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In a differential manometer, a head of 0.5 m of fluid A in limb 1 is found to balance a head of 0.3 m of fluid B in limb 2. The atmospheric pressure is 760 mm of mercury. The ratio of specific gravities of A to B is-
- a)0.25
- b)2
- c)0.6
- d)4
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a differential manometer, a head of 0.5 m of fluid A in limb 1 is f...
Differential manometers are devices used to measure pressure differences between two points in a fluid system. They consist of a U-shaped tube filled with a liquid, with one end connected to the point where the pressure is to be measured and the other end open to the atmosphere.
Given:
Head of fluid A in limb 1 = 0.5 m
Head of fluid B in limb 2 = 0.3 m
Atmospheric pressure = 760 mmHg
We need to find the ratio of specific gravities of fluid A to fluid B.
Let's solve this step by step:
1. Convert the given heads into the same unit:
Since the atmospheric pressure is given in mmHg, let's convert the heads of fluid A and fluid B into mmHg as well.
Head of fluid A in limb 1 = 0.5 m = 0.5 * 1000 mm = 500 mmHg
Head of fluid B in limb 2 = 0.3 m = 0.3 * 1000 mm = 300 mmHg
2. Determine the pressure difference between the two limbs:
The pressure difference between the two limbs is given by the height difference between the fluid levels in the U-shaped tube.
Pressure difference = (Head of fluid A in limb 1) - (Head of fluid B in limb 2)
= 500 mmHg - 300 mmHg
= 200 mmHg
3. Calculate the specific gravity ratio:
The pressure difference between the two limbs is equal to the difference in heights of the fluid columns. This pressure difference can be related to the specific gravity of the fluids using the equation:
Pressure difference = (Specific gravity of fluid A - Specific gravity of fluid B) * (Density of liquid used in manometer) * (Acceleration due to gravity)
Since the density of the liquid used in the manometer is not given, we can assume it to be water, which has a density of 1000 kg/m³.
1000 mmHg = (Specific gravity of fluid A - Specific gravity of fluid B) * 1000 kg/m³ * 9.81 m/s²
Simplifying the equation:
Specific gravity of fluid A - Specific gravity of fluid B = 0.2
4. Find the ratio of specific gravities:
The ratio of specific gravities of fluid A to fluid B can be found by dividing the specific gravity difference by the specific gravity of fluid B.
(Specific gravity of fluid A) / (Specific gravity of fluid B) = (Specific gravity of fluid A - Specific gravity of fluid B) / (Specific gravity of fluid B)
= 0.2 / (Specific gravity of fluid B)
= 0.2 / 1
= 0.2
Therefore, the ratio of specific gravities of fluid A to fluid B is 0.2.
However, none of the given options match this result. The correct option might be misprinted in the question or there might be an error in the solution.
Given:
Head of fluid A in limb 1 = 0.5 m
Head of fluid B in limb 2 = 0.3 m
Atmospheric pressure = 760 mmHg
We need to find the ratio of specific gravities of fluid A to fluid B.
Let's solve this step by step:
1. Convert the given heads into the same unit:
Since the atmospheric pressure is given in mmHg, let's convert the heads of fluid A and fluid B into mmHg as well.
Head of fluid A in limb 1 = 0.5 m = 0.5 * 1000 mm = 500 mmHg
Head of fluid B in limb 2 = 0.3 m = 0.3 * 1000 mm = 300 mmHg
2. Determine the pressure difference between the two limbs:
The pressure difference between the two limbs is given by the height difference between the fluid levels in the U-shaped tube.
Pressure difference = (Head of fluid A in limb 1) - (Head of fluid B in limb 2)
= 500 mmHg - 300 mmHg
= 200 mmHg
3. Calculate the specific gravity ratio:
The pressure difference between the two limbs is equal to the difference in heights of the fluid columns. This pressure difference can be related to the specific gravity of the fluids using the equation:
Pressure difference = (Specific gravity of fluid A - Specific gravity of fluid B) * (Density of liquid used in manometer) * (Acceleration due to gravity)
Since the density of the liquid used in the manometer is not given, we can assume it to be water, which has a density of 1000 kg/m³.
1000 mmHg = (Specific gravity of fluid A - Specific gravity of fluid B) * 1000 kg/m³ * 9.81 m/s²
Simplifying the equation:
Specific gravity of fluid A - Specific gravity of fluid B = 0.2
4. Find the ratio of specific gravities:
The ratio of specific gravities of fluid A to fluid B can be found by dividing the specific gravity difference by the specific gravity of fluid B.
(Specific gravity of fluid A) / (Specific gravity of fluid B) = (Specific gravity of fluid A - Specific gravity of fluid B) / (Specific gravity of fluid B)
= 0.2 / (Specific gravity of fluid B)
= 0.2 / 1
= 0.2
Therefore, the ratio of specific gravities of fluid A to fluid B is 0.2.
However, none of the given options match this result. The correct option might be misprinted in the question or there might be an error in the solution.
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Community Answer
In a differential manometer, a head of 0.5 m of fluid A in limb 1 is f...
- Using Hydrostatic law which states the variation of pressure in the vertical direction in a fluid is equal to the specific weight.
Pgauge = ρgh
- As we move vertically down in a fluid, the pressure increases as +ρgh.
- As we vertically move up in a fluid, the pressure decreases as -ρgh.
Po + ρAgh1 = Po + ρBgh2
where ρA and ρB are densities of fluid A and B, h1 and h2 are heights of fluid in limbs 1 and 2, Po is the atmospheric pressure.
Calculation:
Given:
h1 = 0.5 m and h2 = 0.3 m
ρAh1 = ρBh2
where ρA and ρB are densities of fluid A and B, h1 and h2 are heights of fluid in limbs 1 and 2, Po is the atmospheric pressure.
Calculation:
Given:
h1 = 0.5 m and h2 = 0.3 m
ρAh1 = ρBh2
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In a differential manometer, a head of 0.5 m of fluid A in limb 1 is found to balance a head of 0.3 m of fluid B in limb 2. The atmospheric pressure is 760 mm of mercury. The ratio of specific gravities of A to B is-a)0.25b)2c)0.6d)4Correct answer is option 'C'. Can you explain this answer?
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In a differential manometer, a head of 0.5 m of fluid A in limb 1 is found to balance a head of 0.3 m of fluid B in limb 2. The atmospheric pressure is 760 mm of mercury. The ratio of specific gravities of A to B is-a)0.25b)2c)0.6d)4Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about In a differential manometer, a head of 0.5 m of fluid A in limb 1 is found to balance a head of 0.3 m of fluid B in limb 2. The atmospheric pressure is 760 mm of mercury. The ratio of specific gravities of A to B is-a)0.25b)2c)0.6d)4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a differential manometer, a head of 0.5 m of fluid A in limb 1 is found to balance a head of 0.3 m of fluid B in limb 2. The atmospheric pressure is 760 mm of mercury. The ratio of specific gravities of A to B is-a)0.25b)2c)0.6d)4Correct answer is option 'C'. Can you explain this answer?.
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