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Two venturi meters, with the same manometers, of different area ratios are installed in the same pipeline. The reading of 1st manometer is h and the area ratio is 2. If the 2nd manometer reads 8h, its area ratio is
- a)4
- b)6
- c)3
- d)5
Correct answer is option 'D'. Can you explain this answer?
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Two venturi meters, with the same manometers, of different area ratio...
Since both the manometers are installed on a same pipeline, their discharge is same
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ar2 = 5
Most Upvoted Answer
Two venturi meters, with the same manometers, of different area ratio...
Explanation:
Given:
- Two venturi meters with the same manometers are installed in the same pipeline.
- The reading of the first manometer is h.
- The area ratio for the first venturi meter is 2.
- The reading of the second manometer is 8h.
To find:
The area ratio for the second venturi meter.
Solution:
Let's assume the area ratio for the second venturi meter is x.
Using Bernoulli's equation:
The equation for Bernoulli's principle is given as:
P1 + 0.5 * ρ * V1^2 + ρ * g * h1 = P2 + 0.5 * ρ * V2^2 + ρ * g * h2
Where:
P1 and P2 are the pressures at two different points in the pipeline.
ρ is the density of the fluid.
V1 and V2 are the velocities of the fluid at points 1 and 2 respectively.
g is the acceleration due to gravity.
h1 and h2 are the heights of the fluid columns in the manometers at points 1 and 2 respectively.
For the first venturi meter:
Let's assume the pressure at point 1 is P1, the velocity at point 1 is V1, and the area at point 1 is A1.
Similarly, let's assume the pressure at point 2 is P2, the velocity at point 2 is V2, and the area at point 2 is A2.
Using the given information:
The reading of the first manometer is h.
The area ratio for the first venturi meter is 2.
So, the area at point 2 (A2) is 2 * A1.
The equation for the first venturi meter becomes:
P1 + 0.5 * ρ * V1^2 + ρ * g * h = P2 + 0.5 * ρ * V2^2
Since the fluid is incompressible, the mass flow rate (m_dot) is constant.
m_dot = ρ * A1 * V1 = ρ * A2 * V2
Dividing the above equation by ρ, we get:
A1 * V1 = A2 * V2
Since A2 = 2 * A1, the equation becomes:
A1 * V1 = 2 * A1 * V2
Simplifying the equation, we get:
V1 = 2 * V2
Substituting this equation back into the Bernoulli's equation, we get:
P1 + 2 * (0.5 * ρ * V2^2) + ρ * g * h = P2 + 0.5 * ρ * V2^2
Simplifying the equation further, we get:
P1 + ρ * V2^2 + ρ * g * h = P2 + 0.5 * ρ * V2^2
P1 - P2 = 0.5 * ρ * V2^2 - ρ * V2^2 - ρ * g * h
P1 - P2 = -0.5 * ρ * V2^2 -
Given:
- Two venturi meters with the same manometers are installed in the same pipeline.
- The reading of the first manometer is h.
- The area ratio for the first venturi meter is 2.
- The reading of the second manometer is 8h.
To find:
The area ratio for the second venturi meter.
Solution:
Let's assume the area ratio for the second venturi meter is x.
Using Bernoulli's equation:
The equation for Bernoulli's principle is given as:
P1 + 0.5 * ρ * V1^2 + ρ * g * h1 = P2 + 0.5 * ρ * V2^2 + ρ * g * h2
Where:
P1 and P2 are the pressures at two different points in the pipeline.
ρ is the density of the fluid.
V1 and V2 are the velocities of the fluid at points 1 and 2 respectively.
g is the acceleration due to gravity.
h1 and h2 are the heights of the fluid columns in the manometers at points 1 and 2 respectively.
For the first venturi meter:
Let's assume the pressure at point 1 is P1, the velocity at point 1 is V1, and the area at point 1 is A1.
Similarly, let's assume the pressure at point 2 is P2, the velocity at point 2 is V2, and the area at point 2 is A2.
Using the given information:
The reading of the first manometer is h.
The area ratio for the first venturi meter is 2.
So, the area at point 2 (A2) is 2 * A1.
The equation for the first venturi meter becomes:
P1 + 0.5 * ρ * V1^2 + ρ * g * h = P2 + 0.5 * ρ * V2^2
Since the fluid is incompressible, the mass flow rate (m_dot) is constant.
m_dot = ρ * A1 * V1 = ρ * A2 * V2
Dividing the above equation by ρ, we get:
A1 * V1 = A2 * V2
Since A2 = 2 * A1, the equation becomes:
A1 * V1 = 2 * A1 * V2
Simplifying the equation, we get:
V1 = 2 * V2
Substituting this equation back into the Bernoulli's equation, we get:
P1 + 2 * (0.5 * ρ * V2^2) + ρ * g * h = P2 + 0.5 * ρ * V2^2
Simplifying the equation further, we get:
P1 + ρ * V2^2 + ρ * g * h = P2 + 0.5 * ρ * V2^2
P1 - P2 = 0.5 * ρ * V2^2 - ρ * V2^2 - ρ * g * h
P1 - P2 = -0.5 * ρ * V2^2 -
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Two venturi meters, with the same manometers, of different area ratios are installed in the same pipeline. The reading of 1st manometer is h and the area ratio is 2. If the 2nd manometer reads 8h, its area ratio isa)4b)6c)3d)5Correct answer is option 'D'. Can you explain this answer?
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Two venturi meters, with the same manometers, of different area ratios are installed in the same pipeline. The reading of 1st manometer is h and the area ratio is 2. If the 2nd manometer reads 8h, its area ratio isa)4b)6c)3d)5Correct answer is option 'D'. 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 Two venturi meters, with the same manometers, of different area ratios are installed in the same pipeline. The reading of 1st manometer is h and the area ratio is 2. If the 2nd manometer reads 8h, its area ratio isa)4b)6c)3d)5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two venturi meters, with the same manometers, of different area ratios are installed in the same pipeline. The reading of 1st manometer is h and the area ratio is 2. If the 2nd manometer reads 8h, its area ratio isa)4b)6c)3d)5Correct answer is option 'D'. Can you explain this answer?.
Two venturi meters, with the same manometers, of different area ratios are installed in the same pipeline. The reading of 1st manometer is h and the area ratio is 2. If the 2nd manometer reads 8h, its area ratio isa)4b)6c)3d)5Correct answer is option 'D'. 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 Two venturi meters, with the same manometers, of different area ratios are installed in the same pipeline. The reading of 1st manometer is h and the area ratio is 2. If the 2nd manometer reads 8h, its area ratio isa)4b)6c)3d)5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two venturi meters, with the same manometers, of different area ratios are installed in the same pipeline. The reading of 1st manometer is h and the area ratio is 2. If the 2nd manometer reads 8h, its area ratio isa)4b)6c)3d)5Correct answer is option 'D'. Can you explain this answer?.
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