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A longitudinal rectangular surface is hanged into the water such that its top and bottom points are at depth of 1.5 m and 6.0 m respectively. The depth of center of pressure (m) from the top surface is _____.
- a)3.8
- b)4.2
- c)4.6
- d)4.8
Correct answer is option 'B'. Can you explain this answer?
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A longitudinal rectangular surface is hanged into the water such that ...
θ = 90°
A = 1 × 4.5 m2
h¯CP= 4.2 metre
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A longitudinal rectangular surface is hanged into the water such that ...
Given:
- Depth of top point of the rectangular surface = 1.5 m
- Depth of bottom point of the rectangular surface = 6.0 m
To find: Depth of center of pressure from the top surface
Solution:
- Center of pressure is the point where the resultant force acts on the submerged surface.
- To find the depth of center of pressure, we can use the following formula:
Depth of center of pressure = [(Moment of force about the top edge) / (Resultant force)] + Depth of top edge
- Let's assume that the rectangular surface has a length L and a width B.
- The area of the submerged surface will be LxB.
- The centroid of the submerged surface will be located at a depth of (1.5+6)/2 = 3.75 m from the top edge.
- The resultant force will act vertically upwards and will be equal to the weight of the water displaced by the submerged surface.
- The weight of the water displaced is given by:
Weight of water = Volume of water x Density of water x Gravity
Volume of water = Length x Width x Depth of submerged surface = LxBx(6-1.5) = 4.5LxB
Density of water = 1000 kg/m^3
Gravity = 9.81 m/s^2
Weight of water = 4.5LxBx1000x9.81 N
- The moment of force about the top edge will be equal to the weight of the water displaced multiplied by the distance between the centroid and the top edge:
Moment of force = Weight of water x (3.75 - 1.5)
Moment of force = 4.5LxBx1000x9.81x2.25 Nm
- Now we can substitute these values in the formula to find the depth of center of pressure:
Depth of center of pressure = [(4.5LxBx1000x9.81x2.25) / (4.5LxBx1000x9.81)] + 1.5
Depth of center of pressure = 4.2 m
Therefore, the depth of center of pressure from the top surface is 4.2 m.
Answer: Option B.
- Depth of top point of the rectangular surface = 1.5 m
- Depth of bottom point of the rectangular surface = 6.0 m
To find: Depth of center of pressure from the top surface
Solution:
- Center of pressure is the point where the resultant force acts on the submerged surface.
- To find the depth of center of pressure, we can use the following formula:
Depth of center of pressure = [(Moment of force about the top edge) / (Resultant force)] + Depth of top edge
- Let's assume that the rectangular surface has a length L and a width B.
- The area of the submerged surface will be LxB.
- The centroid of the submerged surface will be located at a depth of (1.5+6)/2 = 3.75 m from the top edge.
- The resultant force will act vertically upwards and will be equal to the weight of the water displaced by the submerged surface.
- The weight of the water displaced is given by:
Weight of water = Volume of water x Density of water x Gravity
Volume of water = Length x Width x Depth of submerged surface = LxBx(6-1.5) = 4.5LxB
Density of water = 1000 kg/m^3
Gravity = 9.81 m/s^2
Weight of water = 4.5LxBx1000x9.81 N
- The moment of force about the top edge will be equal to the weight of the water displaced multiplied by the distance between the centroid and the top edge:
Moment of force = Weight of water x (3.75 - 1.5)
Moment of force = 4.5LxBx1000x9.81x2.25 Nm
- Now we can substitute these values in the formula to find the depth of center of pressure:
Depth of center of pressure = [(4.5LxBx1000x9.81x2.25) / (4.5LxBx1000x9.81)] + 1.5
Depth of center of pressure = 4.2 m
Therefore, the depth of center of pressure from the top surface is 4.2 m.
Answer: Option B.
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A longitudinal rectangular surface is hanged into the water such that ...
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A longitudinal rectangular surface is hanged into the water such that its top and bottom points are at depth of 1.5 m and 6.0 m respectively. The depth of center of pressure (m) from the top surface is _____.a)3.8b)4.2c)4.6d)4.8Correct answer is option 'B'. Can you explain this answer?
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