Keywords

1 Introduction

Heron’s Fountain is nothing but the perpetual type motion machine or it is also a hydraulic machine. Normally hydropower generation plant is constructed in the region of dam, river, streams which stores the bulk amount of water. But this leads to some disadvantages as the water once is used for the generation of electrical energy cannot be used again or recycled. This makes the hydropower generation is dependent on the season (rain & monsoon). The hydroelectric power plant is also affected by draughts, i.e., when water is not available in the reservoir then the plant cannot produce electricity. For water reservoir, land acquisition is the key that sweeps the agricultural land. Because of the hydropower plant more land goes under the water so the community reestablishment problem arises. Due to the insufficient water supply in the summer season, the hydropower plant is unable to produce electricity. To get rid of these drawbacks a Heron’s Fountain is proposed to ensure continuous water flow. Some modifications are proposed to make this Heron Fountain a near-perpetual motion machine. Flow rate, water head, water pressure, kinetic energy of water are some of the parameters which play an important role in hydropower generation are modeled with MATLAB, and simulation results are discussed [1].

1.1 Hydropower Generation System

This is a renewable energy source that depending on the water flow cycle. Hydropower generation is cost-effective more reliable and mature energy generation system. Hydropower is been so largest generation system which contributes total of 16% of electrical energy in the world. More than 25 countries are 90% of demand fulfills by this hydropower generation. The hydropower plant is a more flexible source of generation it will fast responding to the fluctuations in load demand within a minute when the reservoir is available then the generated power electricity can be stored for the week, month and year also. In the conventional mainly the thermal power plant is not as much as flexible of hydropower generation plant. In the thermal power generation, more amount of coal is been used due to this the more carbon is been released in the environment in more amount so the thermal power generation is not eco-friendly or it cannot be constructed in the rural area on the other side in hydropower generation power plant the power is been generated by using the kinetic energy presented in the flow of water. Due to this kinetic energy the turbine blade shafts are started to rotate means there is been kinetic energy is converted into mechanical energy. This shaft is directly connected to the generator so there is been the conversion of mechanical energy into the electrical energy takes place. In this way, there is been a generation of clean energy so this generation plant can be constructed in the rural areas also because of its simple and harmless operation [2].

Figure 1 shows the layout of a conventional hydroelectric power plant. Following are the different types of hydropower generation based on various components:

Fig. 1
figure 1

Layout of hydroelectric power plant

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  • Based on Generation Capacity:

    1. (1)

      Large hydropower plant- more than 100 MW

    2. (2)

      Medium Hydropower plant—15–100 MW

    3. (3)

      Small Hydropower plant—1–15 MW

    4. (4)

      Mini Hydropower plant—100 KW to 1 MW

    5. (5)

      Micro Hydropower plant—up to 100 KW

    6. (6)

      Pico Hydropower plant—up to 5 KW

  • Based on Water Head:

    1. (1)

      High Head—100 m & above

    2. (2)

      Medium Head—30–100 m

    3. (3)

      Low Head—2–30 m

  • Based on Water Supply:

    1. (1)

      Runoff river without poundage

    2. (2)

      Runoff river with poundage

    3. (3)

      Storage type plant

    4. (4)

      Pumped storage plant

  • Based on load nature:

    1. (1)

      Base load power plant

    2. (2)

      Peak load power plant

1.2 Heron’s Fountain

The physicist, mathematician and inventor named Heron of Alexandria invents the Heron’s Fountain which worked as the hydraulic machine that works without any kind of external force or any supply of energy. Firstly the Heron’s Fountain has been constructed using hills to ensure the pressure but heron used vertical shaped table pot. It contains a tube and the airtight chambers to construct Heron’s Fountain. It contains three chambers each contains equally air and the water at the same level. As the water pores in the first upper chamber or container, it will come in the next second chamber from the pipe using the gravitational force. As the water level is been changed from certain level the air pressure also increased from the chamber with the using of this unequal air pressure the water will flow from the tube to another chamber and so on the fountain is been worked with the help of using only air pressure and the earth’s gravitational force. So this fountain is called as first perpetual motion machine [3]. Figure 2 has shown below displays conventional Heron’s Fountain.

Fig. 2
figure 2

Heron’s fountain

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As we discussed in the above point hydropower generation plant requires the continuous supply of water flow with the pressure so we can use this modified heron’s fountain to ensure the water supply to the turbine and the shaft blade to generate the electricity.

2 System Development

In conventional hydropower plant, all require continuous water supply, i.e., water dams, river, stream, large water reservoir to operate turbine to power production. In this, re-designed closed process of water supply to hydraulic turbines for energy power production. The main components selections will depend on or based on the capacity of the turbine it will be verified on the basis of the analysis of variance There are three main components of the design.

2.1 Hydraulic Ram Pump

This is the main component used to initiating re-circulation process of water in the system which will drive the hydraulic turbine to produce mechanical force. The component of hydraulic ram pump are waste valve and other moving parts is delivery check valve and the stationary parts are drive, delivery pipe, which will supply water from the source and deliver water in more height, respectively.

First delivery valve is been closed and waste valve is opened the water supply is supplied from an elevated source the water came from drive pipe make kinetic energy when waste valve closed the water open delivery check valve due to compressed air the water gets high elevation after this the water flow slows down because of the lower air pressure so water gets reversed in this manner this ram pump is worked.

$$qh = QH$$
(1)

where

Q—Output flow of system (gpm)

h—Output height (feet)

Q—Drive flow (gpm)

H—Drive head (feet)

After considering efficiency then the Eq. 1 becomes,

$${\acute{\eta}} = {qh}/{QH}$$

Therefore,

$$q = {QH} {\acute{\eta }} /{h}$$
(2)

To calculate hydraulic ram pump power,

$$P = 9.81(q/60) \, h$$

where,

P—Power (watt)

q—Water flow (lt/min)

h—Head delivery (m)

9.81—coefficient of gravity.

