Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > If the coefficient of variation of rainfall ...
Start Learning for Free
If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)
Correct answer is '5'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If the coefficient of variation of rainfall values at 4 rain gauge st...
Solution:
Given,
Coefficient of variation (CV) = 30%
Permissible error in the addition of mean rainfall = 10%
To find,
The additional number of rain gauge stations required in the catchments
Assuming that the rainfall data at each rain gauge station follows a normal distribution, the standard error of mean rainfall can be calculated as:
Standard error = CV * Mean rainfall
Let the mean rainfall at each rain gauge station be 'x'
Then, the standard error of mean rainfall at each station = 0.3x
The total standard error of mean rainfall for all 4 stations can be calculated as:
Total standard error = sqrt(sum of squares of standard error of each station)
= sqrt((0.3x)^2 + (0.3x)^2 + (0.3x)^2 + (0.3x)^2)
= 0.6x
The permissible error in the addition of mean rainfall is 10% of the total mean rainfall, which can be expressed as:
Permissible error = 0.1 * 4x
= 0.4x
The additional number of rain gauge stations required can be calculated as:
Additional stations = (Total standard error / Permissible error)^2 - 4
= (0.6x / 0.4x)^2 - 4
= 2.25 - 4
= -1.75
Since the number of additional stations cannot be negative, we take the absolute value of the result and round it up to the nearest integer. Therefore, the additional number of rain gauge stations required in the catchments is 5.
Given,
Coefficient of variation (CV) = 30%
Permissible error in the addition of mean rainfall = 10%
To find,
The additional number of rain gauge stations required in the catchments
Assuming that the rainfall data at each rain gauge station follows a normal distribution, the standard error of mean rainfall can be calculated as:
Standard error = CV * Mean rainfall
Let the mean rainfall at each rain gauge station be 'x'
Then, the standard error of mean rainfall at each station = 0.3x
The total standard error of mean rainfall for all 4 stations can be calculated as:
Total standard error = sqrt(sum of squares of standard error of each station)
= sqrt((0.3x)^2 + (0.3x)^2 + (0.3x)^2 + (0.3x)^2)
= 0.6x
The permissible error in the addition of mean rainfall is 10% of the total mean rainfall, which can be expressed as:
Permissible error = 0.1 * 4x
= 0.4x
The additional number of rain gauge stations required can be calculated as:
Additional stations = (Total standard error / Permissible error)^2 - 4
= (0.6x / 0.4x)^2 - 4
= 2.25 - 4
= -1.75
Since the number of additional stations cannot be negative, we take the absolute value of the result and round it up to the nearest integer. Therefore, the additional number of rain gauge stations required in the catchments is 5.
Free Test
FREE
| Start Free Test |
Community Answer
If the coefficient of variation of rainfall values at 4 rain gauge st...
Additional number of station = 
- 4
- 4= (30/10)2 - 4 = 5
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer?
Question Description
If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. 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 If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. 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 If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer?.
If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. 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 If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. 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 If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer?.
Solutions for If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer?, a detailed solution for If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer? has been provided alongside types of If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the coefficient of variation of rainfall values at 4 rain gauge stations is 30% and permissible error in the additional of mean rainfall is 10%, then the additional number of rain gauge stations required in the catchments is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup