![]() This same graphical approach can be used for plane surfaces that do not extend up to the fluid surface as illustrated in Fig. This result can readily be shown to be consistent with that obtained from Eqs. For the volume under consideration the centroid is located along the vertical axis of symmetry of the surface, and at a distance of h/3 above the base (since the centroid of a triangle is located at h/3 above its base). The resultant force must pass through the centroid of the pressure prism. ![]() The magnitude of the resultant fluid force is equal to the volume of the pressure prism and passes through its centroid. Graphical representation of hydrostatic forces on a vertical rectangular surface. Pressure prism for vertical rectangular area. To find the area, we will multiply all of that by the change in height, which is Δx.Where bh is the area of the rectangular surface, A. Now we can find the area of the trapezoid, which is the base added to double the width of the triangle (a), since the triangle is on both sides of the trapezoid. This is equal to the line from the base to the surface of the water (2 - x) divided by a, which is the width at 2-x. Set up the equation so that you divide the total height (4m) by the maximum width of this section (2m since (8m - 4m)/2, there's 2m on each side). First you need to find an area equation for the triangle section of the trapezoid where the width is increasing from 4m to 8m, keeping in mind that we're only interested in the area that is submerged in water (2m).
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