and natural-base kd = 0.20 day^-1. After 3 days, what are the approximate BOD exerted and BOD remaining, respectively?
Explanation:
The first-order remaining demand is L(t) = L0 exp(-kd t). Inserting kd = 0.20 day^-1 and t = 3 days gives L(3) = 20 exp(-0.6). The remaining demand is approximately 10.98 mg/L. The exerted demand is 20 - 10.98 = 9.02 mg/L. These quantities describe cumulative biochemical oxygen use and the demand still available for exertion.
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Question 10
ప్రశ్న 10
Suppose a stream has no modeled deoxygenation load and only first-order reaeration acts, with D0 = 4 mg/L, kr = 0.40 day^-1 and constant saturation DO = 9 mg/L. What is DO after 2 days?
Explanation:
With no deoxygenation term, oxygen deficit obeys D(t) = D0 exp(-kr t). The exponent at two days is -0.40 times 2, or -0.8. The remaining deficit is 4 exp(-0.8), approximately 1.797 mg/L. Subtracting this from saturation DO of 9 mg/L gives approximately 7.203 mg/L. This scenario isolates reaeration and should not be mistaken for a stream with continuing biodegradable oxygen demand.
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Question 11
ప్రశ్న 11
For the classical model with L(t) = L0 exp(-kd t), deficit D(t), and constant natural-base kd and kr, what is the governing deficit equation?
Explanation:
The carbonaceous oxygen demand remaining decreases exponentially under first-order kinetics. Its oxygen consumption rate is kd L0 exp(-kd t). Atmospheric reaeration acts to reduce the oxygen deficit at rate kr D. The net rate of change of deficit is oxygen use minus oxygen replenishment. Therefore the differential equation is dD/dt = kd L0 exp(-kd t) - kr D.
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Question 12
ప్రశ్న 12
At a particular time in a simplified stream model, kd = 0.25 day^-1, remaining ultimate BOD L = 12 mg/L, kr = 0.60 day^-1 and oxygen deficit D = 3 mg/L. What is the instantaneous trend?
Explanation:
Deoxygenation rate is kd L = 0.25 times 12 = 3.0 mg/L per day. Reaeration rate is kr D = 0.60 times 3 = 1.8 mg/L per day. The deficit's rate of change is 3.0 - 1.8 = +1.2 mg/L per day. A positive deficit derivative means the oxygen deficit is increasing. If saturation DO stays constant, actual DO is therefore decreasing at that instant.
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Question 13
ప్రశ్న 13
A river flows at 20 m^3/s with DO = 8 mg/L and receives 2 m^3/s of effluent with DO = 2 mg/L. Assuming immediate complete mixing, negligible initial reaction and saturation DO = 9 mg/L, what are mixed DO and initial deficit?
Explanation:
The initial mixed DO follows a flow-weighted mass balance. Its value is (20 times 8 + 2 times 2)/(20 + 2). This equals approximately 7.45 mg/L. Oxygen deficit after mixing is 9 - 7.45, approximately 1.55 mg/L. These values provide the initial mixed condition before subsequent modeled deoxygenation and reaeration.
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Question 14
ప్రశ్న 14
A river carrying 12 m^3/s has ultimate carbonaceous BOD of 3 mg/L and receives an effluent of 3 m^3/s having ultimate BOD of 45 mg/L. With instantaneous mixing and no immediate reaction, what is the mixed ultimate BOD?
Explanation:
The initial mixed oxygen demand is found from a flow-weighted balance. The upstream river contributes 12 times 3 in concentration-flow units. The effluent contributes 3 times 45 in the same units. Dividing the total of 171 by the combined flow of 15 m^3/s gives 11.4 mg/L. This value can serve as L0 for a downstream model when the stated carbonaceous-BOD assumptions apply.
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Question 15
ప్రశ్న 15
Which expression correctly represents the classical Streeter–Phelps oxygen deficit D(t), if kd and kr are distinct natural-base day^-1 constants, L0 is mixed initial ultimate carbonaceous BOD, and D0 is the initial deficit?
Explanation:
The classical model combines a first-order biochemical oxygen demand with first-order atmospheric reaeration. The forcing due to demand remaining produces the difference of two exponential terms. The initial deficit contributes the separate term D0 exp(-kr t). With distinct rate constants, the coefficient of the exponential difference is kd L0/(kr - kd). The model assumes constant rates and saturation conditions and excludes additional oxygen sources or sinks unless added explicitly.
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Question 16
ప్రశ్న 16
Use D(t) = [kd L0/(kr-kd)](exp(-kd t)-exp(-kr t)) + D0 exp(-kr t). For kd = 0.20 day^-1, kr = 0.50 day^-1, L0 = 12 mg/L, D0 = 1 mg/L and t = 2 days, what is the approximate deficit?
