For this second problem, you are now Mario, the super$-$plumber, who has been asked by Princess Peach to solve some plumbing issues in her kingdom. The kingdom is divided into two valleys, one of which contains a river where to pump some water, and one where there is no water at all. In the dry valley, there are mines of red and green rubies, so some water needs to be brought to the valley. In between the two valleys, there is a mountain, which altitude is $1200$ meters. The dry valley altitude is $100$ meters, and the wet valley is located at an altitude of $200$ meters. It has been decided to use a siphon to bring the water to the dry valley, i$.$e$.$ a pipe which will go up to the top of the mountain, and then will go down up to the second valley. We will assume that the atmospheric pressure is $100000$ Pascals.

$1.$ Draw a theoretical schema describing the situation. This question provides a lot of points, which means there will be a lot to put onto the schema; use the scale of $1$cm $=100$ meters on the y$-$axis; the x$-$axis scale is let free. Do not forget the forces at play.