In this video I go over another example on hydrostatic pressure and force and this time determine the total force on a circular drum of radius 3 feet that is submerged to a depth of 10 feet. The procedure in determining the force is the same as in example 1, in which we consider the force on a thin horizontal slice and then take the limit to an infinite number of slices at an infinitely small size, and thus getting an integral. What's also useful in this video, is that I show a few tricks to simplify the process of solving the integrals by noticing the integral is the summation of a semi-circle and an odd function. These tricks save a lot of time so make sure to watch this video to the end!
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Applications of Integrals: Hydrostatic Pressure and Force: Example 2
Find the hydrostatic force on one end of a cylindrical drum with radius 3 ft if the drum is submerged in water 10 ft deep.
Solution:
In this example it is convenient to choose the axes so that the origin is placed at the center of the drum.
Then the circle is a simple equation: x2 + y2 = 9.
As in Example 1, we divide the circular region into horizontal strips of equal width.
From the equation of the circle, we see that the length of the ith strip is:
The pressure on this strip is approximately:
Thus the force on the strip is approximately:
The total force is obtained by adding the forces on all the strips and taking the limit:
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