GATE Exam > GATE Questions > In a 30-in diameter pipe, a circular orifice ...
Start Learning for Free
In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?
- a)8.24 ft3/sec
- b)16.48 ft3/sec
- c)4.12 ft3/sec
- d)1.6 ft3/sec
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, ...
The flow rate Q in a differential flow rate meter is given by
Q = K(π/4)(ds/dp)2√2gh
where K is the flow coefficient constant, dS is the diameter of the orifice, dP is the
pipe diameter and h is the difference in height between PH and PL.
Q= 0.97 (3.14/4)(20/30)2 
Q= 4.12 ft3/sec
Most Upvoted Answer
In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, ...
Given data:
Diameter of the pipe (D) = 30 inches
Diameter of the orifice (d) = 20 inches
Difference in the height of the manometer levels (h) = 2.3 ft
Coefficient of discharge (K) = 0.97
To determine the flow rate, we can use the Bernoulli's equation for incompressible fluid flow, which states that the total energy of the fluid remains constant along a streamline.
1. Calculating the velocity of the fluid:
Using the equation of continuity, we can relate the velocities of the fluid at the pipe and the orifice.
- The cross-sectional area of the pipe (A1) = π(D/2)^2
- The cross-sectional area of the orifice (A2) = π(d/2)^2
- The velocity of the fluid at the pipe (v1) = ?
- The velocity of the fluid at the orifice (v2) = ?
According to the equation of continuity: A1v1 = A2v2
Substituting the values: π(D/2)^2v1 = π(d/2)^2v2
Simplifying: (D/2)^2v1 = (d/2)^2v2
Plugging in the values: (15^2)v1 = (10^2)v2
Simplifying further: v1 = 4/9v2
2. Applying Bernoulli's equation:
The Bernoulli's equation can be written as: P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2
- P1 = Pressure at the pipe
- P2 = Pressure at the orifice
- ρ = Density of the fluid
- g = Acceleration due to gravity
- h1 = Height of the manometer fluid column on one side
- h2 = Height of the manometer fluid column on the other side
Since the pressure at both the pipe and the orifice is atmospheric, the pressure terms cancel out.
Simplifying further: (1/2)ρv1^2 + ρgh1 = (1/2)ρv2^2 + ρgh2
Dividing both sides by ρg: (1/2)v1^2 + h1 = (1/2)v2^2 + h2
3. Calculating the flow rate:
The flow rate (Q) can be determined using the equation: Q = A2v2
- A2 = π(d/2)^2
- v2 = (2gh2 - 2gh1)^0.5
Substituting the values and simplifying:
Q = π(d/2)^2(2gh2 - 2gh1)^0.5
4. Plugging in the values:
Q = π(20/2)^2(2(32.2)h)^0.5
Q = π(10)^2(2(32.2)(2.3))^0.5
Q ≈ 4.12 ft^3/sec
Therefore, the flow rate in cubic feet per second is approximately 4.12 ft^3/sec, which corresponds to option C.
Diameter of the pipe (D) = 30 inches
Diameter of the orifice (d) = 20 inches
Difference in the height of the manometer levels (h) = 2.3 ft
Coefficient of discharge (K) = 0.97
To determine the flow rate, we can use the Bernoulli's equation for incompressible fluid flow, which states that the total energy of the fluid remains constant along a streamline.
1. Calculating the velocity of the fluid:
Using the equation of continuity, we can relate the velocities of the fluid at the pipe and the orifice.
- The cross-sectional area of the pipe (A1) = π(D/2)^2
- The cross-sectional area of the orifice (A2) = π(d/2)^2
- The velocity of the fluid at the pipe (v1) = ?
- The velocity of the fluid at the orifice (v2) = ?
According to the equation of continuity: A1v1 = A2v2
Substituting the values: π(D/2)^2v1 = π(d/2)^2v2
Simplifying: (D/2)^2v1 = (d/2)^2v2
Plugging in the values: (15^2)v1 = (10^2)v2
Simplifying further: v1 = 4/9v2
2. Applying Bernoulli's equation:
The Bernoulli's equation can be written as: P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2
- P1 = Pressure at the pipe
- P2 = Pressure at the orifice
- ρ = Density of the fluid
- g = Acceleration due to gravity
- h1 = Height of the manometer fluid column on one side
- h2 = Height of the manometer fluid column on the other side
Since the pressure at both the pipe and the orifice is atmospheric, the pressure terms cancel out.
Simplifying further: (1/2)ρv1^2 + ρgh1 = (1/2)ρv2^2 + ρgh2
Dividing both sides by ρg: (1/2)v1^2 + h1 = (1/2)v2^2 + h2
3. Calculating the flow rate:
The flow rate (Q) can be determined using the equation: Q = A2v2
- A2 = π(d/2)^2
- v2 = (2gh2 - 2gh1)^0.5
Substituting the values and simplifying:
Q = π(d/2)^2(2gh2 - 2gh1)^0.5
4. Plugging in the values:
Q = π(20/2)^2(2(32.2)h)^0.5
Q = π(10)^2(2(32.2)(2.3))^0.5
Q ≈ 4.12 ft^3/sec
Therefore, the flow rate in cubic feet per second is approximately 4.12 ft^3/sec, which corresponds to option C.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer?
Question Description
In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer?.
In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer?.
Solutions for In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a 30-in diameter pipe, a circular orifice has a diameter of 20 in, and the difference in the height of the manometer levels is 2.3 ft. What is the flow rate in cubic feet per second if K is 0.97?a)8.24 ft3/secb)16.48 ft3/secc)4.12 ft3/secd)1.6 ft3/secCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup