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Author Topic: hhop  (Read 149337 times)
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hhop gen 2 Hybrid

Uses atmospheric pressure equalisation to bleed the chamber of a less dense gas.

As a result a reservoir sump can be dug into any stream bed, even a shallow slow running stream, and hhop can be placed below the water line requiring no combustion cycle to function.

 8)

Nice idea. Have you tried this to get an idea of what pump rates are possible vs current drawn.

I guess it would follow simple calculations based on gas evolution and liquid displacement. Just a matter of sizing then.


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Dear evolvingape.

That has got to be the most elegantly simple design to date!!

Based on our experiments here......

https://youtu.be/rqBq5aTvCOE

Six watts input would displace the chamber volume to a height of what material the pump could stand without bursting!! Thousands of feet!!

And we have a fuel as a by product to boot. ;)

Very well done.

Cheers Grum.


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Nice idea. Have you tried this to get an idea of what pump rates are possible vs current drawn.

I guess it would follow simple calculations based on gas evolution and liquid displacement. Just a matter of sizing then.

Yes I have and the rates are favourable for the purpose I designed it for, running from a solar panel. Graham was using 6 Watts, I have used as little as 1/2 a Watt with a resultant loss in fluid flow (as less gas is being created at lower input energies)

The hhop gen 2 hybrid will keep people alive and irrigate the desert land with just a little more work from the community.

Dear evolvingape.

That has got to be the most elegantly simple design to date!!

Based on our experiments here......

https://youtu.be/rqBq5aTvCOE

Six watts input would displace the chamber volume to a height of what material the pump could stand without bursting!! Thousands of feet!!

And we have a fuel as a by product to boot. ;)

Very well done.

Cheers Grum.

Thanks! :)

hhop gen 2 hybrid was the link between hhop gen 2 and hhop gen 3. hhop gen 2 is COP<1, hhop gen 3 is COP>1  O0

The fuel as a byproduct is useful in many ways!

Yes the gas pressure is stable at elevated pressures and is the defining factor of the height the pump can achieve. Here is a nice psi to foot head calculator:

http://www.convertunits.com/from/psi/to/foot+of+head

In hhop gen 3 the vertical axis is a variable that can have its Volume increased by 1 meter for a resultant 1.5psi pressure loss at the turbine input nozzle. The horizontal axis has no such pressure loss associated with it..  ;)


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The horizontal axis has no such pressure loss associated with it..  ;)

What variable is the horizontal liquid axis associated with ? If you change this ratio relationship how will it affect the ratios you have determined within the previous processes ?


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Boyle's law

https://en.wikipedia.org/wiki/Boyle's_law

Boyle's law (sometimes referred to as the Boyle–Mariotte law, or Mariotte's law[1]) is an experimental gas law which describes how the pressure of a gas tends to decrease as the volume of a gas increases. A modern statement of Boyle's law is:

    The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.


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Animated Charles and Gay-Lussac's Law

http://www.grc.nasa.gov/WWW/k-12/airplane/aglussac.html

Air is a gas. Gases have various properties that we can observe with our senses, including the gas pressure, temperature (T), mass, and the volume (V) that contains the gas. Careful, scientific observation has determined that these variables are related to one another and that the values of these properties determine the state of the gas.

The relationship between temperature and volume, at a constant number of moles and pressure, is called Charles and Gay-Lussac's Law in honor of the two French scientists who first investigated this relationship. Charles did the original work, which was verified by Gay-Lussac. They observed that if the pressure is held constant, the volume V is equal to a constant times the temperature T

V = constant * T

In a scientific manner, we can fix any two of the four primary properties and study the nature of the relationship between the other two by varying one and observing the variation of the other. This slide shows a schematic "gas lab" in which we can illustrate the variation of the gas properties. In the lab a theoretical gas is confined in a blue container. The volume of the gas is shown in yellow and is determined by the position of a red piston. The volume can be changed by moving the red piston using the red screw at the top of the piston. The number of moles of the gas is indicated by the number of small black "molecules" in the volume. The number of moles can be changed by injecting or withdrawing molecules using the pump at the left. There are two probes inserted into the bottom of the container to measure the pressure and the temperature. The pressure can be changed by adding or removing green weights from the top of the red piston, and the temperature can be changed by heating the container with the "torch" at the bottom.

