Unified Potential Theory & dynamic velocity

The invention “(WO/2009/074834) ring wing type & actinic fluid drive” can not be explained by current aerodynamics.

I believe that every application of electromagnetism may have its counterpart application in fluid mechanics which can be calculated using common equations. Thus the inductive magnetic field due to electrical flow conductor (inductor) is no different from the jet pump phenomenon, where a main flow accelerates a second phase.

After many years of personal research and relevant inventions, I arrived at the unified potential theory, which redefines fundamental parameters of physics and introduces the definition of dynamic velocity of fluids, by virtue of which I propose the integrated equations for electromagnetism and gravity.

To prove my propostion, I solve known exercises using the new equations, whereby a given amount of data allows for the calculation of additional physical quantities, such as determining the surface of pipeline flow without using empirical tables.

Introduction

Physics is the system we employ to study natural phenomena. Therefore, the introduction to physics requires the definition of the system, in such a way that it then becomes possible to define its parameters.

Proposed Definitions:

·         System is an agreement based on certain limits, where (field) defined physical quantities interact, serving at least one purpose or goal.

·         Potential field is the mathematical area or volume V of a system, any point of which can be matched with measurable physical quantities (system parameters). Its main physical quantity is the field intensity g, while acceleration is the algebraic sum of the fields’ intensities, which interact.

     The potential field can occur with induction of a main flow, such as the inductive magnetic field in electromagnetism, or the inductive flow (multiple phase flow) in fluids (e.g. jet pump effect).

·         Charge Q is a source of potential field. The most common charges are mass (m) and electric. Related charges interact. In a closed system the total charge is maintained.

·         Potential U is the product of the dynamic field intensity g and the distance r from the centre of its source. Potential is a vector.

U = g r     (1)

For example the potential U of a spherical mass m (G the gravitational field constant) equals:

U = gr = Gmr / r ² = Gm / r

whereas the potential of an electric charge Q in a radial dynamic field of a point charge is given by:

U_el = g r = Q r/ 4πεr² = Q / 4π ε r

In a closed system the total potential is maintained.

·         Voltage is the potential difference either of two points with different distance from the centre of a dynamic field, such as elevation near the surface of the Earth:

ΔU = (Δg) r + (Δr) g = (g₁ - g₂₎ r + g (r₁ - r₂₎ ≈ g (r₁ - r₂)

or the algebraic sum of potentials of two or more dynamic fields (e.g. Lagrange points between Sun and Earth).

·         Pressure P is the product of the charge density ρ (ρ = Q / V, charge by volume) and the potential U of a dynamic field. Pressure is vector (stress is Tensor)

P =  ρ U = ρ g r     (2)

If we first define energy, then pressure is the volumetric energy density

·         Potential energy E is the product of pressure P and volume V, i.e. the product charge Q and the potential U, or the ability of a dynamic system to produce work (the product of charge and potential difference).

E = PV = QU = m g r (for Q = m)     (3)

·         Force F is the ratio of Work ΔW to the distance r, i.e. charge Q multiplied by the intensity of potential field g.

F = QU / r = Q g (4)

·         Dynamic (potential) Velocity u

Since the potential field intensity g (g = u / t) is equal to the ratio of velocity to time and the distance r (r = u t) equals velocity multiplied  by time, the Potential provides a dynamic velocity u, where:

U = g r = u ² 

u = (P / ρ) ^{1 / 2}   (5)

Dynamic velocity u of a monopole potential field is the product of the field intensity g multiplied by its period T e.g.

u = g T/2π  = g / ω= ωr

Sympols

g	field intensity	r	distance	U	potential
Q	charge	ρ	charge density	P	pressure
V	volume	A	surface	E	energy
T	period	t	time	F	force
ω	angular velocity	uk	transition velocity	u	dynamic velocity

Equation of state

• The principle of energy conservation, 
• the proposal that energy can not be combined in a single form 
• positive or negative sign as a statement of the direction and 
• the total energy is zero, 

are expressed by the equation of state:   PV = QU

Both expressions of equality state energy E, while their change states work.

The charge density ρ (charge to volume, or pressure to potential) has upper and lower limits, i.e. it can’t be zeroed nor increased infinitely, because energy can not be combined in a single form.

