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A vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface. The position of the centre of pressure below the free surface will be?
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A vertical rectangular plane surface is submerged in water such that i...
- **Given Data**
- Top surface of the surface: 1.5m below the free surface
- Bottom surface of the surface: 6.0m below the free surface
- **Calculating the depth of the centroid**
- The depth of the centroid of the plane surface can be calculated using the formula:
\[ \text{Depth of centroid} = \frac{h_1 + h_2}{2} \]
\[ \text{Depth of centroid} = \frac{1.5 + 6.0}{2} = 3.75m \]
- **Calculating the position of the centre of pressure**
- The position of the centre of pressure can be calculated using the formula:
\[ \text{Position of centre of pressure} = \frac{I_c}{A} \]
where:
- \( I_c \) = Moment of inertia of the plane surface about the centroid
- \( A \) = Area of the plane surface
- Since the plane surface is rectangular, the moment of inertia about the centroid can be calculated as:
\[ I_c = \frac{bh^3}{12} \]
where:
- \( b \) = Width of the plane surface
- \( h \) = Height of the plane surface
- Therefore, the position of the centre of pressure can be calculated as:
\[ \text{Position of centre of pressure} = \frac{bh^3}{12 \times bh} = \frac{h}{3} \]
\[ \text{Position of centre of pressure} = \frac{3.75}{3} = 1.25m \]
- **Conclusion**
- The position of the centre of pressure below the free surface is 1.25m.
- Top surface of the surface: 1.5m below the free surface
- Bottom surface of the surface: 6.0m below the free surface
- **Calculating the depth of the centroid**
- The depth of the centroid of the plane surface can be calculated using the formula:
\[ \text{Depth of centroid} = \frac{h_1 + h_2}{2} \]
\[ \text{Depth of centroid} = \frac{1.5 + 6.0}{2} = 3.75m \]
- **Calculating the position of the centre of pressure**
- The position of the centre of pressure can be calculated using the formula:
\[ \text{Position of centre of pressure} = \frac{I_c}{A} \]
where:
- \( I_c \) = Moment of inertia of the plane surface about the centroid
- \( A \) = Area of the plane surface
- Since the plane surface is rectangular, the moment of inertia about the centroid can be calculated as:
\[ I_c = \frac{bh^3}{12} \]
where:
- \( b \) = Width of the plane surface
- \( h \) = Height of the plane surface
- Therefore, the position of the centre of pressure can be calculated as:
\[ \text{Position of centre of pressure} = \frac{bh^3}{12 \times bh} = \frac{h}{3} \]
\[ \text{Position of centre of pressure} = \frac{3.75}{3} = 1.25m \]
- **Conclusion**
- The position of the centre of pressure below the free surface is 1.25m.
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A vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface. The position of the centre of pressure below the free surface will be?
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A vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface. The position of the centre of pressure below the free surface will be? 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 vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface. The position of the centre of pressure below the free surface will be? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface. The position of the centre of pressure below the free surface will be?.
A vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface. The position of the centre of pressure below the free surface will be? 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 vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface. The position of the centre of pressure below the free surface will be? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface. The position of the centre of pressure below the free surface will be?.
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