http://www.grc.nasa.gov/WWW/k-12/airplane/glussac.html


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Fluid Dynamics involves the interactions between an object and a surrounding fluid, a liquid, or a gas. Fluid dynamics play a major role in the development of thrust in a gas turbine engine, and in the generation of aerodynamic drag for flight within the atmosphere. To better understand these interactions, we need to know some things about gases.

http://www.grc.nasa.gov/WWW/K-12/airplane/gasprop.html

Characteristics of Gases

All matter is made from atoms with the configuration of the atom (number of protons, number of neutrons ..) determining the kind of matter present (oxygen, lead, silver, neon ...). Individual atoms can combine with other atoms to form molecules. Oxygen and nitrogen, which are the major components of air on Earth, occur in nature as diatomic (2 atom) molecules. The atmosphere of Mars is mostly composed of carbon dioxide, a molecule with one carbon atom and two oxygen atoms. Under normal conditions, matter exists as either a solid, a liquid, or a gas. Atmospheres are composed of gases. In any gas, we have a very large number of molecules that are only weakly attracted to each other and are free to move about in space. When studying gases, we can investigate the motions and interactions of individual molecules, or we can investigate the large scale action of the gas as a whole. Scientists refer to the large scale motion of the gas as the macro scale and the individual molecular motions as the micro scale. Some phenomenon are easier to understand and explain based on the macro scale, while other phenomenon are more easily explained on the micro scale. Macro scale investigations are based on things that we can easily observe and measure. But micro scale investigations are based on rather simple theories because we cannot actually observe an individual gas molecule in motion. Macro scale and micro scale investigations are just two views of the same thing.
« Last Edit: 2015-09-15, 20:08:15 by evolvingape »


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Hydrostatic equilibrium

https://en.wikipedia.org/wiki/Hydrostatic_equilibrium

In continuum mechanics, a fluid is said to be in hydrostatic equilibrium or hydrostatic balance when it is at rest, or when the flow velocity at each point is constant over time. This occurs when external forces such as gravity are balanced by a pressure gradient force.[1] For instance, the pressure-gradient force prevents gravity from collapsing Earth's atmosphere into a thin, dense shell, whereas gravity prevents the pressure gradient force from diffusing the atmosphere into space.

Hydrostatic equilibrium is the current distinguishing criterion between dwarf planets and small Solar System bodies, and has other roles in astrophysics and planetary geology. This qualification typically means that the object is symmetrically rounded into a spheroid or ellipsoid shape, where any irregular surface features are due to a relatively thin solid crust. There are 31 observationally confirmed such objects (apart from the Sun), sometimes called planemos,[2] in the Solar System, seven more[3] that are virtually certain, and a hundred or so more that are likely.[3]

Pressure-gradient force

https://en.wikipedia.org/wiki/Pressure-gradient_force

The pressure gradient force is the force which results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area, across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law, if there is no additional force to balance it. The resulting force is always directed from the region of higher-pressure to the region of lower-pressure. When a fluid is in an equilibrium state (i.e. there are no net forces, and no acceleration), the system is referred to as being in hydrostatic equilibrium. In the case of atmospheres, the pressure gradient force is balanced by the gravitational force, maintaining hydrostatic equilibrium. In the Earth's atmosphere, for example, air pressure decreases at increasing altitudes above the Earth's surface, thus providing a pressure gradient force which counteracts the force of gravity on the atmosphere.


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Gas laws

https://en.wikipedia.org/wiki/Gas_laws

The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold to a good approximation for all gases. Gases behave in a similar way over a wide variety of conditions because they all have molecules which are widely spaced, and the equation of state for an ideal gas is derived from kinetic theory. The earlier gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables held constant.

Boyle's Law

Boyle's Law, published in 1662, states that, at constant temperature, the product of the pressure and volume of a given mass of an ideal gas in a closed system is always constant. It can be verified experimentally using a pressure gauge and a variable volume container. It can also be derived from the kinetic theory of gases: if a container, with a fixed number of molecules inside, is reduced in volume, more molecules will strike a given area of the sides of the container per unit time, causing a greater pressure.

Charles' Law

Charles' Law, or the law of volumes, was found in 1787 by Jacques Charles. It states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature, assuming a closed system.

Gay-Lussac's Law

Gay-Lussac's Law, or the Pressure Law, was found by Joseph Louis Gay-Lussac in 1809. It states that, for a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.