Explanation:
The coefficient kd L0/(kr-kd) equals 0.20 times 12 divided by 0.30, or 8. The two exponential factors at two days are exp(-0.4) and exp(-1.0). Their difference is approximately 0.30244, contributing about 2.4195 mg/L. The initial-deficit term contributes exp(-1.0), or about 0.3679 mg/L. Summing both terms gives an oxygen deficit of approximately 2.79 mg/L.
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Question 17
ప్రశ్న 17
A stream follows the classical model with D0 = 0, kd = 0.20 day^-1, kr = 0.60 day^-1, L0 = 10 mg/L and saturation DO = 9 mg/L. What is DO after 2 days?
Explanation:
With D0 = 0, the deficit is kd L0/(kr-kd) times the difference of the exponential factors. The coefficient is 0.20 times 10 divided by 0.40, or 5. At two days, the factors are exp(-0.4) and exp(-1.2). Their difference gives a deficit of approximately 1.846 mg/L. Actual DO is 9 - 1.846, or approximately 7.15 mg/L.
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Question 18
ప్రశ్న 18
Under the classical Streeter–Phelps model with D0 = 0, kd = 0.20 day^-1 and kr = 0.60 day^-1, what is the time to an interior maximum deficit?
Explanation:
For zero initial deficit and distinct positive rate constants, critical time is ln(kr/kd)/(kr-kd). The ratio kr/kd is 0.60/0.20 = 3. The denominator is 0.60 - 0.20 = 0.40 day^-1. Hence critical time equals ln(3)/0.40, approximately 2.75 days. This is elapsed travel time from the mixing point, not a laboratory BOD incubation period.
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Question 19
ప్రశ్న 19
For D0 = 0, L0 = 12 mg/L, kd = 0.20 day^-1, kr = 0.60 day^-1 and constant saturation DO = 9 mg/L, critical time is 2.7465 days. What are the approximate critical deficit and minimum DO?
Explanation:
At an interior critical point, deoxygenation and reaeration rates are equal. Therefore the critical deficit is Dc = (kd/kr)L0 exp(-kd tc). With the stated values it is (0.20/0.60) times 12 times exp(-0.20 times 2.7465). This evaluates to approximately 2.31 mg/L. The minimum DO is 9 - 2.31, approximately 6.69 mg/L.
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Question 20
ప్రశ్న 20
The modeled critical time from a wastewater outfall is 2.7465 days, and stream velocity is constant at 0.25 m/s. What is the downstream critical distance, assuming plug-flow travel?
Explanation:
Downstream distance equals mean stream velocity multiplied by travel time. The time is 2.7465 days, with 86400 seconds in each day. Thus distance in metres is 0.25 times 2.7465 times 86400. This gives approximately 59324 m. The corresponding critical distance is about 59.3 km under the specified constant-velocity assumption.
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Question 21
ప్రశ్న 21
Use the classical critical-time expression tc = ln[(kr/kd){1 - D0(kr-kd)/(kd L0)}]/(kr-kd). For kd = 0.20, kr = 0.60 day^-1, L0 = 12 mg/L and D0 = 1 mg/L, what is tc when an interior maximum exists?
Explanation:
The rate-constant difference is kr - kd = 0.40 day^-1. The correction factor inside the brackets is 1 - (1 times 0.40)/(0.20 times 12), or 5/6. Multiplying by kr/kd = 3 gives the logarithm argument 2.5. Thus tc = ln(2.5)/0.40, approximately 2.29 days. The positive result identifies an interior modeled maximum deficit downstream of the mixing point.
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Question 22
ప్రశ్న 22
At the wastewater mixing point, kd = 0.20 day^-1, L0 = 10 mg/L, kr = 0.50 day^-1 and D0 = 5 mg/L. Under the classical model with no additional loads, which conclusion best describes the immediate downstream oxygen-deficit trend?
Explanation:
The deoxygenation rate immediately after mixing is kd L0 = 0.20 times 10 = 2.0 mg/L per day. Reaeration at that point is kr D0 = 0.50 times 5 = 2.5 mg/L per day. The initial deficit derivative is 2.0 - 2.5 = -0.5 mg/L per day. Thus the deficit initially decreases and DO rises when saturation is constant. An interior downstream maximum should not be assumed when the initial deficit is already large.
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Question 23
ప్రశ్న 23
Two otherwise identical modeled stream reaches have the same kd, L0, D0, temperature and travel time, but Reach X has a larger positive reaeration constant kr than Reach Y. In the classical model, which conclusion is justified?
