Greetings now, let's explore hydroelectric energy. So in hydroelectric energy what we have to remember is that now we're going to be dealing with fluids. So fluids are this sort of substance, the state of matter where the container will define the shape of the matter. So you know that if you pour water in a container, it will take the shape of the container. And it is also very sensitive to pressure, so actually what drives tnHH1he flow it's fundamentally the difference in pressure. So that's what people in fluid dynamics are constantly have to deal with. And what we would like to do in hydroelectric systems is to see how we can transform the weight of the water, so the water have some weight. And the motion of the water, so therefore it will have velocity, therefore it will have kinetic energy, if we can transform that into electrical energy. So what we are going to be doing it's moving or transforming gravitational potential energy and kinetic energy into electrical energy. So remember, water is much more dense, so density no mass per unit volume. It's far more dense than air, so it's about a thousand times denser than air. So one cubic meter of water it's approximately one metric ton, but one cubic meter of air is about 1.3 kilograms or something like that a couple of pounds. So we can obtain the energy of interaction between all that mass and the Earth as potential energy and the motion of all that mass as kinetic energy. There is a little problem that we all have to face and it is that for all hydroelectric systems application. We need to be close to water to free water. Otherwise, it's very difficult because that is not something that occurs generally in all places. So we are going to be limited by the geography, by the location of the place where we want to set up our hydroelectric setup. So we have general hydroelectric systems. Those are the ones that you see when you go during the weekends to the park and you see the lake and you see the impoundments there, and you said, hmm, but all the water is quiet, there's no motion of water. Actually what happened is that what the damn it's doing is storing water, no, storing mass. So if you store mass the mass interact with the Earth through gravitational energy and potential energy and you're storing gravitational potential energy. So now if at the bottom of that damn you bore a hole, there is a great deal of mass on top of that hole and that mass interact with the Earth through a weight, weight is a force so it's a force along the radius of the Earth. And it's pushing all the water below it to go through that little hole at the bottom and that little hole at the bottom defines the area. So force per unit area is pressure. So there is a huge pressure at the bottom of that damn and that's where you connect your turbine and you obtain all the electrical energy. We're going to look now at low-head hydroelectrics. So low head hydroelectrics is where the fall of the water, the distance between the surface of the water and where we're going to utilize the water or the distance through which the water has fall if it's close to a cascade or something like that. It's of the order of about 20 meters is about 66 feet or something like that is of that order and that it's called low-head hydroelectrics. And of course, 20 meters it's sort of an average it can be maybe five or ten meter less and five or ten meter higher. Of course, there is a micro hydroelectric and micro hydroelectric, it's from five meter or less and that it's far more common because having a large head a large difference in the input of the water to the system. To the output it's more uncommon than the low-heads and they're always a path of the water through whatever is the channel. The channel is the place where the water flows this our fluid the water it can be substantial, it can be very short and they are going to be some interactions of the water with things. Okay, so there might be the breed, there might be pieces of wood, there might be stones and we have to take into consideration all those things. So that's always what we have to really keep in mind is to keep the losses as low as possible. In our case, most of the losses are frictional losses are the losses of the water interacting with the material of the channel or with devices that we put in front of the flow on purpose like our turbines. And one thing that we would like to remember is that the larger the diameter or the width and height of the of the channel the less the possibility of interacting with the walls. And we don't want to have a very quick turn in the direction of the flow, the so-called elbows or 45 degrees bends. What happened there, is that imagine that you have an elbow in here. So the water comes in this direction and suddenly it goes perpendicular to the original direction. So the particles of the flow closer to this end have to traverse a smaller distance than the one in the outside that has to traverse a larger distance. What happened when they traverse larger distance is that they tend to cavitate, cavitation is the formation of bubbles and to form bubbles, you have to spend energy and the bubbles interact with the channel in different forms that also utilize energy. So you are losing energy. So you're making your system less efficient if you try to use too many changes in direction and a small channels. One clear example is if you mix with the water some of the sand or you mix some of the material that are part of the sediment in the channel abrasion will occur. It will start scratching the surface of your channel. Your channel can be a polymer plastic or it can be metal or it can be cement concrete. In the case of a metal, it's constantly exposing new metal but because of abrasion and the action of oxygen that is dissolved in the water will oxidize the metal and form rust and you're going to be losing material in your channel. So you want to have materials that are chemically stable that means very high quality steel, that means they are expensive unfortunately and you would like to keep straight geometries and you want to use material that it's reasonably hard. So if you have some strong interaction between your whatever, it's been carried by your flow and the channel, it's kept to a minimum. So people have been looking at the relations that controls getting energy out of the fluid like water. We already discuss about a fluid like air. And there is a relation that tells you that the amount of energy per unit time, the power that we can obtain from moving water is proportional to how high the water falls. Okay, and how much water is there. So the hive it's a symbolized or labeled h lowercase h for heights, that's the head that is the distance between the inlet to your whole system and the outlet. And Q is the amount of water the flow rate, and the flow rate is in cubic meters per second for example, the height it's obviously in meters and it's also there's two other factors in there. One of the factors is the density because it can be a less dense material than water, it can be a hydrocarbon and the density can be different. And the acceleration of gravity, so every time you have mass and the mass is acted by the Earth in gravitational potential energy. You have that acceleration of gravity G, which is night 9.8 meters per second square, so all in meters. And you remember that actually a cubic meter is fairly substantial amount of a liquid of of water. Actually, there's a thousand liters in a cubic meter. So it's an important parameter for you. So what will decide which system you are going to design and what will be the hardware that you're going to utilize is that product of these two factors, their height or the head and the flow rate q. And it is important that you utilize it because you have to do a assessment of what is the power or the energy if you know the period of time that you're going to use the power. The energy that you're going to be used with your load so you can decide what it will be the hardware that you're going to use when you're going to put together your hydroelectric system. So usually you have to find out what is the flow rate and what is the height in your system not for the river, the river you can attach your system to different places, different locations in the river. But in this case, you would like to do it just for your system. So there is a recipient that received the water from the flow of the river and that is called the penstock and the penstock it's usually conical in shape. But if it's conical in shape, look what this characteristic of a cone, the first part where the diameter is large at the opening of the cone there is this much amount of water, so mass and this much of the diameter of the cone. But at the bottom of the cone you have this much amount of water and the diameter is really really small. But remember, that the pressure is force per unit area. So in the top the unit area is the area is much larger than at the bottom. So the pressure at the bottom, which is very very high. So what does it tells you about the penstock you have to use very strong materials because they are going to sustain pressures that are very high and therefore can really destroy or band or affect lesser materials. So one of the fundamentals of our design is that you have to know what is Q, the flow rate. You have to know what is h, the head in order to satisfy the demands of your load.