Avogadro's Law

Avogadro's Law states that the volume occupied by an ideal gas is directly proportional to the number of molecules of the gas present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm3 (or litres).

Combined gas law

https://en.wikipedia.org/wiki/Combined_gas_law

The combined gas law is a gas law that combines Charles's law, Boyle's law, and Gay-Lussac's law. There is no official founder for this law; it is merely an amalgamation of the three previously discovered laws. These laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Charles's law states that volume and temperature are directly proportional to each other as long as pressure is held constant. Boyle's law asserts that pressure and volume are inversely proportional to each other at fixed temperature. Finally, Gay-Lussac's law introduces a direct proportionality between temperature and pressure as long as it is at a constant volume. The inter-dependence of these variables is shown in the combined gas law, which clearly states that:

       "The ratio between the pressure-volume product and the temperature of a system remains constant."


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Audi creates green 'e-diesel fuel of the future' using just carbon dioxide and water

http://www.ibtimes.co.uk/audi-creates-green-e-diesel-fuel-future-using-just-carbon-dioxide-water-1498524

German car manufacturer Audi says it has created the "fuel of the future" made solely from water, carbon dioxide and renewable sources.

The synthetic "e-diesel" was made following a commissioning phase of just four months at a plant in Dresden, Germany.Unlike regular diesel, the clear fuel does not contain any sulphur or fossil oil, while it has an overall energy efficiency of around 70%.

Germany's federal minister of education and research, Dr Johanna Wanka, said she has already used the fuel in her Audi A8, while the company hopes the Dresden factory, operated by clean tech company Sunfire, will produce 160 litres of it every day in the coming months.

"This synthetic diesel, made using CO2, is a huge success for our sustainability research," Wanka said. "If we can make widespread use of CO2 as a raw material, we will make a crucial contribution to climate protection and the efficient use of resources, and put the fundamentals of the 'green economy' in place."

Kolbe electrolysis

https://en.wikipedia.org/wiki/Kolbe_electrolysis

electrolysis of acetic acid yields ethane and carbon dioxide

Alkane

https://en.wikipedia.org/wiki/Alkane

In organic chemistry, an alkane, or paraffin (a historical name that also has other meanings), is a saturated hydrocarbon. Alkanes consist only of hydrogen and carbon atoms and all bonds are single bonds.[1] Alkanes (technically, always acyclic or open-chain compounds) have the general chemical formula CnH2n+2. For example, Methane is CH4, in which n=1 (n being the number of Carbon atoms). Alkanes belong to a homologous series of organic compounds in which the members differ by a molecular mass of 14.03u (mass of a methanediyl group, —CH2—, one carbon atom of mass 12.01u, and two hydrogen atoms of mass ≈1.01u each). There are two main commercial sources: petroleum (crude oil)[2] and natural gas.

Sabatier reaction

https://en.wikipedia.org/wiki/Sabatier_reaction

The Sabatier reaction or Sabatier process was discovered by the French chemist Paul Sabatier in the 1910s. It involves the reaction of hydrogen with carbon dioxide at elevated temperatures (optimally 300–400 °C) and pressures in the presence of a nickel catalyst to produce methane and water. Optionally, ruthenium on alumina (aluminium oxide) makes a more efficient catalyst.

It has been proposed in a renewable-energy-dominated energy system to use the excess electricity generated by wind, solar photovoltaic, hydro, marine current, etc. to make methane (natural gas) via water electrolysis and the subsequent application of the Sabatier reaction.[1][2] In contrast to a direct usage of hydrogen for transport or energy storage applications,[3] the methane can be injected into the existing gas network, which in many countries has one or two years of gas storage capacity. The methane can then be used on demand to generate electricity (and heat—combined heat and power) overcoming low points of renewable energy production. The process is electrolysis of water by electricity to create hydrogen (which can partly be used directly in fuel cells) and the addition of carbon dioxide CO2 (Sabatier process) to create methane. The CO2 can be extracted from the air or fossil fuel waste gases by the amine process, amongst many others. It is a low-CO2 system, and has similar efficiencies of today's energy system. A 250 kW demonstration plant was ready in 2012 in Germany.[4]

hhop gen 3 is designed to plug in as the energy source, providing the electrical energy and electrolysis byproduct fuel, in place of a traditional renewable energy power source.

