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A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. If the model discharge were 0.1 m3/s, then the discharge in the river is 10n m3/sec. The value of n is (Answer up to the nearest integer)
Correct answer is '5'. Can you explain this answer?
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A river model is constructed to a horizontal scale of 1 : 1000 and a ...
Solution:
Given,
Horizontal Scale = 1 : 1000
Vertical Scale = 1 : 100
Model discharge = 0.1 m3/s
Let us assume that the actual discharge in the river is Q m3/s.
Then, the discharge in the model can be given by,
Qm = KQ, where K is the model scale factor.
The model scale factor can be given as follows,
K = (Lm/L)2 x (Hm/H)
where Lm and Hm are the model length and height, respectively, and L and H are the actual length and height, respectively.
Given that the horizontal scale is 1 : 1000, i.e., Lm/L = 1/1000.
Given that the vertical scale is 1 : 100, i.e., Hm/H = 1/100.
Substituting the values of Lm/L and Hm/H in the above equation, we get
K = (1/1000)2 x (1/100) = 1/10,000,000
Therefore, the discharge in the river can be given as follows,
Q = KQm = (1/10,000,000) x 0.1 = 10-7 x 0.1 = 10-8 m3/s
We need to find the value of n such that the discharge in the river is 10n m3/s.
Therefore,
10n = 10-8
n = -8/10 = -0.8
Rounding off to the nearest integer, we get n = -1.
However, the answer given in the question is '5'. This seems to be a mistake as it is not possible for the value of n to be positive when the model discharge is less than the actual discharge.
Therefore, the correct answer is 'n = -1'.
Given,
Horizontal Scale = 1 : 1000
Vertical Scale = 1 : 100
Model discharge = 0.1 m3/s
Let us assume that the actual discharge in the river is Q m3/s.
Then, the discharge in the model can be given by,
Qm = KQ, where K is the model scale factor.
The model scale factor can be given as follows,
K = (Lm/L)2 x (Hm/H)
where Lm and Hm are the model length and height, respectively, and L and H are the actual length and height, respectively.
Given that the horizontal scale is 1 : 1000, i.e., Lm/L = 1/1000.
Given that the vertical scale is 1 : 100, i.e., Hm/H = 1/100.
Substituting the values of Lm/L and Hm/H in the above equation, we get
K = (1/1000)2 x (1/100) = 1/10,000,000
Therefore, the discharge in the river can be given as follows,
Q = KQm = (1/10,000,000) x 0.1 = 10-7 x 0.1 = 10-8 m3/s
We need to find the value of n such that the discharge in the river is 10n m3/s.
Therefore,
10n = 10-8
n = -8/10 = -0.8
Rounding off to the nearest integer, we get n = -1.
However, the answer given in the question is '5'. This seems to be a mistake as it is not possible for the value of n to be positive when the model discharge is less than the actual discharge.
Therefore, the correct answer is 'n = -1'.
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A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. If the model discharge were 0.1 m3/s, then the discharge in the river is 10n m3/sec. The value of n is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer?
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A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. If the model discharge were 0.1 m3/s, then the discharge in the river is 10n m3/sec. The value of n 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 A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. If the model discharge were 0.1 m3/s, then the discharge in the river is 10n m3/sec. The value of n 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 A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. If the model discharge were 0.1 m3/s, then the discharge in the river is 10n m3/sec. The value of n is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer?.
A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. If the model discharge were 0.1 m3/s, then the discharge in the river is 10n m3/sec. The value of n 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 A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. If the model discharge were 0.1 m3/s, then the discharge in the river is 10n m3/sec. The value of n 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 A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. If the model discharge were 0.1 m3/s, then the discharge in the river is 10n m3/sec. The value of n is (Answer up to the nearest integer)Correct answer is '5'. Can you explain this answer?.
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