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An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.?
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An inverted U-tube manometer is connected to two horizontal pipes A an...
Given:
- Specific gravity of oil (gauge fluid), S = 0.8
- Vertical distance between the axes of pipes A and B, d = 30 cm
- Vertical heights of water columns in the two limbs of the inverted manometer, h = 35 cm
To find:
Difference in pressure between pipes A and B
Assumptions:
1. The density of water remains constant throughout the system.
2. The pressure at the bottom of the manometer is atmospheric pressure (P0).
Solution:
Step 1: Calculate the pressure difference between the two limbs of the manometer
The pressure difference between the two limbs of the manometer is given by the hydrostatic pressure formula:
ΔP = ρgh
where:
- ΔP is the pressure difference
- ρ is the density of the fluid (water in this case)
- g is the acceleration due to gravity
- h is the height of the fluid column
Since the heights of the water columns in the two limbs are the same, the pressure difference between them is zero:
ΔP = 0
Step 2: Calculate the pressure difference between pipes A and B
The pressure difference between two points in a fluid can be calculated using the hydrostatic pressure formula:
ΔP = ρgh
In this case, the pressure difference between pipes A and B is equal to the pressure difference between the bottom of the manometer and pipe A. Let's assume the pressure at the bottom of the manometer is P1 and the pressure at pipe A is P2.
ΔP = P1 - P2
Step 3: Calculate the pressure at the bottom of the manometer
The pressure at the bottom of the manometer can be calculated using the hydrostatic pressure formula:
P1 = P0 + ρgh
where:
- P0 is the atmospheric pressure
- ρ is the density of the fluid (water in this case)
- g is the acceleration due to gravity
- h is the height of the fluid column
In this case, the height of the fluid column is the sum of the heights of the water column and the oil column:
h_total = h_water + h_oil
Since the specific gravity of oil is defined as the ratio of the density of the oil to the density of water, we can write:
S = ρ_oil / ρ_water
ρ_oil = S * ρ_water
Substituting the value of ρ_oil in the equation for h_total:
h_total = h_water + (S * ρ_water * g) / ρ_water
Simplifying the equation:
h_total = h_water + S * g
Since the heights of the water columns in the two limbs are the same, we can write:
h_water = h / 2
Substituting this value in the equation for h_total:
h_total = h / 2 + S * g
Step 4: Calculate the pressure at pipe A
The pressure at pipe A can be calculated using the hydrostatic pressure formula:
P2 = P0 + ρgh
where:
- P0 is the atmospheric pressure
- ρ is the density of the fluid (water in this case)
- g
- Specific gravity of oil (gauge fluid), S = 0.8
- Vertical distance between the axes of pipes A and B, d = 30 cm
- Vertical heights of water columns in the two limbs of the inverted manometer, h = 35 cm
To find:
Difference in pressure between pipes A and B
Assumptions:
1. The density of water remains constant throughout the system.
2. The pressure at the bottom of the manometer is atmospheric pressure (P0).
Solution:
Step 1: Calculate the pressure difference between the two limbs of the manometer
The pressure difference between the two limbs of the manometer is given by the hydrostatic pressure formula:
ΔP = ρgh
where:
- ΔP is the pressure difference
- ρ is the density of the fluid (water in this case)
- g is the acceleration due to gravity
- h is the height of the fluid column
Since the heights of the water columns in the two limbs are the same, the pressure difference between them is zero:
ΔP = 0
Step 2: Calculate the pressure difference between pipes A and B
The pressure difference between two points in a fluid can be calculated using the hydrostatic pressure formula:
ΔP = ρgh
In this case, the pressure difference between pipes A and B is equal to the pressure difference between the bottom of the manometer and pipe A. Let's assume the pressure at the bottom of the manometer is P1 and the pressure at pipe A is P2.
ΔP = P1 - P2
Step 3: Calculate the pressure at the bottom of the manometer
The pressure at the bottom of the manometer can be calculated using the hydrostatic pressure formula:
P1 = P0 + ρgh
where:
- P0 is the atmospheric pressure
- ρ is the density of the fluid (water in this case)
- g is the acceleration due to gravity
- h is the height of the fluid column
In this case, the height of the fluid column is the sum of the heights of the water column and the oil column:
h_total = h_water + h_oil
Since the specific gravity of oil is defined as the ratio of the density of the oil to the density of water, we can write:
S = ρ_oil / ρ_water
ρ_oil = S * ρ_water
Substituting the value of ρ_oil in the equation for h_total:
h_total = h_water + (S * ρ_water * g) / ρ_water
Simplifying the equation:
h_total = h_water + S * g
Since the heights of the water columns in the two limbs are the same, we can write:
h_water = h / 2
Substituting this value in the equation for h_total:
h_total = h / 2 + S * g
Step 4: Calculate the pressure at pipe A
The pressure at pipe A can be calculated using the hydrostatic pressure formula:
P2 = P0 + ρgh
where:
- P0 is the atmospheric pressure
- ρ is the density of the fluid (water in this case)
- g
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An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.?
Question Description
An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.? for RRB NTPC/ASM/CA/TA 2024 is part of RRB NTPC/ASM/CA/TA preparation. The Question and answers have been prepared according to the RRB NTPC/ASM/CA/TA exam syllabus. Information about An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.? covers all topics & solutions for RRB NTPC/ASM/CA/TA 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.?.
An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.? for RRB NTPC/ASM/CA/TA 2024 is part of RRB NTPC/ASM/CA/TA preparation. The Question and answers have been prepared according to the RRB NTPC/ASM/CA/TA exam syllabus. Information about An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.? covers all topics & solutions for RRB NTPC/ASM/CA/TA 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.?.
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An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.?, a detailed solution for An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.? has been provided alongside types of An inverted U-tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30 cm. When an oil of specific gravity 0.8 is used as gauge fluid, the vertical heights of water columns in the two limbs of the inverted manometer (When measured from the centre lines of the pipes) are found to be same and equal to 35 cm. Determine the difference of pressure between the pipes.? theory, EduRev gives you an
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