Now you can start fuel processing and work your way up the Alkane chain.




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Hydrostatics

http://mysite.du.edu/~jcalvert/tech/fluids/hydstat.htm

Hydrostatics is about the pressures exerted by a fluid at rest. Any fluid is meant, not just water. It is usually relegated to an early chapter in Fluid Mechanics texts, since its results are widely used in that study. The study yields many useful results of its own, however, such as forces on dams, buoyancy and hydraulic actuation, and is well worth studying for such practical reasons. It is an excellent example of deductive mathematical physics, one that can be understood easily and completely from a very few fundamentals, and in which the predictions agree closely with experiment. There are few better illustrations of the use of the integral calculus, as well as the principles of ordinary statics, available to the student. A great deal can be done with only elementary mathematics. Properly adapted, the material can be used from the earliest introduction of school science, giving an excellent example of a quantitative science with many possibilities for hands-on experiences.

The definition of a fluid deserves careful consideration. Although time is not a factor in hydrostatics, it enters in the approach to hydrostatic equilibrium. It is usually stated that a fluid is a substance that cannot resist a shearing stress, so that pressures are normal to confining surfaces. Geology has now shown us clearly that there are substances which can resist shearing forces over short time intervals, and appear to be typical solids, but which flow like liquids over long time intervals. Such materials include wax and pitch, ice, and even rock. A ball of pitch, which can be shattered by a hammer, will spread out and flow in months. Ice, a typical solid, will flow in a period of years, as shown in glaciers, and rock will flow over hundreds of years, as in convection in the mantle of the earth. Shear earthquake waves, with periods of seconds, propagate deep in the earth, though the rock there can flow like a liquid when considered over centuries. The rate of shearing may not be strictly proportional to the stress, but exists even with low stress. Viscosity may be the physical property that varies over the largest numerical range, competing with electrical resistivity.

There are several familiar topics in hydrostatics which often appear in expositions of introductory science, and which are also of historical interest that can enliven their presentation. The following will be discussed briefly here:

    Pressure and its measurement
    Atmospheric pressure and its effects
    Maximum height to which water can be raised by a suction pump
    The siphon
    Discovery of atmospheric pressure and invention of the barometer
    Hydraulic equivalent of a lever
    Pumps
    Forces on a submerged surface
    The Hydrostatic Paradox
    Buoyancy (Archimedes' Principle)
    Measurement of Specific Gravity
    References

A study of hydrostatics can also include capillarity, the ideal gas laws, the velocity of sound, and hygrometry. These interesting applications will not be discussed in this article. At a beginning level, it may also be interesting to study the volumes and areas of certain shapes, or at a more advanced level, the forces exerted by heavy liquids on their containers. Hydrostatics is a very concrete science that avoids esoteric concepts and advanced mathematics. It is also much easier to demonstrate than Newtonian mechanics.

Hydrostatic Pressure in a Liquid

http://faculty.wwu.edu/vawter/PhysicsNet/Topics/Pressure/HydroStatic.html

    The pressure at a given depth in a static liquid is a result the weight of the liquid acting on a unit area at that depth plus any pressure acting on the surface of the liquid.

    The pressure due to the liquid alone (i.e. the gauge pressure) at a given depth depends only upon the density of the liquid ρ and the distance below the surface of the liquid h.

    Pressure is not really a vector even though it looks like it in the sketches. The arrows indicate the direction of the force that the pressure would exert on a surface it is contact with.

Liquid can be both a hydrostatic pressure and a weight.. the weight has gravitational potential energy because the scalar hydrostatic fields are seperated by a piston face preventing pressure equalisation.

The hollow core of the piston has its density manipulated within the specific gravity field invoking new forces to the system. The gravitational potential energy input is directly related to the electromagnetic energy output via phase change within the specific gravity field.

A hhop gen 3 COP<1 device will have a density and resultant force within the SGF ratio of less than 1. The opposite is also true, a COP>1 hhop gen 3 will have a larger input potential than output energy required to trigger buoyancy of the piston (via density change because you pumped water out using gas). Taller water reservoir has more potential energy but same amount of force is required to trigger buoyancy force zero point polarity switch as the dimensions (length, width, height) have not changed for_the_ piston.

