00:04
Now here in this question, we look at a devonpool, right, which is six meter deep and a flow of water.
00:10
And it has a viewing window on one of its vertical walls, right? so suppose this is something like this, right? and it has a window, which is something like this, is tangent to the bottom according to the bathroom.
00:23
And it has a radius one meter, right? so the radius is one meter.
00:28
And the water actually is very deep, right? the water, of course, is very deep.
00:32
Is actually six meters deep from here to here, and that's six meters deep.
00:38
And basically you asked to find the force on the wind well, that's what was given by the pressure, you know, pressure, the total force is given by the pressure multiple the area, right? the point is we need to work out the pressure, right? so to find the pressure, what we could do, i'm going to set up a coordinate system first.
01:02
So i'm going to call this is one.
01:04
And the bottom is y equals zero and therefore here is y equals six right and the center of this of course is y equals one right the center here and this is obviously y equals one so that's y equals one right now the pressure what we can do in other pressure if you to do this let's look at for example a little segment right here right if you look at the little segment here and it has an area right so suppose this segment has a thickness of d y right and and then you look at the, if you look at this and the height of the second minuses of why, right, as according to the y.
01:41
And the water would bridge the pressure at this point, of course, is going to be given by m.
01:46
Yeah, it's not really m.
01:48
It's given by density, right, of the water.
01:50
Row, i'm going to row.
01:51
Ro is dense water.
01:53
And times the g, which is acceleration to gravity.
01:58
And times the y, right? that would be, and actually six minus why, because we look at depth.
02:04
So that would be six minus y.
02:10
So that would be the pressure.
02:11
And this pressure has to multiply by the area of this part, right? what is the area of this part? and of course, that's going to be given by d -y and times the lens, right? the lane, we need to work out kind of the, i mean, how long this segment is, right? so the lens, we have to work it out.
02:30
And we know that here is wire, right? so what will be the segment? well, we can work it out using some geometry ideas, right? so let me try to get this out.
02:43
So you look at this anger, right? and here, you know, that this is anger.
02:50
This is y, right? this is y.
02:52
And then how much would this be, right? and this is why, and you can work out this, right? that's, of course, 1 minus y, right? so how about this? this equals 1 squared.
03:03
So in other words, it's going to multiply, multiple by the length which is going to be by, you know, this part, plus of this part, so i put it two here, and then this part is going to be given one squared minus one minus one squared, right? one minus one squared.
03:21
So that would be basically the expression, the force on this, right? so in the end, the total force, of course, we just need to integrate from zero to six, right? that would be the answer.
03:33
So lower and j constant, we take it out, and two is the constants, so we get 2 row g integrated from 0 to 6, d, y, and then you have 6 minus 1 ,000, and then at times the square of 12.
03:46
1 minus this, what do you get? well, that, of course, gives you 1 minus 1 square, right? so that's given by, you know, 1 is gone, and you have 2 y, basically, and minus y squared.
04:00
Okay, so that seems to be, well, that, of course, is something we would expect for.
04:09
The length, sorry, right? that's what we would expect for this lens.
04:16
But this seems to be true, i mean, this expression is true only for why actually is below, only for why actually from here to here, right? here to here.
04:31
Oh, actually we don't have to integrate from zero to six because the window actually is only cut up to this point, right? so we only have to integrate from zero to two actually.
04:41
Sorry, it's a mistake.
04:43
We only have to integrate from zero to two, actually, not to six.
04:48
That was a mistake.
04:49
Because the height of the winter is two, right? so it's from two to two...