Explanation:
The reaeration term in the deficit balance is kr D. For otherwise identical loads and conditions, a larger kr removes a positive deficit more rapidly. The biochemical deoxygenation rate kd L(t) remains the same when kd and the initial demand are unchanged. Accordingly, the modeled deficit in the higher-reaeration reach is lower at the same positive travel time. Real streams may also differ in temperature, sediment demand and other processes, but these have been excluded by the question.
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Question 24
ప్రశ్న 24
A river has constant velocity 0.50 m/s and saturation DO = 9 mg/L. At 43.2 km downstream, use the classical model with kd = 0.20 day^-1, kr = 0.60 day^-1, L0 = 12 mg/L and D0 = 1 mg/L; what DO is predicted?
Explanation:
The travel time is 43200 metres divided by 0.50 m/s, or 86400 seconds = 1 day. The deficit coefficient kd L0/(kr-kd) is 0.20 times 12 divided by 0.40, or 6. At one day, D = 6[exp(-0.2) - exp(-0.6)] + exp(-0.6). This gives a deficit of approximately 2.168 mg/L. Subtracting from 9 mg/L gives predicted DO approximately 6.83 mg/L.
వివరణ:
Question 25
ప్రశ్న 25
A treatment improvement lowers the initial mixed ultimate carbonaceous BOD L0 from 12 to 8 mg/L while leaving D0 = 1 mg/L, kd = 0.20 day^-1, kr = 0.60 day^-1 and saturation DO unchanged. In the classical model, how much higher is DO after 2 days?
Explanation:
Under unchanged D0 and coefficients, the difference in modeled deficits comes only from the difference in L0. The coefficient multiplying that difference is kd/(kr-kd) times [exp(-kd t)-exp(-kr t)]. Here L0 decreases by 4 mg/L and kd/(kr-kd) equals 0.5. At two days the exponential difference is exp(-0.4)-exp(-1.2), approximately 0.36913. The decrease in deficit, and therefore the increase in DO at unchanged saturation, is approximately 0.738 mg/L.
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Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. Processes including dilution, sedimentation, biological oxidation and atmospheric reaeration, without guaranteeing complete safety. సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: C. Deoxygenation = kd L(t) and reaeration = kr D. సమాధానం: C.
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Question 3 ప్రశ్న 3Answer: A. 3.6 mg/L సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: D. Saturation DO generally decreases as temperature increases, while reaction-rate changes can also affect the sag. సమాధానం: D.
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Question 5 ప్రశ్న 5Answer: B. The oxygen deficit is locally maximum and DO is locally minimum. సమాధానం: B.
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Question 6 ప్రశ్న 6Answer: C. Degradation, active decomposition, recovery, clear water. సమాధానం: C.
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Question 7 ప్రశ్న 7Answer: A. Very low dissolved oxygen with intense organic decomposition and possible anaerobic conditions. సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: D. The reaeration rate exceeds the remaining deoxygenation rate, causing the deficit to decrease. సమాధానం: D.
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Question 9 ప్రశ్న 9Answer: B. 9.02 mg/L exerted and 10.98 mg/L remaining. సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: D. 7.20 mg/L సమాధానం: D.
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Question 11 ప్రశ్న 11Answer: A. dD/dt = kd L0 exp(-kd t) - kr D సమాధానం: A.
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Question 12 ప్రశ్న 12Answer: C. Deficit is increasing at 1.2 mg/L per day, so DO is falling if saturation is constant. సమాధానం: C.
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Question 13 ప్రశ్న 13Answer: B. 7.45 mg/L and 1.55 mg/L. సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: A. 11.4 mg/L సమాధానం: A.
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Question 15 ప్రశ్న 15Answer: D. D(t) = kd L0/(kr - kd) [exp(-kd t) - exp(-kr t)] + D0 exp(-kr t) సమాధానం: D.
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Question 16 ప్రశ్న 16Answer: C. 2.79 mg/L సమాధానం: C.
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Question 17 ప్రశ్న 17Answer: A. Approximately 7.15 mg/L సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: D. Approximately 2.75 days సమాధానం: D.
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Question 19 ప్రశ్న 19Answer: B. Critical deficit 2.31 mg/L and minimum DO 6.69 mg/L. సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: D. 59.3 km సమాధానం: D.
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Question 21 ప్రశ్న 21Answer: A. Approximately 2.29 days సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: B. The deficit initially falls at 0.5 mg/L per day, so DO initially rises if saturation remains constant. సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: C. Reach X generally has a lower modeled oxygen deficit after positive travel time due to faster oxygen replenishment. సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: D. 6.83 mg/L సమాధానం: D.
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Question 25 ప్రశ్న 25Answer: A. Approximately 0.74 mg/L higher సమాధానం: A.
