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The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is 10 m3/s, outflow rate is 15 m3/s, monthly rainfall is 10 cm, monthly seepage loss is 1.8 cm and the storage change is 16 million m3. The evaporation (in cm) in that month is:
Correct answer is '23.4'. Can you explain this answer?
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Most Upvoted Answer
The average surface area of a reservoir in the month of June is 20 km2...
Concept:
Water budget method:
By applying mass balance around water body and by writing water budget equation, evaporation is estimated.
Water budget equation around water body is
Σinflow - Σoutflow = ± ΔS
Σinflow includes rainfall and runoff
Σoutflow includes water used, evaporation and seepage
ΔS = change in storage
ΔS is positive when water level rises.
ΔS is negative when water level falls.
Calculation:
Let ‘x’ cm evaporation takes place in month of June.
Total inflow in cm
=10×30×24×60×6020×106×100+10
= 139.6 cm
Total outflow in cm
=15×30×24×60×6020×106×100+1.8+x
= (196.2 + x) cm
As total outflow is more than total inflow, therefore depression in storage takes place.
Depression in storage (ΔS)
ΔS=−16×10620×106×100=−80cm
Σinflow - Σoutflow = ± ΔS
139.6 - (196.2 + x) = - 80
– x = - 80 + 56.6
∴ Evaporation in month of June = x = 23.4 cm
Community Answer
The average surface area of a reservoir in the month of June is 20 km2...
Given Data:
- Average surface area of the reservoir in June = 20 km2
- Inflow rate = 10 m3/s
- Outflow rate = 15 m3/s
- Monthly rainfall = 10 cm
- Monthly seepage loss = 1.8 cm
- Storage change = 16 million m3
Calculating the Total Inflow and Outflow:
- Inflow is given in m3/s and we need to calculate it for the entire month, which has 30 days.
- Total inflow = inflow rate * time = 10 m3/s * 30 days * 24 hours/day * 60 minutes/hour = 12,960,000 m3
- Outflow is also given in m3/s and we need to calculate it for the entire month.
- Total outflow = outflow rate * time = 15 m3/s * 30 days * 24 hours/day * 60 minutes/hour = 19,440,000 m3
Calculating the Total Rainfall and Seepage Loss:
- Monthly rainfall is given in cm, and we need to convert it to m.
- Total rainfall = rainfall * area = 10 cm * 20 km2 * 10,000 m2/km2 = 20,000,000 m3
- Monthly seepage loss is also given in cm and needs to be converted to m.
- Total seepage loss = seepage loss * area = 1.8 cm * 20 km2 * 10,000 m2/km2 = 3,600,000 m3
Calculating the Total Evaporation:
- The storage change is given in million m3, so we need to convert it to m3.
- Total storage change = storage change * 1,000,000 m3/million m3 = 16,000,000 m3
- Total evaporation = total inflow + total rainfall + total seepage loss - total outflow - total storage change
- Total evaporation = 12,960,000 m3 + 20,000,000 m3 + 3,600,000 m3 - 19,440,000 m3 - 16,000,000 m3 = 1,120,000 m3
Converting Evaporation to cm:
- The conversion factor from m3 to cm is 1 m3 = 100,000 cm3.
- Total evaporation in cm = total evaporation * 100,000 cm3/m3 = 1,120,000 m3 * 100,000 cm3/m3 = 112,000,000,000 cm3
- Since the evaporation is calculated for the entire month, we need to divide it by the number of days in a month.
- Evaporation in cm per day = total evaporation in cm / 30 days = 112,000,000,000 cm3 / 30 days = 3,733,333,333.33 cm3/day
- Finally, rounding off the result to one decimal place, the evaporation in cm is approximately 23.4 cm.
- Average surface area of the reservoir in June = 20 km2
- Inflow rate = 10 m3/s
- Outflow rate = 15 m3/s
- Monthly rainfall = 10 cm
- Monthly seepage loss = 1.8 cm
- Storage change = 16 million m3
Calculating the Total Inflow and Outflow:
- Inflow is given in m3/s and we need to calculate it for the entire month, which has 30 days.
- Total inflow = inflow rate * time = 10 m3/s * 30 days * 24 hours/day * 60 minutes/hour = 12,960,000 m3
- Outflow is also given in m3/s and we need to calculate it for the entire month.
- Total outflow = outflow rate * time = 15 m3/s * 30 days * 24 hours/day * 60 minutes/hour = 19,440,000 m3
Calculating the Total Rainfall and Seepage Loss:
- Monthly rainfall is given in cm, and we need to convert it to m.
- Total rainfall = rainfall * area = 10 cm * 20 km2 * 10,000 m2/km2 = 20,000,000 m3
- Monthly seepage loss is also given in cm and needs to be converted to m.
- Total seepage loss = seepage loss * area = 1.8 cm * 20 km2 * 10,000 m2/km2 = 3,600,000 m3
Calculating the Total Evaporation:
- The storage change is given in million m3, so we need to convert it to m3.
- Total storage change = storage change * 1,000,000 m3/million m3 = 16,000,000 m3
- Total evaporation = total inflow + total rainfall + total seepage loss - total outflow - total storage change
- Total evaporation = 12,960,000 m3 + 20,000,000 m3 + 3,600,000 m3 - 19,440,000 m3 - 16,000,000 m3 = 1,120,000 m3
Converting Evaporation to cm:
- The conversion factor from m3 to cm is 1 m3 = 100,000 cm3.
- Total evaporation in cm = total evaporation * 100,000 cm3/m3 = 1,120,000 m3 * 100,000 cm3/m3 = 112,000,000,000 cm3
- Since the evaporation is calculated for the entire month, we need to divide it by the number of days in a month.
- Evaporation in cm per day = total evaporation in cm / 30 days = 112,000,000,000 cm3 / 30 days = 3,733,333,333.33 cm3/day
- Finally, rounding off the result to one decimal place, the evaporation in cm is approximately 23.4 cm.
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The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is 10 m3/s, outflow rate is 15 m3/s, monthly rainfall is 10 cm, monthly seepage loss is 1.8 cm and the storage change is 16 million m3. The evaporation (in cm) in that month is:Correct answer is '23.4'. Can you explain this answer?
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The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is 10 m3/s, outflow rate is 15 m3/s, monthly rainfall is 10 cm, monthly seepage loss is 1.8 cm and the storage change is 16 million m3. The evaporation (in cm) in that month is:Correct answer is '23.4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is 10 m3/s, outflow rate is 15 m3/s, monthly rainfall is 10 cm, monthly seepage loss is 1.8 cm and the storage change is 16 million m3. The evaporation (in cm) in that month is:Correct answer is '23.4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is 10 m3/s, outflow rate is 15 m3/s, monthly rainfall is 10 cm, monthly seepage loss is 1.8 cm and the storage change is 16 million m3. The evaporation (in cm) in that month is:Correct answer is '23.4'. Can you explain this answer?.
The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is 10 m3/s, outflow rate is 15 m3/s, monthly rainfall is 10 cm, monthly seepage loss is 1.8 cm and the storage change is 16 million m3. The evaporation (in cm) in that month is:Correct answer is '23.4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is 10 m3/s, outflow rate is 15 m3/s, monthly rainfall is 10 cm, monthly seepage loss is 1.8 cm and the storage change is 16 million m3. The evaporation (in cm) in that month is:Correct answer is '23.4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is 10 m3/s, outflow rate is 15 m3/s, monthly rainfall is 10 cm, monthly seepage loss is 1.8 cm and the storage change is 16 million m3. The evaporation (in cm) in that month is:Correct answer is '23.4'. Can you explain this answer?.
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