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A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :
Correct answer is between '678,679'. Can you explain this answer?
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A lake has a maximum depth of 60 m. If the mean atmospheric pressure i...
Given:
- Maximum depth of the lake = 60 m
- Mean atmospheric pressure in the lake region = 91 kPa
- Unit weight of lake = 9790 N/m3
To find:
- Absolute pressure at the maximum depth of the lake
Assumptions:
- The density of water is considered constant throughout the depth of the lake.
- The acceleration due to gravity is considered constant.
Explanation:
To find the absolute pressure at the maximum depth of the lake, we need to consider the hydrostatic pressure due to the water column above and the atmospheric pressure.
Hydrostatic Pressure:
The hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it. It can be calculated using the formula:
P = ρgh
where:
- P is the hydrostatic pressure
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the height or depth of the fluid column
In this case, the fluid is water and the depth is 60 m. The density of water is approximately 9790 N/m3 and the acceleration due to gravity is approximately 9.81 m/s2.
Substituting the given values:
P = 9790 N/m3 × 9.81 m/s2 × 60 m
P = 5720340 N/m2
Converting to kPa:
1 N/m2 = 0.001 kPa
5720340 N/m2 = 5720.34 kPa
Total Pressure:
To find the absolute pressure at the maximum depth of the lake, we need to add the hydrostatic pressure to the atmospheric pressure.
Total pressure = Hydrostatic pressure + Atmospheric pressure
Total pressure = 5720.34 kPa + 91 kPa
Rounding off to two decimal places:
Total pressure = 5811.34 kPa
Therefore, the absolute pressure at the maximum depth of the lake is approximately 5811.34 kPa, which falls between 678 and 679 when rounded off to two decimal places.
- Maximum depth of the lake = 60 m
- Mean atmospheric pressure in the lake region = 91 kPa
- Unit weight of lake = 9790 N/m3
To find:
- Absolute pressure at the maximum depth of the lake
Assumptions:
- The density of water is considered constant throughout the depth of the lake.
- The acceleration due to gravity is considered constant.
Explanation:
To find the absolute pressure at the maximum depth of the lake, we need to consider the hydrostatic pressure due to the water column above and the atmospheric pressure.
Hydrostatic Pressure:
The hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it. It can be calculated using the formula:
P = ρgh
where:
- P is the hydrostatic pressure
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the height or depth of the fluid column
In this case, the fluid is water and the depth is 60 m. The density of water is approximately 9790 N/m3 and the acceleration due to gravity is approximately 9.81 m/s2.
Substituting the given values:
P = 9790 N/m3 × 9.81 m/s2 × 60 m
P = 5720340 N/m2
Converting to kPa:
1 N/m2 = 0.001 kPa
5720340 N/m2 = 5720.34 kPa
Total Pressure:
To find the absolute pressure at the maximum depth of the lake, we need to add the hydrostatic pressure to the atmospheric pressure.
Total pressure = Hydrostatic pressure + Atmospheric pressure
Total pressure = 5720.34 kPa + 91 kPa
Rounding off to two decimal places:
Total pressure = 5811.34 kPa
Therefore, the absolute pressure at the maximum depth of the lake is approximately 5811.34 kPa, which falls between 678 and 679 when rounded off to two decimal places.
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Community Answer
A lake has a maximum depth of 60 m. If the mean atmospheric pressure i...
Given : Patm = 91 KPa = , h = 60 m
Unit weight of lake water = 9790N/m2
Absolute pressure at maximum depth of the lake = Patm + ρgh
Unit weight of lake water = 9790N/m2
Absolute pressure at maximum depth of the lake = Patm + ρgh
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A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer?
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A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer?.
A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer?.
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A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer?, a detailed solution for A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer? has been provided alongside types of A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and unit weight of lake is 9790 N/m3. The absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is :Correct answer is between '678,679'. Can you explain this answer? theory, EduRev gives you an
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