Three Ways to Generate Energy Using the Subtle Properties of Water and Three Models of Energy Generator
This part is made in the form of presenting the results of the design of three models of devices (hereinafter, as before, simply devices) capable of implementing the three selected ways of energy generation. Schematically, these devices are presented in
Figure 4,
Figure 5 and
Figure 6 using a familiar set of basic elements: evaporator E, cells C1 and C2, source S, trough T and switching locks, to which is added a water wheel WW - with its help is realized the selection of the won energy.
Figure 4 shows a device that uses the gravitational property of water and the property to evaporate;
Figure 5 shows a device that uses two subtle properties of water;
Figure 6 shows a device that uses all three properties of water. The drawings are performed in a style that emphasizes the following attractive fact: the devices depicted in
Figure 4 and
Figure 5 appear to be special cases of the device depicted in
Figure 6. (It is easy to make sure of it: it is enough to mentally transform
Figure 6 by alternately zeroing first h and then h
h, and we will get first the analog of
Figure 4 and then the analog of
Figure 5). This fact allows us to limit ourselves to analyzing the operation of only the device in
Figure 6 as a general case.
The operation of the device in
Figure 6 is described in the following terms. It is assumed that at the initial moment all locks are closed and all vessels (cells C1 and C2, source S and trough T) are filled, as shown in the
Figure 6, and evaporator E is free of water. Also, to simplify the reasoning, it is assumed that all actions to monitor changes in the water level in the vessels and to control the locks in a correct way are performed by the operator. The operation of the device is carried out in two stages.
The first stage begins after opening the locks L1 and L5 (the rest remain closed). Then begins a relatively rapid process of sucking water into the evaporator E, generating rarefaction in cells C1 and C2 and raising water from the source S to the cell C2, as described in the case of the devices in
Figure 1 and
Figure 2. When the water level in cells C1 and C2 reaches the dotted lines, the first stage ends and the second stage begins. Locks L1 and L5 are closed and locks L2, L3, L4 are opened, thus restoring the previous water level in both cells C1 and C2 and supplying a portion of water from cell C2 to the blades of the water wheel WW. (The source S is assumed to be inexhaustible, and the capacity of the trough T is assumed to be much larger than the capacity of cell C1, so that the outflow of a portion of water from the trough into cell C1 does not lead to a noticeable change in the water level in the trough). After water level is restored, all locks are closed, but the second stage does not end: the slow process of evaporation of water available in evaporator E continues. How short is the process of water level restoration in the vessels and how long is the process of water evaporation in the second stage is determined by the operator; the duration of both processes depends on the general characteristics of the device. Replacing each other, both stages can be repeated indefinitely.
The subject of main interest in the analysis is the performance of the device in
Figure 6, i.e. its power as an energy generator. Let us perform the power calculation.
The power of the device in
Figure 6 is most correctly calculated using the formula (1) obtained in the first part. In this case, the power is completely determined by the characteristics of the evaporator E: it is only necessary to calculate the total internal surface area of the capillaries or pores forming the evaporator and subject to regular wetting, and multiply it by the surface tension force (σcosΘ), and then divide by the time spent on wetting. However, this way turns out to be complicated (calculating the total area of capillaries is too difficult, especially in the case of porous evaporator material) and not transparent. The way of taking into account the secondary parameters characterizing the device operation is much simpler. These parameters are: the volume of water evaporating from the evaporator surface per unit time and the height of rise of exactly the same volume of water from the source S to the cell C2. Simple multiplication of the two parameters gives the power of the device. The volume of evaporating water in our case is determined by multiplying the value of the evaporator surface area by the evaporation rate from open surfaces, determined by generally recognized tables depending on the ambient conditions [
4]. Taking this path, let us determine in what range the capacity of the device in
Figure 6 can be.
We take into account the following circumstances. First, the larger the open area of the evaporator E available for water evaporation, the larger the volume of evaporated water. Second, the smaller the internal diameter of capillaries (pores) forming the evaporator, the greater the sucking force of the evaporator, i.e., the greater the height of water rise h from the source S to the cell C2. Third, the amount of energy obtained also depends on the height hh to which the trough T and the evaporator E are lowered. In pursuit of maximum device performance, we should use evaporators with maximum (within reasonable limits) open surface area and with maximum sucking power, and aim to use as large a hh as possible. With respect to the choice of the evaporator with maximum sucking power, there is a natural limitation: the rarefaction in cells C1 and C2 cannot be greater than pure vacuum and, accordingly, the height of water rise h from source S to cell C2 cannot exceed 10 meters. As a result, the pursuit of the maximum sucking force of the evaporator becomes meaningless: when building an evaporator, it is reasonable to choose available materials that provide it with a moderate sucking force of no more than 10 meters of water column in absolute measurement. As a result, the range of our choice of parameters is narrowed: we must choose a height h not exceeding 10 meters, but we are still free to choose the height hh and the size of the evaporator.
