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Section 8.4 : Hydrostatic Pressure and Force

Find the hydrostatic force on the following plates submerged in water as shown in each image. In each case consider the top of the blue “box” to be the surface of the water in which the plate is submerged. Note as well that the dimensions in many of the images will not be perfectly to scale in order to better fit the plate in the image. The lengths given in each image are in meters.

  1. This is the sketch of a rectangular plate with a horizontal length of 10 and vertical height of 5. The top of the plate is level with the water surface.
  2. This is the sketch of a rectangular plate with a horizontal length of 10 and vertical height of 5. The top of the plate is a distance of 2 below the water surface.
  3. This is the sketch of a plate in the share of the lower half of a disk with diameter 16. The top, i.e. the wide part of the half disk, is out of the water and is a distance of 2 above the water surface. The rest of the plate is submerged in the water.
  4. This is the sketch of a triangular plate that is an equilateral triangle whose sides all have a length of 4. The point of the triangle is just at the water surface and the base of the triangle is submerged in the water and parallel to the water surface.
  5. This is a sketch of plate in the shape of a trapezoid. The two parallel sides of the trapezoid are horizontal and parallel to the water surface. The larger of the two horizontal sides has a length of 6 and is a distance of 1 out of the water. The smaller of the two horizontal sides is a distance of 4 below (and so is submerged in the water) the larger horizontal side, has a length of 1 and is perfectly centered under the larger horizontal side. The angled sides of the plate do not have any lengths given.
  6. The plate in this sketch is a little more complex than the first few above. The top of the plate is a rectangle with horizontal length of 6 and a vertical length of 2. The top of rectangle is parallel to the water surface and is a distance of 1 below the water surface. The bottom of the plate is a triangle whose base is on the bottom of the rectangle (and so has a base length of 6). The point of the triangle is a distance of 2 below the base of the triangle and perfectly centered under the rectangle (i.e. has a horizontal distance of 3 from a line extended down from the vertical side of the rectangle).
  7. The plate in this sketch is a little more complex than the first few above. The top of the plate is a rectangle with horizontal length of 6 and a vertical length of 1. The top of this rectangle is just at the water surface and is parallel to the water surface. The bottom of the plate consists of two upside down right triangles. The base of each triangle has a distance of 3 and the height of the triangles extend down below the right/left edges of the rectangle on top. Or, another way to describe them is to say that the hypotenuse of each of the triangles starts at the center point of the bottom edge of the rectangles and slope down into the water until they are under the vertical right/left edges of the rectangle. The total vertical length of the plate (vertical rectangle length plus height of the right triangle) is given at 3.
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