The limits of the charge density are determined by the potential and that by at least a constant specific to each type of charge (gravitational constant G, electric constant, wing roughness, viscosity etc.).

The relationship between dynamic u and transition velocity u_k (time dependent) is calculated by converting potential energy into kinetic energy,

E = m g r = mu² = ½ m u_k² (for Q = m)         (6)

which shows that the potential can not exceed the half square of the light transition velocity c (in vacuum),

U = u² = u_k²/2 →. U_max ≤ c² / 2,           (7)

which is limiting for maximum density charge (e.g. mass of stars) and an absolute relationship between charge density - radius of a sphere (the Planck voltage: 10²⁷ V can not exist).

For maximum potential of a spherical mass

U_max = c² /2 = Gm/r = GρV/r = 4Gρ π r² / 3

the relationship: ρr² = 3c² / 8πG = constant   (8)

Obviously both the gravitational constant G, and the electric field constant (ε) are inversely proportional to maximum charge density (limited possible compression) and proportional to minimum pressure (limited possible relief).

The dependence of the source centre of the field makes Potential a vector and therefore the potential difference (voltage) of two or more dynamic fields’ dependent of the vector angle.

The angular change of potential due to an airfoil (form Resistance because of airfoil thickness distribution) generates the lift in an airplane wing or propeller turbine torque, which usually creates two (open on one side) nozzles and a Diffuser, calculated on the triangle between chord leading edge, maximum thickness deviation (depending on the angle of attack) trailing edge, chord airfoil.

Potential corresponds to a rotation velocity (U = g r = u² = ω² r²) u = ω r, to which corresponds, in turn, a negative acceleration (equal and opposite centrifugal):

–g = ω² r = u x ω        (9)

which as it follows define the field density of a spring, Coriolis and Lorenz force (as result of Voltage of usually more than two different dynamic fields).

Flow resistance R

The voltage U of a flow (potential difference of liquid or electromagnetism) can be connected to the flow current (I) with flow resistance (R) through dynamic velocity u.

U = R I = u²    (10)

I = Q / t = ρ A u    (11)

R = u / ρA     (12)

The voltage drop U in pipe flow equals the flow resistance R by the flow current I (not necessary supply Is), can also result from solid friction surfaces (pipes), the change of surface flow (form Resistance) and generally from change of the internal energy of liquid (thermal voltage)

Enthalpy W = Q ΔU = Q ci ΔΤ (13)

Because pressure P is the energy density (Nm / m3) and equal to charge density p and potential U, the relative voltage Ui of two ideal gases at the same temperature and pressure is

U₁ / U₂ = ρ₂ / ρ₁          (14)

which shows the relationship Molar mass, the ratio of specific heat coefficient ci, and the link of the sound velocity.

Equations (electromagnetism, fluid & gravity Q = m)

As applies to electricity and liquid Kirchhoff's law is given by resistors

in series: ΣU = 0, I_s = constant, or

parallel connection: supply ΣI = 0, where P, U = constant,

which is only another expression of thermodynamics balance ΣQU - PV = 0.

E = PV = Q U = Q g r = Q u²            Potential energy {Nm}

P = E / V = ρ U = ρ u²   Pressure, volumetric energy density {Nm/m³}

u = (P / ρ) ^1/2                           Dynamic velocity {m/s}

U = E / Q                            Potential Conservation {m²/s², or Volt*}

I = L / U = P/ ρR = U/R          flow current [A*}

I_s = Q / t = ρ A u_s                     flow supply {Kg /s, or A*}

L = U I = RI² = ρ A u³             power {W}

F = E / r = Q g = PA = u I = u Q / t    Force {N},

R = u / ρA                                                       flow Resistance {Ω} *

C = Q / U = I t / U = t / R                                Capacity {F} *

U = g r = P / ρ                                                potential {V} *

P / r = g ρ                                                       top momentum

U = ω² r² = g r,   -g = ω² r = ω x u    inductive acceleration

F = Q (ω x u)                                      Coriolis, Lorenz Force

U = (ω x u) r                           inductive voltage (r = length of flows’ contact)

ΔU = c_j ΔΤ                              thermal voltage

U = R_s T                                  thermal potential

R_s = P /ρ Τ = c_p - c_v                specific constant

* For Ampere → Kg / sec, Volt = (m / sec) ² ,   g = V / m,   Tesla = ω {1/s}


examples