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The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??
- a)8.6 years
- b)12.0 years
- c)15.0 years
- d)16.5 years
Correct answer is option 'B'. Can you explain this answer?
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The present population of a community is 28000 with an average water d...
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The present population of a community is 28000 with an average water d...
Given data:
Population (P) = 28000
Water demand = 150 Lpcd
Design capacity of water treatment plant (Qd) = 6000 m3/d
Calculation:
Total water demand = P × water demand
= 28000 × 150
= 4200000 L/d
Converting L/d to m3/d:
1 L/d = 0.001 m3/d
∴ Total water demand = 4200000 × 0.001
= 4200 m3/d
Deficit in water treatment plant = Total water demand - Design capacity
= 4200 - 6000
= -1800 m3/d
Negative sign indicates that the present water treatment plant has excess capacity to meet the present water demand.
Arithmetic rate of population growth can be calculated using the formula:
r = (Pn - P0) / (n × P0) × 100
where,
r = Arithmetic rate of population growth
P0 = Initial population
Pn = Population after 'n' years
n = Number of years
Assuming the arithmetic rate of population growth to be constant for the next 20 years, we can use the above formula to calculate the population after 20 years.
Let the population after 20 years be P20.
Then,
r = (P20 - P0) / (20 × P0) × 100
Assuming r to be same for the next 20 years, the population after 't' years can be calculated using the formula:
Pt = P0 (1 + r/100)t
where,
Pt = Population after 't' years
P0 = Initial population
r = Arithmetic rate of population growth
t = Number of years
As per the given data, the water demand is expected to increase in proportion to the population growth. Therefore, the water demand after 't' years can be calculated using the formula:
Qt = Qd × (Pt / P)
where,
Qt = Water demand after 't' years
Qd = Design capacity of water treatment plant
Pt = Population after 't' years
P = Present population
The number of years from now when the plant will reach its design capacity can be calculated by equating the water demand after 't' years to the design capacity and solving for 't'.
Mathematically, the above steps can be summarized as follows:
- Calculate the total water demand at present.
- Calculate the deficit in the present water treatment plant.
- Assume an arithmetic rate of population growth and calculate the population after 20 years.
- Use the population after 20 years to calculate the population after 't' years using the formula Pt = P0 (1 + r/100)t.
- Use the population after 't' years to calculate the water demand after 't' years using the formula Qt = Qd × (Pt / P).
- Equate the water demand after 't' years to the design capacity and solve for 't'.
Substituting the given values in the above formulae, we get:
r = (P20 - P0) / (20 × P0) × 100
= (P20 - 28000) / (20 × 28000) × 100
Assuming an arithmetic rate of population growth of 'r' %, we can calculate the population after 't' years using
Population (P) = 28000
Water demand = 150 Lpcd
Design capacity of water treatment plant (Qd) = 6000 m3/d
Calculation:
Total water demand = P × water demand
= 28000 × 150
= 4200000 L/d
Converting L/d to m3/d:
1 L/d = 0.001 m3/d
∴ Total water demand = 4200000 × 0.001
= 4200 m3/d
Deficit in water treatment plant = Total water demand - Design capacity
= 4200 - 6000
= -1800 m3/d
Negative sign indicates that the present water treatment plant has excess capacity to meet the present water demand.
Arithmetic rate of population growth can be calculated using the formula:
r = (Pn - P0) / (n × P0) × 100
where,
r = Arithmetic rate of population growth
P0 = Initial population
Pn = Population after 'n' years
n = Number of years
Assuming the arithmetic rate of population growth to be constant for the next 20 years, we can use the above formula to calculate the population after 20 years.
Let the population after 20 years be P20.
Then,
r = (P20 - P0) / (20 × P0) × 100
Assuming r to be same for the next 20 years, the population after 't' years can be calculated using the formula:
Pt = P0 (1 + r/100)t
where,
Pt = Population after 't' years
P0 = Initial population
r = Arithmetic rate of population growth
t = Number of years
As per the given data, the water demand is expected to increase in proportion to the population growth. Therefore, the water demand after 't' years can be calculated using the formula:
Qt = Qd × (Pt / P)
where,
Qt = Water demand after 't' years
Qd = Design capacity of water treatment plant
Pt = Population after 't' years
P = Present population
The number of years from now when the plant will reach its design capacity can be calculated by equating the water demand after 't' years to the design capacity and solving for 't'.
Mathematically, the above steps can be summarized as follows:
- Calculate the total water demand at present.
- Calculate the deficit in the present water treatment plant.
- Assume an arithmetic rate of population growth and calculate the population after 20 years.
- Use the population after 20 years to calculate the population after 't' years using the formula Pt = P0 (1 + r/100)t.
- Use the population after 't' years to calculate the water demand after 't' years using the formula Qt = Qd × (Pt / P).
- Equate the water demand after 't' years to the design capacity and solve for 't'.
Substituting the given values in the above formulae, we get:
r = (P20 - P0) / (20 × P0) × 100
= (P20 - 28000) / (20 × 28000) × 100
Assuming an arithmetic rate of population growth of 'r' %, we can calculate the population after 't' years using
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The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??a)8.6 yearsb)12.0 yearsc)15.0 yearsd)16.5 yearsCorrect answer is option 'B'. Can you explain this answer?
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The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??a)8.6 yearsb)12.0 yearsc)15.0 yearsd)16.5 yearsCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??a)8.6 yearsb)12.0 yearsc)15.0 yearsd)16.5 yearsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??a)8.6 yearsb)12.0 yearsc)15.0 yearsd)16.5 yearsCorrect answer is option 'B'. Can you explain this answer?.
The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??a)8.6 yearsb)12.0 yearsc)15.0 yearsd)16.5 yearsCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??a)8.6 yearsb)12.0 yearsc)15.0 yearsd)16.5 yearsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??a)8.6 yearsb)12.0 yearsc)15.0 yearsd)16.5 yearsCorrect answer is option 'B'. Can you explain this answer?.
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