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During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall?
Most Upvoted Answer
During a 3 hour storm event if was observed that all abstractions othe...
**Effective Rainfall Calculation**
The effective rainfall can be calculated by subtracting the total infiltration from the total rainfall.
**Total Rainfall Calculation**
To calculate the total rainfall, we need to find the sum of the rainfall intensities for each hour.
1st hour rainfall intensity = 10mm/hr
2nd hour rainfall intensity = 20mm/hr
3rd hour rainfall intensity = 10mm/hr
Total rainfall = 10mm/hr + 20mm/hr + 10mm/hr = 40mm
**Infiltration Calculation**
The Horton curve equation is given by f = 6.8 * 8.7 * exp(-t), where f is the infiltration rate in mm/hr and t is the time in hours.
To calculate the infiltration for each hour, we substitute the values of t into the equation.
1st hour infiltration = 6.8 * 8.7 * exp(-1) ≈ 6.8 * 8.7 * 0.368 ≈ 21.85mm/hr
2nd hour infiltration = 6.8 * 8.7 * exp(-2) ≈ 6.8 * 8.7 * 0.135 ≈ 7.07mm/hr
3rd hour infiltration = 6.8 * 8.7 * exp(-3) ≈ 6.8 * 8.7 * 0.05 ≈ 2.94mm/hr
**Total Infiltration Calculation**
To calculate the total infiltration, we need to find the sum of the infiltrations for each hour.
Total infiltration = 21.85mm/hr + 7.07mm/hr + 2.94mm/hr ≈ 31.86mm
**Effective Rainfall Calculation**
The effective rainfall is obtained by subtracting the total infiltration from the total rainfall.
Effective rainfall = Total rainfall - Total infiltration
Effective rainfall = 40mm - 31.86mm ≈ 8.14mm
Therefore, the effective rainfall during the 3-hour storm event is approximately 8.14mm.
**Explanation**
In this question, we are given the rainfall intensities for each hour of a 3-hour storm event and the infiltration rate based on the Horton curve equation. We use the rainfall intensities to calculate the total rainfall, and the Horton curve equation to calculate the infiltration for each hour. By summing up the infiltrations, we find the total infiltration. Finally, we subtract the total infiltration from the total rainfall to obtain the effective rainfall. The effective rainfall represents the amount of rainfall that contributes to the runoff and is not absorbed by the soil.
The effective rainfall can be calculated by subtracting the total infiltration from the total rainfall.
**Total Rainfall Calculation**
To calculate the total rainfall, we need to find the sum of the rainfall intensities for each hour.
1st hour rainfall intensity = 10mm/hr
2nd hour rainfall intensity = 20mm/hr
3rd hour rainfall intensity = 10mm/hr
Total rainfall = 10mm/hr + 20mm/hr + 10mm/hr = 40mm
**Infiltration Calculation**
The Horton curve equation is given by f = 6.8 * 8.7 * exp(-t), where f is the infiltration rate in mm/hr and t is the time in hours.
To calculate the infiltration for each hour, we substitute the values of t into the equation.
1st hour infiltration = 6.8 * 8.7 * exp(-1) ≈ 6.8 * 8.7 * 0.368 ≈ 21.85mm/hr
2nd hour infiltration = 6.8 * 8.7 * exp(-2) ≈ 6.8 * 8.7 * 0.135 ≈ 7.07mm/hr
3rd hour infiltration = 6.8 * 8.7 * exp(-3) ≈ 6.8 * 8.7 * 0.05 ≈ 2.94mm/hr
**Total Infiltration Calculation**
To calculate the total infiltration, we need to find the sum of the infiltrations for each hour.
Total infiltration = 21.85mm/hr + 7.07mm/hr + 2.94mm/hr ≈ 31.86mm
**Effective Rainfall Calculation**
The effective rainfall is obtained by subtracting the total infiltration from the total rainfall.
Effective rainfall = Total rainfall - Total infiltration
Effective rainfall = 40mm - 31.86mm ≈ 8.14mm
Therefore, the effective rainfall during the 3-hour storm event is approximately 8.14mm.
**Explanation**
In this question, we are given the rainfall intensities for each hour of a 3-hour storm event and the infiltration rate based on the Horton curve equation. We use the rainfall intensities to calculate the total rainfall, and the Horton curve equation to calculate the infiltration for each hour. By summing up the infiltrations, we find the total infiltration. Finally, we subtract the total infiltration from the total rainfall to obtain the effective rainfall. The effective rainfall represents the amount of rainfall that contributes to the runoff and is not absorbed by the soil.
Community Answer
During a 3 hour storm event if was observed that all abstractions othe...
F = 6.8 + 8.7 e–t
t = 0, f = 6.8 + 8.7 = 15.5 > 10 mm
t = 0 to 1
Infiltration = ¹∫0(6.8 + 8.7 e-t)dt
= 6.8t +
8.7 e-t
¹
- 1 0
= 12.3 mm > 10 mm
∴ No excess rainfall t = 1 to 2
Total infiltration = ²∫1(6.8 + 8.7 e-t)dt
= 6.8t +
8.7 e-t
²
- 1 1
= 8.82 < 20="" />
∴ Rainfall excess = 20 – 8.82 = 11.17 mm
t = 2 to 3
Total infiltration = ³∫2(6.8 + 8.7 e-t)dt
= 7.54 > 10 mm
Rainfall excess = 10 – 7.54 = 2.45
Total rainfall excess = 10 + 11.17 + 2.45 = 13.63 mm.
t = 0, f = 6.8 + 8.7 = 15.5 > 10 mm
t = 0 to 1
Infiltration = ¹∫0(6.8 + 8.7 e-t)dt
= 6.8t +
8.7 e-t
¹
- 1 0
= 12.3 mm > 10 mm
∴ No excess rainfall t = 1 to 2
Total infiltration = ²∫1(6.8 + 8.7 e-t)dt
= 6.8t +
8.7 e-t
²
- 1 1
= 8.82 < 20="" />
∴ Rainfall excess = 20 – 8.82 = 11.17 mm
t = 2 to 3
Total infiltration = ³∫2(6.8 + 8.7 e-t)dt
= 7.54 > 10 mm
Rainfall excess = 10 – 7.54 = 2.45
Total rainfall excess = 10 + 11.17 + 2.45 = 13.63 mm.
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During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall?
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During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall?.
During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall?.
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During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall?, a detailed solution for During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall? has been provided alongside types of During a 3 hour storm event if was observed that all abstractions other than in filtration are negligible. The rain fall was idealized as 3 one hour storms of intensity 10mm / hr, 20mm / hr and 10mm / hr respectively and the infiltration was idealized as a Horton curve f=6.8 8.7 exp (-t) (f in, mm / hr and t in hr) What is the effective rain fall? theory, EduRev gives you an
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