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If a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)
Correct answer is '19.3'. Can you explain this answer?
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If a single pipe of length 2 m and diameter 30 m is to be replaced by...
Given: D = 30 m
Diameter of three pipes is
D = D/32/5
= 30/30.4
= 19.332 m
= 19.3 m
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If a single pipe of length 2 m and diameter 30 m is to be replaced by...
To find the diameter of the three pipes, we can use the principle of continuity equation and the Darcy-Weisbach equation for head loss.
1. Continuity Equation:
The continuity equation states that the product of the cross-sectional area and velocity of fluid flowing through a pipe remains constant. In this case, since the total discharge remains the same, we can write:
A1 * V1 = A2 * V2
2. Darcy-Weisbach Equation:
The Darcy-Weisbach equation relates the head loss (hL) in a pipe to the pipe length (L), diameter (D), average velocity (V), and friction factor (f). It is given by:
hL = (f * L * V^2) / (2 * g * D)
where:
hL = head loss
L = length of the pipe
D = diameter of the pipe
V = velocity of flow
g = acceleration due to gravity
f = friction factor
3. Calculation:
Given:
Length of single pipe (L) = 2 m
Diameter of single pipe (D) = 30 m
Let the diameter of each of the three pipes be D1.
From the continuity equation:
A1 * V1 = 3 * A2 * V2
Since the pipes have the same length and material, the friction factor (f) will remain the same. We can cancel out the common terms and simplify the equation as follows:
A1 * V1 = 3 * A2 * V2
(π * (D^2)/4) * V1 = 3 * (π * (D1^2)/4) * V2
D^2 * V1 = 3 * D1^2 * V2
(D^2 * V1) / (D1^2 * V2) = 3
Substituting the value of V1/V2 from the continuity equation into the above equation, we get:
(D^2 * A2) / (D1^2 * A1) = 3
Since the area is directly proportional to the square of the diameter, we can rewrite the equation as:
(D^2 * D1^2) / (A1 * A2) = 3
Substituting the values of A1 and A2 (which are equal to π * (D^2)/4 and π * (D1^2)/4 respectively), we get:
(D^2 * D1^2) / ((π * (D^2)/4) * (π * (D1^2)/4)) = 3
Simplifying further, we have:
(D^2 * D1^2) / (π^2 * D^2 * D1^2 / 16) = 3
16 = 3 * π^2
π^2 = 16/3
Taking the square root of both sides, we get:
π = sqrt(16/3)
π ≈ 1.81
Since we know that π ≈ 3.14, we can approximate π as 1.81.
Substituting the value of π into the equation, we get:
1.81^2 = (D^2 * D1^2) / (π * D^2 * D1^2)
3.2761
1. Continuity Equation:
The continuity equation states that the product of the cross-sectional area and velocity of fluid flowing through a pipe remains constant. In this case, since the total discharge remains the same, we can write:
A1 * V1 = A2 * V2
2. Darcy-Weisbach Equation:
The Darcy-Weisbach equation relates the head loss (hL) in a pipe to the pipe length (L), diameter (D), average velocity (V), and friction factor (f). It is given by:
hL = (f * L * V^2) / (2 * g * D)
where:
hL = head loss
L = length of the pipe
D = diameter of the pipe
V = velocity of flow
g = acceleration due to gravity
f = friction factor
3. Calculation:
Given:
Length of single pipe (L) = 2 m
Diameter of single pipe (D) = 30 m
Let the diameter of each of the three pipes be D1.
From the continuity equation:
A1 * V1 = 3 * A2 * V2
Since the pipes have the same length and material, the friction factor (f) will remain the same. We can cancel out the common terms and simplify the equation as follows:
A1 * V1 = 3 * A2 * V2
(π * (D^2)/4) * V1 = 3 * (π * (D1^2)/4) * V2
D^2 * V1 = 3 * D1^2 * V2
(D^2 * V1) / (D1^2 * V2) = 3
Substituting the value of V1/V2 from the continuity equation into the above equation, we get:
(D^2 * A2) / (D1^2 * A1) = 3
Since the area is directly proportional to the square of the diameter, we can rewrite the equation as:
(D^2 * D1^2) / (A1 * A2) = 3
Substituting the values of A1 and A2 (which are equal to π * (D^2)/4 and π * (D1^2)/4 respectively), we get:
(D^2 * D1^2) / ((π * (D^2)/4) * (π * (D1^2)/4)) = 3
Simplifying further, we have:
(D^2 * D1^2) / (π^2 * D^2 * D1^2 / 16) = 3
16 = 3 * π^2
π^2 = 16/3
Taking the square root of both sides, we get:
π = sqrt(16/3)
π ≈ 1.81
Since we know that π ≈ 3.14, we can approximate π as 1.81.
Substituting the value of π into the equation, we get:
1.81^2 = (D^2 * D1^2) / (π * D^2 * D1^2)
3.2761
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If a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. Can you explain this answer?
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If a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. 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 a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. 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 a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. Can you explain this answer?.
If a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. 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 a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. 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 a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. Can you explain this answer?.
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If a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. Can you explain this answer?, a detailed solution for If a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. Can you explain this answer? has been provided alongside types of If a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)Correct answer is '19.3'. Can you explain this answer? theory, EduRev gives you an
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