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A 5 m long vertical tube having cross sectional area 200 cm2 is placed in water. It is filled with 15°C water, with the bottom closed and the top open to 100 kPa atmosphere. What is the pressure at the bottom of the tube ?
- a)119 kPa
- b)129 kPa
- c)139 kPa
- d)149 kPa
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A 5 m long vertical tube having cross sectional area 200 cm2 is place...
∆P = ρ gH = gH/v = 9.80665 × 5/0.001001
= 48.98 kPa
P(total) = P(top) + ∆P = 149 kPa.
Most Upvoted Answer
A 5 m long vertical tube having cross sectional area 200 cm2 is place...
To find the pressure at the bottom of the tube, we can use the concept of hydrostatic pressure.
Hydrostatic pressure:
Hydrostatic pressure is the pressure exerted by a fluid at a given point in a fluid column due to the weight of the fluid above it. The pressure at any point in a fluid is the same in all directions and is transmitted equally in all directions.
Key Points:
- The tube is vertical, which means the pressure at the bottom is directly proportional to the height of the water column above it.
- The pressure at the top of the tube is 100 kPa and the atmospheric pressure at the top is also 100 kPa.
- We are given that the tube is filled with 15°C water, but the temperature of the water does not affect the pressure at a given point.
Solution:
1. Convert the cross-sectional area of the tube to square meters:
Area = 200 cm² = 200 × 10⁻⁴ m² = 0.02 m²
2. The pressure at the top of the tube is 100 kPa.
3. We know that the pressure at any point in a fluid is the same in all directions and is transmitted equally in all directions. Therefore, the pressure at the bottom of the tube is also 100 kPa.
4. To find the pressure at the bottom of the tube, we need to find the height of the water column above it.
5. The pressure at the bottom of the tube can be calculated using the formula for hydrostatic pressure:
Pressure = ρgh
Where,
ρ = density of the fluid
g = acceleration due to gravity
h = height of the fluid column
6. The density of water at 15°C is 1000 kg/m³.
7. The acceleration due to gravity is approximately 9.8 m/s².
8. The height of the water column can be calculated using the formula:
Volume = Area × Height
Height = Volume / Area
Height = 5 m
9. Now we can calculate the pressure at the bottom of the tube:
Pressure = ρgh
= 1000 kg/m³ × 9.8 m/s² × 5 m
= 49000 N/m² = 49 kPa
10. Therefore, the pressure at the bottom of the tube is 49 kPa.
Answer:
The correct option is (D) 149 kPa.
Hydrostatic pressure:
Hydrostatic pressure is the pressure exerted by a fluid at a given point in a fluid column due to the weight of the fluid above it. The pressure at any point in a fluid is the same in all directions and is transmitted equally in all directions.
Key Points:
- The tube is vertical, which means the pressure at the bottom is directly proportional to the height of the water column above it.
- The pressure at the top of the tube is 100 kPa and the atmospheric pressure at the top is also 100 kPa.
- We are given that the tube is filled with 15°C water, but the temperature of the water does not affect the pressure at a given point.
Solution:
1. Convert the cross-sectional area of the tube to square meters:
Area = 200 cm² = 200 × 10⁻⁴ m² = 0.02 m²
2. The pressure at the top of the tube is 100 kPa.
3. We know that the pressure at any point in a fluid is the same in all directions and is transmitted equally in all directions. Therefore, the pressure at the bottom of the tube is also 100 kPa.
4. To find the pressure at the bottom of the tube, we need to find the height of the water column above it.
5. The pressure at the bottom of the tube can be calculated using the formula for hydrostatic pressure:
Pressure = ρgh
Where,
ρ = density of the fluid
g = acceleration due to gravity
h = height of the fluid column
6. The density of water at 15°C is 1000 kg/m³.
7. The acceleration due to gravity is approximately 9.8 m/s².
8. The height of the water column can be calculated using the formula:
Volume = Area × Height
Height = Volume / Area
Height = 5 m
9. Now we can calculate the pressure at the bottom of the tube:
Pressure = ρgh
= 1000 kg/m³ × 9.8 m/s² × 5 m
= 49000 N/m² = 49 kPa
10. Therefore, the pressure at the bottom of the tube is 49 kPa.
Answer:
The correct option is (D) 149 kPa.
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A 5 m long vertical tube having cross sectional area 200 cm2 is placed in water. It is filled with 15°C water, with the bottom closed and the top open to 100 kPa atmosphere. What is the pressure at the bottom of the tube ?a)119 kPab)129 kPac)139 kPad)149 kPaCorrect answer is option 'D'. Can you explain this answer?
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A 5 m long vertical tube having cross sectional area 200 cm2 is placed in water. It is filled with 15°C water, with the bottom closed and the top open to 100 kPa atmosphere. What is the pressure at the bottom of the tube ?a)119 kPab)129 kPac)139 kPad)149 kPaCorrect answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A 5 m long vertical tube having cross sectional area 200 cm2 is placed in water. It is filled with 15°C water, with the bottom closed and the top open to 100 kPa atmosphere. What is the pressure at the bottom of the tube ?a)119 kPab)129 kPac)139 kPad)149 kPaCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 5 m long vertical tube having cross sectional area 200 cm2 is placed in water. It is filled with 15°C water, with the bottom closed and the top open to 100 kPa atmosphere. What is the pressure at the bottom of the tube ?a)119 kPab)129 kPac)139 kPad)149 kPaCorrect answer is option 'D'. Can you explain this answer?.
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