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A manometer contains a fluid having a density of 1200kg per meter cube the difference in height of two columns is 400nm what would be height difference if the same pressure difference is to be measured by a mercury manometer having mass density of mercury 13600 kg per meter cube (a) 0.533mm (b)533.3mm (c) 5.33mm (d) 53.3 mm?
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A manometer contains a fluid having a density of 1200kg per meter cube...
Understanding the Problem
To find the height difference in a mercury manometer when given the height difference in a fluid with a different density, we can use the hydrostatic pressure principle. The relationship between the heights and densities of the fluids involved is given by the equation:
Pressure Difference (ΔP) = ρgh
Where:
- ρ = Density of the fluid
- g = Acceleration due to gravity (approximately 9.81 m/s²)
- h = Height difference
Given Values
- Density of fluid (ρ₁) = 1200 kg/m³
- Height difference (h₁) = 400 nm (which is 400 x 10^-9 m)
- Density of mercury (ρ₂) = 13600 kg/m³
Calculating Pressure Difference Using the First Fluid
Using the first fluid:
- ΔP = ρ₁ * g * h₁
- ΔP = 1200 kg/m³ * 9.81 m/s² * (400 x 10^-9 m)
This gives us the pressure difference in terms of the first fluid.
Finding Height Difference in Mercury Manometer
Using the same pressure difference for mercury:
- ΔP = ρ₂ * g * h₂
- Rearranging gives us: h₂ = ΔP / (ρ₂ * g)
Now substituting our previous expression for ΔP:
- h₂ = (ρ₁ * g * h₁) / (ρ₂ * g)
The gravitational factors cancel out:
- h₂ = (ρ₁ * h₁) / ρ₂
Substituting Values
- h₂ = (1200 kg/m³ * 400 x 10^-9 m) / 13600 kg/m³
Calculating this gives:
- h₂ ≈ 0.0353 m or 35.3 mm
Conclusion
The closest answer from the options provided is (d) 53.3 mm, which is the height difference in the mercury manometer.
To find the height difference in a mercury manometer when given the height difference in a fluid with a different density, we can use the hydrostatic pressure principle. The relationship between the heights and densities of the fluids involved is given by the equation:
Pressure Difference (ΔP) = ρgh
Where:
- ρ = Density of the fluid
- g = Acceleration due to gravity (approximately 9.81 m/s²)
- h = Height difference
Given Values
- Density of fluid (ρ₁) = 1200 kg/m³
- Height difference (h₁) = 400 nm (which is 400 x 10^-9 m)
- Density of mercury (ρ₂) = 13600 kg/m³
Calculating Pressure Difference Using the First Fluid
Using the first fluid:
- ΔP = ρ₁ * g * h₁
- ΔP = 1200 kg/m³ * 9.81 m/s² * (400 x 10^-9 m)
This gives us the pressure difference in terms of the first fluid.
Finding Height Difference in Mercury Manometer
Using the same pressure difference for mercury:
- ΔP = ρ₂ * g * h₂
- Rearranging gives us: h₂ = ΔP / (ρ₂ * g)
Now substituting our previous expression for ΔP:
- h₂ = (ρ₁ * g * h₁) / (ρ₂ * g)
The gravitational factors cancel out:
- h₂ = (ρ₁ * h₁) / ρ₂
Substituting Values
- h₂ = (1200 kg/m³ * 400 x 10^-9 m) / 13600 kg/m³
Calculating this gives:
- h₂ ≈ 0.0353 m or 35.3 mm
Conclusion
The closest answer from the options provided is (d) 53.3 mm, which is the height difference in the mercury manometer.
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A manometer contains a fluid having a density of 1200kg per meter cube the difference in height of two columns is 400nm what would be height difference if the same pressure difference is to be measured by a mercury manometer having mass density of mercury 13600 kg per meter cube (a) 0.533mm (b)533.3mm (c) 5.33mm (d) 53.3 mm?
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A manometer contains a fluid having a density of 1200kg per meter cube the difference in height of two columns is 400nm what would be height difference if the same pressure difference is to be measured by a mercury manometer having mass density of mercury 13600 kg per meter cube (a) 0.533mm (b)533.3mm (c) 5.33mm (d) 53.3 mm? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A manometer contains a fluid having a density of 1200kg per meter cube the difference in height of two columns is 400nm what would be height difference if the same pressure difference is to be measured by a mercury manometer having mass density of mercury 13600 kg per meter cube (a) 0.533mm (b)533.3mm (c) 5.33mm (d) 53.3 mm? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A manometer contains a fluid having a density of 1200kg per meter cube the difference in height of two columns is 400nm what would be height difference if the same pressure difference is to be measured by a mercury manometer having mass density of mercury 13600 kg per meter cube (a) 0.533mm (b)533.3mm (c) 5.33mm (d) 53.3 mm?.
A manometer contains a fluid having a density of 1200kg per meter cube the difference in height of two columns is 400nm what would be height difference if the same pressure difference is to be measured by a mercury manometer having mass density of mercury 13600 kg per meter cube (a) 0.533mm (b)533.3mm (c) 5.33mm (d) 53.3 mm? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A manometer contains a fluid having a density of 1200kg per meter cube the difference in height of two columns is 400nm what would be height difference if the same pressure difference is to be measured by a mercury manometer having mass density of mercury 13600 kg per meter cube (a) 0.533mm (b)533.3mm (c) 5.33mm (d) 53.3 mm? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A manometer contains a fluid having a density of 1200kg per meter cube the difference in height of two columns is 400nm what would be height difference if the same pressure difference is to be measured by a mercury manometer having mass density of mercury 13600 kg per meter cube (a) 0.533mm (b)533.3mm (c) 5.33mm (d) 53.3 mm?.
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