Communicating vessels

Communicating vessels is a name given to a set of containers containing a homogeneous fluid: when the liquid settles, it balances out to the same level in all of the containers regardless of the shape and volume of the containers. If additional liquid is added to one vessel, the liquid will again find a new equal level in all the connected vessels.This process is part of Stevin's Law[1] and occurs because gravity and pressure are constant in each vessel (hydrostatic pressure).[2]

Blaise Pascal proved in the seventeenth century that the pressure exerted on a molecule of a liquid is transmitted in full and with the same intensity in all directions.

Applications

Since the days of ancient Rome, the concept of communicating vessels has been used for indoor plumbing, via aquifers and lead pipes. Water will reach the same level in all parts of the system, which acts as communicating vessels, regardless of what the lowest point is of the pipes – although in practical terms the lowest point of the system depends on the ability of the plumbing to withstand the pressure of the liquid. In cities, water towers are frequently used so that city plumbing will function as communicating vessels, distributing water to higher floors of buildings with sufficient pressure.

Hydraulic presses, using systems of communicating vessels, are widely used in various applications of industrial processes.

Artesian aquifer

An artesian aquifer is a confined aquifer containing groundwater under positive pressure. This causes the water level in a well to rise to a point where hydrostatic equilibrium has been reached.

A well drilled into such an aquifer is called an artesian well. If water reaches the ground surface under the natural pressure of the aquifer, the well is called a flowing artesian well.[1]

An aquifer is a geologic layer of porous and permeable material such as sand and gravel, limestone, or sandstone, through which water flows and is stored. An artesian aquifer is confined between impermeable rocks or clay which causes this positive pressure. Not all the aquifers are artesian, because the water table must reach the surface (not the case for underground groundwater such as, for example, the Nubian Sandstone Aquifer System). The recharging of aquifers happens when the water table at its recharge zone is at a higher elevation than the head of the well.

Fossil water aquifers can also be artesian if they are under sufficient pressure from the surrounding rocks. This is similar to how many newly tapped oil wells are pressurized.

Artesian wells were named after the former province of Artois in France, where many artesian wells were drilled by Carthusian monks from 1126.


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Speed of sound

https://en.wikipedia.org/wiki/Speed_of_sound

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the metre per second (m/s). In dry air at 20 °C, the speed of sound is 343.2 metres per second (1,126 ft/s). This is 1,236 kilometres per hour (768 mph; 667 kn), or a kilometre in 2.914 s or a mile in 4.689 s.

The speed of sound in an ideal gas is independent of frequency, but does vary slightly with frequency in a real gas. It is proportional to the square root of the absolute temperature, but is independent of pressure or density for a given ideal gas. Sound speed in air varies slightly with pressure only because air is not quite an ideal gas. Although (in the case of gases only) the speed of sound is expressed in terms of a ratio of both density and pressure, these quantities cancel in ideal gases at any given temperature, composition, and heat capacity. This leads to a velocity formula for ideal gases which includes only the latter independent variables.

In common everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance. Sound travels faster in liquids and non-porous solids than it does in air. It travels about 4.3 times as fast in water (1,484 m/s), and nearly 15 times as fast in iron (5,120 m/s), as in air at 20 °C. Sound waves in solids are composed of compression waves (just as in gases and liquids), but there is also a different type of sound wave called a shear wave, which occurs only in solids. These different types of waves in solids usually travel at different speeds, as exhibited in seismology. The speed of a compression sound wave in solids is determined by the medium's compressibility, shear modulus and density. The speed of shear waves is determined only by the solid material's shear modulus and density.

In fluid dynamics, the speed of sound in a fluid medium (gas or liquid) is used as a relative measure for the speed of an object moving through the medium. The speed of an object divided by the speed of sound in the fluid is called the Mach number. Objects moving at speeds greater than Mach1 are travelling at supersonic speeds.


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It's turtles all the way down
Hi Rob and thanks for all the refresher courses, nice to brush up on this stuff.


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Hi Rob and thanks for all the refresher courses, nice to brush up on this stuff.

No worries  O0

what pump rates are possible vs current drawn.
at what pressure, (gravitational resistance, weight) as well as friction resistance and foot head.

