Problem 31
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Section 6.6: Applications to Physics and Engineering
Chapter 6: Application of Integration
Given information
the shape of the water tank is given as follows:
Step-by-step explanation
The hydrostatic pressure of a water of density at a depth d from the surface of the water is .
The force on a surface due to pressure exerted is , where is the area of the surface being considered.
If is the angle with the horizontal made by a radius passing through a point located on the circular edge of the plate.
The depth of the point is ,The width of horizontal strip of the plate passing through the point is and the length of an infinitesimal section of perimeter around the point making an angle with the center of the disc is .
The height of the horizontal strip of disc that corresponds to this small section of perimeter is .Therefore, the area of the infinitesimally thin strip is
The hydrostatic pressure at the level of point is .