Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > An error of 0.5% in the measurement of head i...
Start Learning for Free
An error of 0.5% in the measurement of head in a v-notch vauses an error of
- a)0.5% in the discharge
- b)1% in the discharge
- c)1.25% in the discharge
- d)1.5% in the discharge
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
An error of 0.5% in the measurement of head in a v-notch vauses an err...
Explanation:
When the head is measured using a v-notch, the discharge can be calculated using the formula:
Q = 8/15 x Cd x b x h^(5/2)
Where,
Q = Discharge
Cd = Coefficient of discharge (a constant value for a particular v-notch shape and size)
b = Width of the v-notch
h = Head measured using the v-notch
Now, let's see how an error of 0.5% in the head measurement affects the discharge calculation.
Calculation:
Let the actual head measurement be h and the measured head be h'.
Error in head measurement = h - h'
Percentage error in head measurement = (h - h')/h x 100
Given, error in head measurement = 0.5%
Therefore, (h - h')/h x 100 = 0.5%
Solving for h',
h' = h - 0.005h
Substituting this value in the discharge formula,
Q' = 8/15 x Cd x b x (h - 0.005h)^(5/2)
Expanding the term (h - 0.005h)^(5/2),
(h - 0.005h)^(5/2) = h^(5/2) x (1 - 0.005/2) = h^(5/2) x 0.9975
Substituting in the discharge formula,
Q' = 8/15 x Cd x b x h^(5/2) x 0.9975
Q' = Q x 0.9975
Therefore, the percentage error in discharge is:
(Q - Q')/Q x 100 = (Q - Q x 0.9975)/Q x 100 = 0.25%
Therefore, the error in discharge is 1.25% (0.5% error in head measurement causes 1.25% error in discharge calculation).
Hence, option C is the correct answer.
When the head is measured using a v-notch, the discharge can be calculated using the formula:
Q = 8/15 x Cd x b x h^(5/2)
Where,
Q = Discharge
Cd = Coefficient of discharge (a constant value for a particular v-notch shape and size)
b = Width of the v-notch
h = Head measured using the v-notch
Now, let's see how an error of 0.5% in the head measurement affects the discharge calculation.
Calculation:
Let the actual head measurement be h and the measured head be h'.
Error in head measurement = h - h'
Percentage error in head measurement = (h - h')/h x 100
Given, error in head measurement = 0.5%
Therefore, (h - h')/h x 100 = 0.5%
Solving for h',
h' = h - 0.005h
Substituting this value in the discharge formula,
Q' = 8/15 x Cd x b x (h - 0.005h)^(5/2)
Expanding the term (h - 0.005h)^(5/2),
(h - 0.005h)^(5/2) = h^(5/2) x (1 - 0.005/2) = h^(5/2) x 0.9975
Substituting in the discharge formula,
Q' = 8/15 x Cd x b x h^(5/2) x 0.9975
Q' = Q x 0.9975
Therefore, the percentage error in discharge is:
(Q - Q')/Q x 100 = (Q - Q x 0.9975)/Q x 100 = 0.25%
Therefore, the error in discharge is 1.25% (0.5% error in head measurement causes 1.25% error in discharge calculation).
Hence, option C is the correct answer.
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
An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. Can you explain this answer?
Question Description
An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. 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 An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. 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 An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. Can you explain this answer?.
An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. 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 An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. 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 An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. Can you explain this answer?.
Solutions for An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. 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 An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An error of 0.5% in the measurement of head in a v-notch vauses an error ofa)0.5% in the dischargeb)1% in the dischargec)1.25% in the discharged)1.5% in the dischargeCorrect answer is option 'C'. 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