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A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will be
- a)2.5 m/s
- b)5.55 m/s
- c)7.25 m/s
- d)9.56 m/s
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s ...
Concept:
According to continuity, the liquid flow rate will be conserved.
Q1 = Q2 + Q3
In a pipe, flow rate is given by
Q = AV
Calculation:
Given V1 = 3 m/s, D1 = 450 mm, V2 = 2.5 m/s, D2 = 300 mm, D3 = 200 mm;
From continuity,
D12 V1 = D22 V2 + D32 V3
⇒ 4502 × 3 = 3002 × 2.5 + 2002 × V3
⇒ V3 = 9.56 m/s
According to continuity, the liquid flow rate will be conserved.
Q1 = Q2 + Q3
In a pipe, flow rate is given by
Q = AV
Calculation:
Given V1 = 3 m/s, D1 = 450 mm, V2 = 2.5 m/s, D2 = 300 mm, D3 = 200 mm;
From continuity,
D12 V1 = D22 V2 + D32 V3
⇒ 4502 × 3 = 3002 × 2.5 + 2002 × V3
⇒ V3 = 9.56 m/s
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Community Answer
A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s ...
Given data:
Diameter of main pipe (D1) = 450 mm
Velocity in main pipe (V1) = 3 m/s
Diameter of first pipe (D2) = 300 mm
Velocity in first pipe (V2) = 2.5 m/s
To find:
Velocity in second pipe (V3)
Using the equation of continuity, the product of the area and velocity of flow is constant.
𝐴1𝑉1 = 𝐴2𝑉2 + 𝐴3𝑉3
Where:
A1, A2, A3 = Cross-sectional areas of the main pipe, first pipe, and second pipe respectively
𝐴1 = π(D1/2)^2
𝐴2 = π(D2/2)^2
𝐴3 = π(D3/2)^2
𝐴1 = π(450/2)^2 = 159,154 mm^2
𝐴2 = π(300/2)^2 = 70,685 mm^2
To find 𝐴3, we can use the equation of continuity:
159,154 mm^2 * 3 m/s = 70,685 mm^2 * 2.5 m/s + 𝐴3 * 𝑉3
Rearranging the equation:
𝐴3 * 𝑉3 = (159,154 mm^2 * 3 m/s) - (70,685 mm^2 * 2.5 m/s)
𝐴3 * 𝑉3 = 477,462 mm^3/s - 176,713 mm^3/s
𝐴3 * 𝑉3 = 300,749 mm^3/s
Now, we need to find the cross-sectional area of the second pipe, 𝐴3.
𝐴3 = 300,749 mm^3/s / 𝑉3
To convert the flow rate from mm^3/s to m^3/s, we divide by 1,000,000:
𝐴3 = (300,749 mm^3/s / 𝑉3) / 1,000,000
The diameter of the second pipe (D3) is given as 200 mm, so we can find the cross-sectional area 𝐴3:
𝐴3 = π(200/2)^2 = 31,416 mm^2
Now, we can substitute the value of 𝐴3 in the equation:
31,416 mm^2 * 𝑉3 = 300,749 mm^3/s / 1,000,000
Simplifying the equation:
𝑉3 = (300,749 mm^3/s / 1,000,000) / 31,416 mm^2
𝑉3 ≈ 9.56 m/s
Therefore, the velocity of flow through the 200 mm diameter pipe is approximately 9.56 m/s. Hence, the correct answer is option D.
Diameter of main pipe (D1) = 450 mm
Velocity in main pipe (V1) = 3 m/s
Diameter of first pipe (D2) = 300 mm
Velocity in first pipe (V2) = 2.5 m/s
To find:
Velocity in second pipe (V3)
Using the equation of continuity, the product of the area and velocity of flow is constant.
𝐴1𝑉1 = 𝐴2𝑉2 + 𝐴3𝑉3
Where:
A1, A2, A3 = Cross-sectional areas of the main pipe, first pipe, and second pipe respectively
𝐴1 = π(D1/2)^2
𝐴2 = π(D2/2)^2
𝐴3 = π(D3/2)^2
𝐴1 = π(450/2)^2 = 159,154 mm^2
𝐴2 = π(300/2)^2 = 70,685 mm^2
To find 𝐴3, we can use the equation of continuity:
159,154 mm^2 * 3 m/s = 70,685 mm^2 * 2.5 m/s + 𝐴3 * 𝑉3
Rearranging the equation:
𝐴3 * 𝑉3 = (159,154 mm^2 * 3 m/s) - (70,685 mm^2 * 2.5 m/s)
𝐴3 * 𝑉3 = 477,462 mm^3/s - 176,713 mm^3/s
𝐴3 * 𝑉3 = 300,749 mm^3/s
Now, we need to find the cross-sectional area of the second pipe, 𝐴3.
𝐴3 = 300,749 mm^3/s / 𝑉3
To convert the flow rate from mm^3/s to m^3/s, we divide by 1,000,000:
𝐴3 = (300,749 mm^3/s / 𝑉3) / 1,000,000
The diameter of the second pipe (D3) is given as 200 mm, so we can find the cross-sectional area 𝐴3:
𝐴3 = π(200/2)^2 = 31,416 mm^2
Now, we can substitute the value of 𝐴3 in the equation:
31,416 mm^2 * 𝑉3 = 300,749 mm^3/s / 1,000,000
Simplifying the equation:
𝑉3 = (300,749 mm^3/s / 1,000,000) / 31,416 mm^2
𝑉3 ≈ 9.56 m/s
Therefore, the velocity of flow through the 200 mm diameter pipe is approximately 9.56 m/s. Hence, the correct answer is option D.
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A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. Can you explain this answer?
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A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. 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 fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. 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 fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. Can you explain this answer?.
A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. 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 fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. 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 fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will bea)2.5 m/sb)5.55 m/sc)7.25 m/sd)9.56 m/sCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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