For simplicity, let us choose a device with heights h and hh both equal to 10 meters, and determine the range of available power in this case, changing only the parameters of the evaporator E. (Further within this part the height hh is assumed to be always equal to 10 meters. Moreover, it should be recognized that the value of hh can be significantly higher than 10 meters only in exceptional cases, for example, when the device is used in mountainous terrain; the option of increasing the height of hh by digging extensive pits is not attractive). Here are two examples of power calculations: for a low-power device and for a high-power device.
A suitable analog of a low-power device can be an average tree on the planet, which, according to [
5], is capable of raising 200 kilograms of soil water to a height of 20 meters during 15 hours of daylight (or about 13 kilograms of water per hour to a height of 20 meters), i.e., to develop a power of about 0.7 watts. It is not difficult to calculate that our device will exhibit the same power of 0.7 watts in the case when evaporator E can evaporate the same 13 kilograms of water per hour into the atmosphere, causing the same amount of water to rise into cell C2 at a height of 20 meters (the sum of h and h
h), to be fed to the blades of water wheel WW. To evaporate 13 kilograms of water per hour, evaporator E must have an area equal to at least 13/0.3 = 43 square meters (a moderate tabulated evaporation rate of 0.3 kilograms of water per hour per square meter of surface area is chosen for this calculation). In this calculation, it is assumed that the entire area of the evaporator is suitable for evaporation; this assumption does not, in our case, lead to gross errors. In general, the evaporator turns out to be a flat structure of small thickness, measured in millimeters, having a relatively large area, measured in 43 square meters. For example, it could be a thin panel a few millimeters thick and measuring about 6 x 7 meters.
To perform the second calculation of the high-power device (the calculation will be refined at the end of this part), we will be guided by the following volume of water consumption (for evaporation) not exceeding the limits of the phenomena observed in nature. As a reference we will take a natural lake of medium size with a surface area of ten square kilometers (ten million square meters), capable of acting as an inexhaustible source of water for our device and located in a terrain, the relief of which allows us to lower the evaporator E to 10 meters below the lake level. Under natural conditions, according to the tables proposed in [
4], such a lake evaporates in summer, on average, at least 3000 tons of water per hour around the clock (the same moderate table evaporation rate equal to 0.3 kilograms of water per hour from one square meter of surface is used in the calculation). We will assume that consumption of additional 300 tons of water per hour from the lake for operation of our device (eventually, for evaporation into the atmosphere) will not lead to violation of the natural water balance. This assumption allows us to determine the power that our device can develop. The power is calculated using a simple formula:
where g is the acceleration due to gravity, ρV is the mass of evaporated water, h + h
h is the height from which water is supplied to the water wheel WW, t is the time during which this process is performed. In our case, g = 9.8 m/s
2, ρV = 300,000 kilograms, h + h
h = 20 meters, t = 3600 seconds. Substituting these values into (3), we obtain that in the described case the device is capable of developing a power W of at least 16 kilowatts (round the clock). In this case, it is easy to determine that the evaporator area E must be equal to one square kilometer (one million square meters). The evaporator E, in the simplest variant, can be made in the form of a flat plate a few millimeters thick and a kilometer by kilometer in size.
This gives a first rough estimate of the range of power that the new type of generator is most likely to have: from a fraction of a watt to about 16 kilowatts. If in the minimum case our generator is equivalent to one average tree, then in the case of 16 kilowatts it becomes equivalent to an average-sized forest of more than 20,000 mature trees in an area of, for example, 100 hectares.
The above two power calculations are easily transferred to the case of the devices in
Figure 4 and
Figure 5 as special cases of the device in
Figure 6. The capacity of the devices in each of these two cases is smaller: at the same evaporator performance, the height h + h
h from which water is supplied to the water wheel WW blades is reduced (one of h and h
h is zero).
The final estimation of the upper power limit of the proposed devices can be done only in conditional sentences. The reason is that in particular cases of mountainous terrain, allowing to lower the evaporator to the height measured in hundreds of meters, and existence of inexhaustible sources of fresh water, allowing evaporation of unlimited volumes of water, the power of hydro stations can reach indefinitely large values; however, these cases cannot be a reference point for a sober assessment. It is most logical to be guided by an estimate of a few tens of kilowatts - such a figure both reflects the modest estimate of 16 kilowatts obtained for the general case of relatively affordable hydro station and, at the same time, takes into account the possibility of the presence, in each individual case, of particularly favorable external conditions.
It is important to note that, in the case of these three devices (
Figure 4,
Figure 5 and
Figure 6), it is not necessary to build and test physical models: the performance of these two-stream devices is confirmed by the performance of the waterwheel WWTD underlying them. The report on testing of the physical model of WWTD is given in [
2].