I guess it would follow simple calculations based on gas evolution and liquid displacement. Just a matter of sizing then.
Exactly, as you are phase transitioning (changing) a liquid to a gas the gas laws must be included in your analysis. It is a matter of sizing yes, but because you are sending all of system 1 output energy (in the form of electricity) back into system 1, and the gas laws have been invoked (huge volume increase) within an environment itself energised by gravitational potential energy (hydraulic reservoir), an imbalance is created. This brings in Archimedes buoyancy force and in so doing the height axis becomes an independant variable, that is able to increase system 1 input potential energy available. There is a minor constant loss associated with this variable (1.5psi per metre pressure loss, pumping water vertically up) and therefore it is not infinite.

The radius of the piston face is locked in the horizontal axis, as changing it will change your ratio of 1 needed to have a negative buoyancy force on the piston. However once you have established your energy ratio required to produce enough from your upper water reservoir to create the amount of gas you need to change the density of the piston and make it ascend. This buoyancy upthrust force is provided by the gravitational force pulling the more dense liquid water down and displacing the less dense gas upwards (and the hollow piston housing that is containing the gas, hence the pressure equalisation valve sleeved through the piston face walls to remove fluid flow resistance [backpressure] at the seal walls).

An interesting observation is that the alternator output is constant and is powered by the water wheel, therefore zero user energy power in is required. COP infinity (whatever that means). The electrical energy produced (COP<1 around 80%+ efficient standard alternator) is fed directly to the electrolysis cell, a resonant situation from this might develop and could enhance gas production requiring less energy in to achieve a ratio of 1 (smaller system footprint).. however.. the established system relationships (ratios) would remain the same!

 :)


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I put the forces at work in buoyancy picture up a while ago.

http://www.overunityresearch.com/index.php?topic=2288.msg49567#msg49567

Is the diagram incorrect, partially correct or fully correct ? (anyone).  


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Geometry

https://en.wikipedia.org/wiki/Geometry

Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.[1] Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.

The introduction of coordinates by René Descartes and the concurrent developments of algebra marked a new stage for geometry, since geometric figures such as plane curves could now be represented analytically in the form of functions and equations. This played a key role in the emergence of infinitesimal calculus in the 17th century. Furthermore, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of projective geometry. The subject of geometry was further enriched by the study of the intrinsic structure of geometric objects that originated with Euler and Gauss and led to the creation of topology and differential geometry.

In Euclid's time, there was no clear distinction between physical and geometrical space. Since the 19th-century discovery of non-Euclidean geometry, the concept of space has undergone a radical transformation and raised the question of which geometrical space best fits physical space. With the rise of formal mathematics in the 20th century, 'space' (whether 'point', 'line', or 'plane') lost its intuitive contents, so today one has to distinguish between physical space, geometrical spaces (in which 'space', 'point' etc. still have their intuitive meanings) and abstract spaces. Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean space, which they only approximately resemble at small scales. These spaces may be endowed with additional structure which allow one to speak about length. Modern geometry has many ties to physics as is exemplified by the links between pseudo-Riemannian geometry and general relativity. One of the youngest physical theories, string theory, is also very geometric in flavour.

While the visual nature of geometry makes it initially more accessible than other mathematical areas such as algebra or number theory, geometric language is also used in contexts far removed from its traditional, Euclidean provenance (for example, in fractal geometry and algebraic geometry).[2]

Euclidean geometry


https://en.wikipedia.org/wiki/Euclidean_geometry

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians,[1] Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.[2] The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.[3]

For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Albert Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only where the gravitational field is weak.[4]

Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms to propositions without the use of coordinates. This is in contrast to analytic geometry, which uses coordinates.

Integral

https://en.wikipedia.org/wiki/Integral

The integral is an important concept in mathematics. Integration is one of the two main operations in calculus, with its inverse, differentiation, being the other.

Derivative

https://en.wikipedia.org/wiki/Derivative

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time is advanced.

The derivative of a function of a single variable at a chosen input value is the slope of the tangent line to the graph of the function at that point. This means that it describes the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable.

Derivatives may be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector.

The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.[1]


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I have put one water tower 'b' on top of another water tower 'a'.. I have isolated the hydrostatic pressure equalisation potential for both chambers, from each other via the piston. System open to atmospheric pressure on both columns. Chamber b acts as a Mass only, gravity filled. Chamber a always has hydrostatic pressure, with bias set by NRV resistance (psi cracking pressure). 1.5 psi loss for every 1 meter of output column elevation, therefore pressure loss through elevation (pumping vertically) considered negligible in a 1 meter high system. Leverage Pascal's principle to extend run time and increase pressure at the expense of flow rate. The electrical energy required to complete the electrolytic reset of the hollow piston will become a constant, and the run time on the turbine at a given RPM will also, so when they match you have COP=1. Increase the sizes of reservoirs a and b and extend the run time of the the water wheel alternator therefore COP>1 becomes a variable.

