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A rectangular plan surface 5 m wide and 7 m deep lies in water in such a way that its plane makes an angle 60⁰ with the free surface of water. Determine the total pressure force when the upper edge is 3 m below the free surface.
- a)311.15 N/cm2
- b)622.3 N/cm2
- c)155.5 N/cm2
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A rectangular plan surface 5 m wide and 7 m deep lies in water in such...
Explanation: Total pressure, F=w*a*ŷ=w*A*(y+dsinθ)=9.81*1000*35*(3+7sin60)=311.15 N/cm2.
Most Upvoted Answer
A rectangular plan surface 5 m wide and 7 m deep lies in water in such...
To determine the total pressure force on the rectangular plane surface, we need to consider the hydrostatic pressure acting on the surface due to the water above it.
1. Hydrostatic Pressure:
The hydrostatic pressure exerted by a fluid at a given depth is given by the equation:
P = ρgh
where:
P is the pressure (force per unit area),
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth of the surface below the free surface of the fluid.
2. Calculation:
Given:
Width of the rectangular surface (w) = 5 m
Depth of the rectangular surface below the free surface of water (h) = 3 m
Angle between the plane of the surface and the free surface of water (θ) = 60°
To calculate the pressure force, we first need to determine the hydrostatic pressure at the upper edge of the surface. Since the surface is inclined at an angle of 60°, we can resolve the depth (h) into its horizontal and vertical components.
The horizontal component of the depth is given by:
h_horizontal = h * cos(θ)
= 3 * cos(60°)
= 3 * 0.5
= 1.5 m
The vertical component of the depth is given by:
h_vertical = h * sin(θ)
= 3 * sin(60°)
= 3 * √3/2
= 3√3/2 m
Now, we can calculate the hydrostatic pressure at the upper edge of the surface using the vertical component of the depth:
P = ρgh_vertical
= ρg * (3√3/2)
3. Density of Water:
The density of water (ρ) is approximately 1000 kg/m³.
4. Acceleration due to Gravity:
The acceleration due to gravity (g) is approximately 9.8 m/s².
Substituting the values, we get:
P = 1000 * 9.8 * (3√3/2)
Calculating the value, we find:
P ≈ 16113.08 N/m²
Since the question asks for the pressure force in N/cm², we need to convert the units:
1 N/m² = 1 Pa
1 N/cm² = 10000 N/m²
Converting the units, we get:
P ≈ 16113.08 * 10000 N/cm²
P ≈ 161130.8 N/cm²
The closest option to the calculated value is option 'A' which is 311.15 N/cm².
1. Hydrostatic Pressure:
The hydrostatic pressure exerted by a fluid at a given depth is given by the equation:
P = ρgh
where:
P is the pressure (force per unit area),
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth of the surface below the free surface of the fluid.
2. Calculation:
Given:
Width of the rectangular surface (w) = 5 m
Depth of the rectangular surface below the free surface of water (h) = 3 m
Angle between the plane of the surface and the free surface of water (θ) = 60°
To calculate the pressure force, we first need to determine the hydrostatic pressure at the upper edge of the surface. Since the surface is inclined at an angle of 60°, we can resolve the depth (h) into its horizontal and vertical components.
The horizontal component of the depth is given by:
h_horizontal = h * cos(θ)
= 3 * cos(60°)
= 3 * 0.5
= 1.5 m
The vertical component of the depth is given by:
h_vertical = h * sin(θ)
= 3 * sin(60°)
= 3 * √3/2
= 3√3/2 m
Now, we can calculate the hydrostatic pressure at the upper edge of the surface using the vertical component of the depth:
P = ρgh_vertical
= ρg * (3√3/2)
3. Density of Water:
The density of water (ρ) is approximately 1000 kg/m³.
4. Acceleration due to Gravity:
The acceleration due to gravity (g) is approximately 9.8 m/s².
Substituting the values, we get:
P = 1000 * 9.8 * (3√3/2)
Calculating the value, we find:
P ≈ 16113.08 N/m²
Since the question asks for the pressure force in N/cm², we need to convert the units:
1 N/m² = 1 Pa
1 N/cm² = 10000 N/m²
Converting the units, we get:
P ≈ 16113.08 * 10000 N/cm²
P ≈ 161130.8 N/cm²
The closest option to the calculated value is option 'A' which is 311.15 N/cm².
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A rectangular plan surface 5 m wide and 7 m deep lies in water in such a way that its plane makes an angle 60⁰ with the free surface of water. Determine the total pressure force when the upper edge is 3 m below the free surface.a)311.15 N/cm2b)622.3 N/cm2c)155.5 N/cm2d)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?
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A rectangular plan surface 5 m wide and 7 m deep lies in water in such a way that its plane makes an angle 60⁰ with the free surface of water. Determine the total pressure force when the upper edge is 3 m below the free surface.a)311.15 N/cm2b)622.3 N/cm2c)155.5 N/cm2d)None of the mentionedCorrect answer is option 'A'. 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 rectangular plan surface 5 m wide and 7 m deep lies in water in such a way that its plane makes an angle 60⁰ with the free surface of water. Determine the total pressure force when the upper edge is 3 m below the free surface.a)311.15 N/cm2b)622.3 N/cm2c)155.5 N/cm2d)None of the mentionedCorrect answer is option 'A'. 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 rectangular plan surface 5 m wide and 7 m deep lies in water in such a way that its plane makes an angle 60⁰ with the free surface of water. Determine the total pressure force when the upper edge is 3 m below the free surface.a)311.15 N/cm2b)622.3 N/cm2c)155.5 N/cm2d)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?.
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