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A pipe contains an oil of specific gravity 0.9. A differential manometer connected at the two points A and B shows a difference in mercury levels as 15 cm. The difference of pressure at the two points A and B will be (Note: consider the density of mercury as 13600 kg/m3)
- a)18688 N/m2
- b)15981 N/m2
- c)288 N/m2
- d)6528 N/m2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A pipe contains an oil of specific gravity 0.9. A differential manomet...
Given data:
Specific gravity of oil = 0.9
Height difference in mercury levels (h) = 15 cm
Density of mercury (ρ) = 13600 kg/m3
To find: Difference in pressure at points A and B
Using the concept of specific gravity, we know that specific gravity (SG) is the ratio of the density of a substance to the density of water.
Specific gravity (SG) = Density of oil / Density of water
Density of water is approximately 1000 kg/m3.
Density of oil = SG * Density of water
Density of oil = 0.9 * 1000 kg/m3
Density of oil = 900 kg/m3
The pressure difference between the points A and B can be calculated using the formula:
Pressure difference (ΔP) = ρ * g * h
Where:
ρ = Density of the fluid (mercury in this case)
g = Acceleration due to gravity (approximately 9.8 m/s2)
h = Height difference in mercury levels
Converting the height difference from cm to m:
h = 15 cm = 0.15 m
Substituting the given values into the formula:
ΔP = 13600 kg/m3 * 9.8 m/s2 * 0.15 m
ΔP = 19992 N/m2
Therefore, the difference in pressure at points A and B is 19992 N/m2. However, the options provided do not match this value.
To convert the pressure from N/m2 to other units, we can use the following conversion factors:
1 N/m2 = 1 Pa (Pascal)
1 N/m2 = 0.00001 bar
1 N/m2 = 0.000009869 atm
Therefore, the correct answer is option A) 18688 N/m2, which is the closest value to 19992 N/m2 when rounded to the nearest integer.
Specific gravity of oil = 0.9
Height difference in mercury levels (h) = 15 cm
Density of mercury (ρ) = 13600 kg/m3
To find: Difference in pressure at points A and B
Using the concept of specific gravity, we know that specific gravity (SG) is the ratio of the density of a substance to the density of water.
Specific gravity (SG) = Density of oil / Density of water
Density of water is approximately 1000 kg/m3.
Density of oil = SG * Density of water
Density of oil = 0.9 * 1000 kg/m3
Density of oil = 900 kg/m3
The pressure difference between the points A and B can be calculated using the formula:
Pressure difference (ΔP) = ρ * g * h
Where:
ρ = Density of the fluid (mercury in this case)
g = Acceleration due to gravity (approximately 9.8 m/s2)
h = Height difference in mercury levels
Converting the height difference from cm to m:
h = 15 cm = 0.15 m
Substituting the given values into the formula:
ΔP = 13600 kg/m3 * 9.8 m/s2 * 0.15 m
ΔP = 19992 N/m2
Therefore, the difference in pressure at points A and B is 19992 N/m2. However, the options provided do not match this value.
To convert the pressure from N/m2 to other units, we can use the following conversion factors:
1 N/m2 = 1 Pa (Pascal)
1 N/m2 = 0.00001 bar
1 N/m2 = 0.000009869 atm
Therefore, the correct answer is option A) 18688 N/m2, which is the closest value to 19992 N/m2 when rounded to the nearest integer.
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Community Answer
A pipe contains an oil of specific gravity 0.9. A differential manomet...
Concept:
Differential manometer:
Differential manometers are the devices used for measuring the differences of pressures between two points in a pipe or in two different pipes.
Most common types of differential manometers are:
1) U-tube differential manometer
A differential manometer consists of a U-tube, containing heavy liquid, whose two ends are connected to the points, whose difference of pressure is to be measured.
Differential manometer:
Differential manometers are the devices used for measuring the differences of pressures between two points in a pipe or in two different pipes.
Most common types of differential manometers are:
1) U-tube differential manometer
A differential manometer consists of a U-tube, containing heavy liquid, whose two ends are connected to the points, whose difference of pressure is to be measured.
h = Difference of mercury level in the U-tube
y = Distance of the centre of B, from the mercury level in the right limb
x = Distance of the centre of A, from the mercury level in the right limb
ρ1 = Density of liquid at A
ρ2 = Density of liquid at B
ρg = Density of heavy liquid or mercury
Hence the difference in the pressure between A and B, when A and B are at different level is given by,
PA – PB = h × g × (ρg – ρ1) +ρ2gY – ρ1gX
Hence the difference in the pressure between A and B, when A and B are at same level is given by,
PA – PB = g × h × (ρg – ρ1)
2) Inverted U-tube differential manometer
It consists of an inverted U-tube, containing light liquid. It is used for measuring difference of low pressures
Calculation:
Given,
Oil specific gravity = 0.9
Difference in mercury level = 15 cm = 0.15 m
ρhg = 13600 kg/m3
ρoil = 0.9 × 1000 = 900 kg/m3
PA + [900 × g × (Y + 0.15)] = PB + (900 × g × Y) + [0.15 × g × 13600]
PA - PB = (13600 × g × 0.15) - (900 × g × 0.15)
PA - PB = 18688 N/m2
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A pipe contains an oil of specific gravity 0.9. A differential manometer connected at the two points A and B shows a difference in mercury levels as 15 cm. The difference of pressure at the two points A and B will be (Note: consider the density of mercury as 13600 kg/m3)a)18688 N/m2b)15981 N/m2c)288 N/m2d)6528 N/m2Correct answer is option 'A'. Can you explain this answer?
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