00:01
In this problem, we're told that in analyzing certain geological features, it's often appropriate to assume that the pressure at some horizontal level of compensation deep inside the earth is the same over a large region and is equal to the pressure due to the gravitational force on the underlying material.
00:17
So the pressure at the level of compensation is given by the fluid pressure formula, but one of the problems is that we have to, whenever there's a mountain or some large perturbanes on top of the continent, here, we have to have a compensation route here of continent sticking down into the mantle such that the pressures in the mantle are equalized.
00:42
So we're told that we have a mountain here that's at a height that has a height of six kilometers.
00:50
The continent has a thickness of 32 kilometers.
00:56
We're told that the density of the continental rock is two point.
01:00
Grams or centimeter cube, which is 2 ,900 kilogram per meter cube.
01:05
And we're told that the density of the mantle is 3 .3 grams per centimeter cubed, which is 3 ,300 kilograms per meter cube.
01:14
And we want to find out if we're given this mountain height and the continent depth thickness, what d needs to be, how deep this root needs to be, so that these pressures are equal down here.
01:26
So we can look at the pressure at a, which is the pressure not under the mountain.
01:34
So we have the density of the continent times g times the thickness of the continent, and then plus the density of the mantle times g times the depth down to the mantle, which is capital d plus little d, which is our distance from the t, the end of the root to where we're measuring pressure at in the mantle.
02:01
And we're told that that will cancel out and we see that in fact it does.
02:04
Pressure at b under the mountain is row of the continental rock, g.
02:12
And so then the depth of continental rock we're down under is h plus t plus d...