00:01
So today, we're given this problem where we have this circular plate, and it has a radius of 8 meters, and it's submerged 2 meters below the water line.
00:11
Okay? and so we're asked to find the hydrostatic force, all right? and so what we can do is we can use the fact that the hydrostatic pressure at any depth in the water will be equal to, so our pressure is going to be equal to the density of the water, times the acceleration due to gravity, times the depth of the water.
00:33
So p equals pg.
00:36
All right.
00:36
And since the circular plate is submerged vertically in water, the hydrostatic pressure on the side will vary with the depth.
00:46
Okay, so what we can do is we can think of the plate like a bunch of small vertical strips.
00:52
Okay, and we can give each of these strips the width of delta x.
00:58
And then we can integrate the pressure over the depth of each strip to help us find the hydrostatic force.
01:05
Okay, so what does this mean? well, let's consider a strip of width delta x.
01:11
And that's going to be at distance x from the center of the plate.
01:16
The depth at the top of the strip, so all the way at the top up here, is going to be equal to 8 minus x.
01:25
And the depth at the bottom is going to be equal to h minus delta x...