When a plane surface is submerged in a fluid, hydrostatic forces develop on the surface due to the fluid's pressure. For horizontal surfaces, the pressure exerted by the fluid is uniform because the depth remains constant. The resultant force is determined by the pressure at the given depth multiplied by the area of the surface, and it acts through the centroid of the surface. For vertical surfaces, the pressure varies with depth, increasing as the distance from the fluid's free surface increases. The resultant force is calculated as the product of the fluid's specific weight, the area of the vertical surface, and the depth of the centroid from the fluid surface.
In the case of an inclined surface, the force acting on each small element of the surface is influenced by its depth and the fluid's specific weight. To find the total force, the contributions from all the surface elements are integrated. Though it may seem that the resultant force acts through the centroid of the surface, it actually acts through a point called the center of pressure, which is located below the centroid. This is the point where the total hydrostatic pressure can be considered to act.
Consider plane surfaces submerged in a fluid with a specific weight. Forces are developed on the surfaces because of the fluid.
The resultant of the forces developed on the horizontal surface is given by the product of pressure exerted by the fluid on the surface and the area of the surface acting through the centroid of the area.
The resultant of the forces on the vertical surface is given by the product of the specific weight of the fluid, the area of the vertical surface, and the depth of the centroid of the area from the fluid surface.
For an inclined submerged surface, the force acting on a small element is the product of the fluid's specific weight, the element's depth from the fluid surface, and its area.
Integrating the force acting on the patch gives the resultant of the pressure acting on the entire incline surface.
The resultant appears to be acting through the centroid, but it actually acts through the point below the centroid called the center of pressure.
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