If you just keep adding chamber b's you will increase the pressure proportionally for each Mass unit added to the system, as long as hydrostatic separation is maintained chamber b will be a weight vector only as seen by the system.

You will not have to adjust the chamber a size as you have already sized it to system closed loop COP=1.

High pressure is usually more efficient  O0


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Weight

https://en.wikipedia.org/wiki/Weight

In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity.[1][2] Weight is a vector whose magnitude (a scalar quantity), often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g;[3] thus: W = mg. The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton. For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, and about one-sixth as much on the Moon. In this sense of weight, a body can be weightless only if it is far away (in principle infinitely far away) from any other mass. Although weight and mass are scientifically distinct quantities, the terms are often confused with each other in everyday use.[4]

There is also a rival tradition within Newtonian physics and engineering which sees weight as that which is measured when one uses scales. There the weight is a measure of the magnitude of the reaction force exerted on a body. Typically, in measuring an object's weight, the object is placed on scales at rest with respect to the earth, but the definition can be extended to other states of motion. Thus, in a state of free fall, the weight would be zero. In this second sense of weight, terrestrial objects can be weightless. Ignoring air resistance, the famous apple falling from the tree, on its way to meet the ground near Isaac Newton, is weightless.

Further complications in elucidating the various concepts of weight have to do with the theory of relativity according to which gravity is modelled as a consequence of the curvature of spacetime. In the teaching community, a considerable debate has existed for over half a century on how to define weight for their students. The current situation is that a multiple set of concepts co-exist and find use in their various contexts.[2]

I created the specific gravity field model to unify the concepts and provide operational capability for the extraction of electrical energy function COP>1.


Vertical pressure variation

https://en.wikipedia.org/wiki/Vertical_pressure_variation

Vertical pressure variation is the variation in pressure as a function of elevation. Depending on the fluid in question and the context being referred to, it may also vary significantly in dimensions perpendicular to elevation as well, and these variations have relevance in the context of pressure gradient force and its effects. However, the vertical variation is especially significant, as it results from the pull of gravity on the fluid; namely, for the same given fluid, a decrease in elevation within it corresponds to a taller column of fluid weighing down on that point.

A relatively simple version [1] of the vertical fluid pressure variation is simply that the pressure difference between two elevations is the product of elevation change, gravity, and density. The equation is as follows: (see link)

    P is pressure,
    ρ is density,
    g is acceleration of gravity, and
    h is height.

The delta symbol indicates a change in a given variable. Since g is negative, an increase in height will correspond to a decrease in pressure, which fits with the previously mentioned reasoning about the weight of a column of fluid.

When density and gravity are approximately constant, simply multiplying height difference, gravity, and density will yield a good approximation of pressure difference. Where different fluids are layered on top of one another, the total pressure difference would be obtained by adding the two pressure differences; the first being from point 1 to the boundary, the second being from the boundary to point 2; which would just involve substituting the ρ and (Δh) values for each fluid and taking the sum of the results. If the density of the fluid varies with height, mathematical integration would be required.

Whether or not density and gravity can be reasonably approximated as constant depends on the level of accuracy needed, but also on the length scale of height difference, as gravity and density also decrease with higher elevation. For density in particular, the fluid in question is also relevant; seawater, for example, is considered an incompressible fluid; its density can vary with height, but much less significantly than that of air, so given the same height difference, water's density can be more reasonably approximated as constant than that of air.


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System

A system is a set of interacting or interdependent component parts forming a complex/intricate whole.[1]

Every system is delineated by its spatial and temporal boundaries, surrounded and influenced by its environment, described by its structure and purpose and expressed in its functioning.

