This dam behaves like a water cannon. Let’s do physics!

When people build the dams — the huge walls that support the lake and the entire river — need to build a flood channel called an outflow, a flood relief.

Discharge water could be as easy or complicated as the way water passes over the dam, like a side canal. Sometimes there is just a big hole at the bottom of the dam (on land) to throw water like a massive water cannon. That’s how it works Hydroelectric power plant in Brazil. Bada nice video shows the water coming out; it looks like a river in the air, basically yes river in the air.

The physics of this discharge is very nice because the speed of the water coming out of the hole depends on the depth of the water behind the dam. Once the water comes out of the pipe, it basically acts like a ball thrown at the same speed. Yes, you know what I’m going to do: I’m going to use the route of the water that comes out of the discharge to calculate the depth of the water in the reservoir.

In fact, it’s called the relationship between water flow and depth Torricelli’s law. Imagine that you have a bucket full of water and you enter a hole near the bottom. We can use physics to find the speed of water.

Let’s start by considering the change in water level over a very short period of time as the water empties. Here is the outline:

Looking at the top of the cube, the water level drops, albeit slightly. It doesn’t matter how much the water level drops; what interests us is the mass of that water, which I label as dm. In physics, we use “d” to denote a differential number of things, so the amount of water can be small. The fact that the water level at the top has dropped means that the water has to go somewhere. In this case, it came out of the hole. The mass of water that comes out must also be dm. (You need to keep track of all the water.)

Now let’s think from an energy perspective. The water system is closed, so the total energy must be constant. There are two types of energy to think about in this case. First, there is the gravitational potential energy (U_g = mgy). This is the energy associated with the height of an object on the Earth’s surface, and depends on its height, mass, and gravitational field (g = 9.8 N / kg). The second type of energy is kinetic energy (K = (1/2) mv²). This is the energy of mass and velocity (v) of an object.