46. A triangle with sides 5,5 and 6 feet is submerged vertically in water (p=62.4 lb/ft³) with the 6 foot side at the surface. Find the force on the plate. 0910
46. A triangle with sides 5,5 and 6 feet is submerged vertically in water (p=62.4 lb/ft³) with the 6 foot side at the surface. Find the force on the plate. 0910
46. A triangle with sides 5,5 and 6 feet is submerged vertically in water (p=62.4 lb/ft³) with the 6 foot side at the surface. Find the force on the plate. 0910
Transcribed Image Text:### Fluid Pressure and Forces on Submerged Surfaces
#### Problem 46
A triangle with sides 5, 5, and 6 feet is submerged vertically in water (density, \( \rho = 62.4 \, \text{lb/ft}^3 \)) with the 6-foot side at the surface. Find the force on the plate.
#### Problem 47
A flat plate in the form of a semicircle 10 meters in diameter is submerged in water (density, \( \rho = 9810 \, \text{N/m}^3 \)). Find the force on the plate.
#### Problem 48
A triangle with sides 13, 13, and 24 feet is submerged vertically in water (density, \( \rho = 62.4 \, \text{lb/ft}^3 \)) with the point up and the long side is parallel to the surface. If the vertex is 4 feet below the surface, find the force on the plate.
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### Explanation:
These problems involve calculating fluid forces on submerged surfaces, a key concept in fluid mechanics and hydrostatics. When an object is submerged in a fluid, the fluid exerts a force on the object. This force can be calculated using principles of pressure.
1. **Fluid Pressure**: The pressure at a depth \(h\) in a fluid of density \(\rho\) is given by \( p = \rho g h \), where \( g \) is the gravitational acceleration.
2. **Force on a Submerged Surface**: The force on a submerged surface due to fluid pressure can be found by integrating the pressure over the area of the surface.
These exercises apply these principles to different shapes and configurations of submerged objects. For more detailed solutions, one would need to use geometrical properties to set up the integrals for the pressure distribution over the surfaces.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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