Fields that study the general properties of systems include systems science, systems theory, systems modeling, systems engineering, cybernetics, dynamical systems, thermodynamics, complex systems, system analysis and design and systems architecture. They investigate the abstract properties of systems' matter and organization, looking for concepts and principles that are independent of domain, substance, type, or temporal scale.[citation needed]

Some systems share common characteristics, including:[citation needed]

    A system has structure, it contains parts (or components) that are directly or indirectly related to each other;
    A system has behavior, it exhibits processes that fulfill its function or purpose;
    A system has interconnectivity: the parts and processes are connected by structural and/or behavioral relationships;
    A system's structure and behavior may be decomposed via subsystems and sub-processes to elementary parts and process steps;
    A system has behavior that, in relativity to its surroundings, may be categorized as both fast and strong.

The term system may also refer to a set of rules that governs structure and/or behavior. Alternatively, and usually in the context of complex social systems, the term institution is used to describe the set of rules that govern structure and/or behavior.


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Cylinder (geometry)

https://en.wikipedia.org/wiki/Cylinder_%28geometry%29

A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"[1]) is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity.

Cone

https://en.wikipedia.org/wiki/Cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

More precisely, it is the solid figure bounded by a base in a plane and by a surface (called the lateral surface) formed by the locus of all straight line segments joining the apex to the perimeter of the base. The term "cone" sometimes refers just to the surface of this solid figure, or just to the lateral surface.

The axis of a cone is the straight line (if any), passing through the apex, about which the base (and the whole cone) has a rotational symmetry.

In common usage in elementary geometry, cones are assumed to be right circular, where circular means that the base is a circle and right means that the axis passes through the centre of the base at right angles to its plane. Contrasted with right cones are oblique cones, in which the axis does not pass perpendicularly through the centre of the base.[1] In general, however, the base may be any shape and the apex may lie anywhere (though it is usually assumed that the base is bounded and therefore has finite area, and that the apex lies outside the plane of the base).

A cone with a polygonal base is called a pyramid.

Frustum

https://en.wikipedia.org/wiki/Frustum

In geometry, a frustum[1] (plural: frusta or frustums) is the portion of a solid (normally a cone or pyramid) that lies between two parallel planes cutting it. A right frustum is a parallel truncation of a right pyramid.[1]

The term is commonly used in computer graphics to describe the three-dimensional region which is visible on the screen, the "viewing frustum", which is formed by a clipped pyramid; in particular, frustum culling is a method of hidden surface determination.

In the aerospace industry, frustum is the common term for the fairing between two stages of a multistage rocket (such as the Saturn V), which is shaped like a truncated cone. It also applies to the essential drive element of the so-far unproven Emdrive.


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hhop gen 3 inverted frustum cone reservoir.

This model keeps the working piston diameter constant, which is a critical COP ratio variable, while leveraging the reservoir weight for increased pressure on the working fluid.


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hhop gen 3

The drawing shows the importance of the hydrostatic isolation valve, creating two bodies from one along the boundary plane (piston) when the valve is closed.

This design does not need magnets or NRV's and is hydrostatically in balance with the atmosphere (air).

The working fluid ejected from the turbine exhaust is pumped directly into the upper reservoir therefore adding mass and increasing weight during the working cycle.

The resultant increase of liquid pressure in the lower chamber increases efficiency at the turbine PMA.

Wireless solenoid actuated valves are employed within the hollow piston to control cycle timing and flip between hydrostatic pressure equalisation and isolation.

An additional valve could be added to the hho cell (not shown on drawing) to isolate it once the piston begins to ascend, building gas pressure for injection on next cycle.

« Last Edit: 2016-01-24, 20:51:04 by evolvingape »


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hhop gen 2 Hybrid

A spring loaded valve set normally closed, is opened when the liquid is pumped out and replaced by the gas, by the increase of weight of the piston minus it's buoyancy force contribution.

When the gas is purged water is pumped in by atmospheric pressure and the buoyancy force returns, closing the valve, and allowing spring pressure and gas pressure to assert themselves.

« Last Edit: 2016-01-24, 20:51:57 by evolvingape »


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A simple home experiment you can have fun with! :)

Add a hho cell as the prime mover, submerge the assembly below the liquid / gas boundary plane, and incorporate a governed valve.. you have a hhop gen 2 Hybrid.

O0

https://www.youtube.com/watch?v=PXTdFvPm8Xk&feature=youtu.be


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Everyman Standing Order 01: In the Face of Tyranny; Everybody Stands, Nobody Runs.
Everyman Standing Order 02: Everyman is Responsible for Energy and Security.
Everyman Standing Order 03: Everyman knows Timing is Critical in any Movement.
   
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