2.2 Hydraulic Turbine

The water flow towards the blades by using these force blades spins the turbine shaft due to this water floating power transferred in the mechanical power and the turbine shaft connected directly to the generator. Mechanical energy is transferred in the electrical energy in this manner.

2.3 Modified Heron’s Fountain

The original Heron’s Fountain invented in the first century by AD inventor, physicist and Mathematician Heron of Alexandria. But it doesn’t have a perpetual capability for circulating the water so modify the design of fountain to make more efficient perpetual water flow motion [3].

Now container A contains the head of water which will come into container B by making the use of the earth’s force of gravity. Container B and container C both are having the same air pressure and the same level of the water which are connected to each other in an air compact format. In starting container B and container C are fixed with the same level but the water came from container A to the container B the water level in the container B increased so the air pressure and the water pressure in container B and C separated due to this the water will flow from pipe to the container C and due to surface tension of water and the increased air pressure the water started to flow from the pipe to the container A with high pressure and this cycle continuously works. Figure 3 shows the Modified Heron’s Fountain below.

Fig. 3
figure 3

Modified Heron’s fountain

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To find the pressure in the water we use Bernoulli’s principle which states that in the liquid dynamics as the pressure decreases then the speed of water is been increased, which means the speed of water is inversely proportional to the pressure of air presented in the container. The equations are as given below [4].

$$P_{1} + \frac{{\rho V_{1}^{2} }}{2} + Pgh_{1} = P_{2} + \frac{{\rho V_{2}^{2} }}{2} + Pgh_{2}$$

To find the pressure difference in two finds use the Pascal’s law

$$\Delta P = P_{2} \cdot P_{1} = \rho gh_{2} \cdot \rho gh_{1} = \rho g\left( {h_{2} - h_{1} } \right)$$

Pressure of the water and air while water came downward from container A to container C at point Q in the above-given figure is

$$P_{\text{air}} = P_{0} + \rho gh_{1}$$

The pressure of water at point Q2 is,

$$P_{\text{water}} = P_{0} + \rho gh_{2}$$

The pressure of water at the jets out or at the tip of the fountain pipe is,

$$\Delta P = P_{\text{air}} - P_{\text{water}} = \rho g\left( {h_{1} - h_{2} } \right)$$

This way found the pressure and the flow rate of water at the tip of fountain theoretically [5].

3 Matlab Modeling

So the principle of Heron’s Fountain worked or simulated in the MATLAB software so that purpose proper blocks are selected from the directory of the MATLAB and the block diagram is as shown in Fig. 4.

Fig. 4
figure 4

Block diagram of program in MATLAB

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The selected blocks are from the Simscape library discussed deeply below,

3.1 Variable Head Two Arm Tank 1

There are three tanks used and all connected in the manner of the Heron’s Fountain design. The parameter of tank 2 and tank 3 are the same and the parameter of tank 1 is different and they are as shown in Figs. 5 and  6.

Fig. 5
figure 5

Parameters of reservoir tank

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Fig. 6
figure 6

Parameters of other two tank

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3.2 Hydraulic Fluid

The hydraulic fluid tank is used to choose the type of fluid which will flow from the pipe and we choose the water as a flowing fluid an all parameters are inbuilt for the water as shown in Fig. 7.

Fig. 7
figure 7

Parameters of the hydraulic fluid

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3.3 Segmented Pipes

This pipe is connected for the way to flow of the water and the characteristics of the pipes the roughness of the pipe inner surface, internal diameter, pipe length, shape, dimensions of pipes, etc. Figure 8 shows the parameters of the segmented pipe.

Fig. 8
figure 8

Parameters of the segmented pipe

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3.4 Gages

These blocks are used to measure the pressure and the flow of water in the pipes for this the subsystems are created in that the flow rate measurement meter and the pressure meter is connected and it is as shown in Fig. 9.

Fig. 9
figure 9

Subsystem in the gages

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3.5 PS Simulink Converter

Using this block the converter converts all readings or outputs to unit less only the magnitude value is been displayed.

3.6 Go to and from Block

The go to blocks are connected in the subsystem to give the call to from bus to display the values in the display.

3.7 Displays

These blocks are been displayed in used to display the output the flow rate and the pressure value is this blocks in the form of numerical value

3.8 Scopes

These blocks are used to display the results and the graphical representation to display the results

4 Results and Discussion

The values of flow rate and the pressure of water are displayed in the blocks of display and they are as given Fig. 10.

Fig. 10
figure 10

Output of the MATLAB simulation

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After running successfully MATLAB program got the pressure of water and the flow rate of water at the end of every tank and display it separately. The blocks Q4, Q5 and Q6 have displayed the flow rate of water presented at the end of tank 1, tank 3 and tank 2, respectively and the blocks P4, P5, and P6 displays the pressure of water presented at the end of tank 1, tank 3, and tank 2, respectively. Flow rate and the pressure of water presented at the end of tank 3 are the same as the flow rate and pressure of water which is emerging from the tip of fountain and used to power generation.

5 Conclusion

The flow rate of the water and the pressure of the water presented in pipe at the tip of the fountain is more efficient for generating the power with the proper selection of turbines we can generate the efficient power with compact design and the water is also reused in this way we can design the hydropower plant in the region where the dam, river, and stream are absent and also called as a renewable power source as the water is reused to generate power and it is eco-friendly and generates clean energy and also it is very economical in cost. So this is totally compacted construction so it does not affect nature and also the required reservoir is also fitted in the small region so there is no wastage of agricultural lands for the water reservoir and this model can be constructed in rural areas also.