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In previous section about Voltage, we learned that a difference in voltage induces a flow of electricity or current, which we can use to do something with it.

In order to understand what exactly the current is, let’s consider the current or flow of water.

In a simple way, it is taught that water maintains the same level or height. It also flows down because of gravity, which is similar to how solids fall down. But you cannot make a wall of water stand, it will all fall down to make a level surface on the top. If two tanks of water are connected with a pipe, and water is at higher level in one tank, it will flow to the other tank until the water level is same in both tanks. We know this happens, and it can be verified by experiments. The equations we have based on these principles also work fine. We have a whole discipline of hydraulics based on these ideas, and we can design all sorts of hydraulic systems using this knowledge.

But is that what really happens? When we say level of water, if you think at a deeper level, it really means the height or distance of the top surface of water from the centre of the earth. We all know top is the upper side, but up isn’t really an absolute direction. Up in the UK is not the same absolute direction as up in Australia. To make things flat in horizontal direction, we use the term level, meaning as flat as surface of water. Now consider that the top surface of water on earth is never flat! It is always a section of a very big sphere, roughly the size of earth itself. So when we say a level surface, what we really mean is a spherical surface which is equidistant from the centre of the earth at all surface points. But while doing hydraulics calculations, in our mind, in our illustrations we think of the level surface as being part of a plane, not a sphere. For an overwhelming majority of works we do, our area of works is so small that practically it doesn’t make a difference if our calculations were based on a plane surface or a spherical surface, and it is a lot easier to do calculations with a plane surface. The point to note here is that if there is a way to do calculations which is a lot easier but doesn’t take into account the reality of the physical world, and the difference is negligible if we did the calculations considering all that we know about the physical world, we invariably pick the easier way in engineering to economise on time and efforts.

We can make flat surfaces (sections of a plane) over a reasonably large area using a water level, which we know in reality is a section of a sphere. So can we not make really flat surfaces if we wanted? Perhaps we can, using lasers for example. But over larger distances, even a laser’s path doesn’t follow a true straight line, it gets bent through the atmosphere due to various factors such as differences in air density, moisture content, etc. Let’s assume we are able to make corrections for those factors as well and manage to create a truly flat surface. Apart from being a very difficult and expensive task, do we really want a truly flat surface? Probably not, under normal circumstances. For example, if we wanted to construct a several miles long channel in a way that water will sit in it at exactly 5mm from the bottom, making this channel surface a part of a plane won’t achieve this. If we made it, water will have different levels at different locations. What we actually need in that case is a section of a sphere. We define vertical as a straight line that passes through the centre of the earth. Vertical is also at 90 degrees to horizontal or the surface of water at that point. When we make walls, we make them vertical so that they don’t fall under gravity as a tilted wall would. If the structure was several miles long, and had columns, we would want them truly vertical, i.e. normal to the spherical water level, not parallel to each other (which they would be if they were perpendicular to a plane surface). So even though we call a surface flat as a plane, but in most practical situations, we don’t even want a plane surface on earth, we really want a curved, spherical surface. We can ignore it in calculations, but the methods we use in practice always attempt to follow the curved spherical surface. The point to note here is that our definitions can be imprecise and different from not only what the physical world really is, but also different from what we want. But because they simplify our understanding, our learning, and our calculating ability, we let them be imprecise, and often don’t even talk about it in text books.

Now let’s come back to the statement that water maintains its level. Is that what really happens? Even though it works find for practical purposes, again it’s not what really happens.

However, if you think at a deeper level, that’s not what the molecules of water are trying to do. All the molecules of water, just like all the other molecules and atoms of everything in the world, are trying to get to the centre of the earth due to the gravitation pull. Solids can’t flow, mix, move around easily like fluids, so we don’t see this for most solids… except if they are thrown up they fall (or try to get to the centre of the earth). Since all the water molecules are experiencing the same pull towards the centre of the earth, they all try with the same force to get to the centre depending on their distance from the centre (or level). To achieve a state with least force possible on all the water molecules, they arrange themselves in spherical layers around the centre. Because the earth is too large compared to our size, we don’t see this spherical shape that water takes in our everyday life, and the radius of this sphere at the earth’s surface level is so large that we are unable to see its curvature and it appears flat to us. Where the external gravitational pull is removed from a body of water, it still becomes a sphere due to the gravitation pull among all the water molecules. Examples are water drops in space, or water drops in free fall on earth. For practical purposes, we will assume that water forms a flat surface, and it flows to achieve same level where possible.

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