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                              Magnetohydrodynamic Water Propulsion

Magnetohydrodynamics relates to the phenomena that comes from the motion
electrically conducting fluids in the presence of electric and magnetic
fields. When an electric current passes through an electrically conducting fluid such as sea water that is within a magnetic field, a force is produced
on the electrically charged fluid the electrolyte. An electrolyte fluid is a liquid that can conduct some electricity. The electrical current I and magnetic
field intensity B has directions perpendicular to each other. The force F of the electrified fluid has a direction perpendicular to both the directions of the electrical current I and magnetic field. Figure 2(a) shows the directions of the current I, force F and magnetic field intensity B. Their
directions are perpendicular or at a 90 degree angles to each other. Electrical current I can be reprented by a vector I. Current vector I is simply electrical current I but with direction. The force F vector symbol is
F, and magnetic field intensity B vector is B. There is an equation that can be used to calculate the resultant force vector F which is the cross product

of B and I. This vector equation called is: F =BI, (1).
This equation is calculated using vector mathematics. This equation indicates that the force F is proportional to the cross product of B and I if the vectors F, B and I have directions perpendicular to each other. Magnetic field intensity has units of the tesla, current I has units of amperes, and force F has units of newtons. Figure 2(b) shows a water propulsion device or magnetohydrodynamic propulsion device. Two metal plates 4, and 5 are electrodes that introduce the electrical current I through the conductive fluid 7 which is brine water. Ceramic magnets or stator 2 and 3 are the magnetic field sources which produces the  magnetic intensity B. An electrical voltage source 10 which can be a battery produces the electric supply voltage V. The supply voltage V or +V causes electric current I to flow through the brine. An ammeter 11 can be used to measure the electrical current I send through the circuit of the conducting fluid. The electrical current amplitude I is partially dependand on the electrical supply voltage V and the static resistance R of the electrically conducting fluid 7 between metal electrodes like 4, 5. It has ceramic magnets 2 and 3 that produces magnetic field intensity B in the water electrolyte or brine 7. It has cathode electrode plate 5 and anode plate electrode 4 that passes electric curent I through the electrolyte 7 with electrical resistance R.
The current I through the electrolyte depends on the electrical resistance R of the same. The electric current amplitude is: I=VR, (2).
The static resistance R is when the fluid 7 is not moving in a particular direction. With the fluid not moving in one direction, the velocity v of this motion has little effect on the statitc resistance R. Metal electrically conducting plates 6 between the input electrodes 4 and 5 reduce the amount of electrolyte 7 between electrodes 4 and 5. This reduces the efffective resistance R of the electrolyte between the electrodes 4 and 5. The static electric resistance R is likely to be: R=aw(AT), where A is the surface area of the electodes 4 and 5 with w the distance between the same electrodes 4 and 5. The static input resistance R of the magnetohydrodynamic propulsion device is not determined by the distance w between the plates, but is determined by the saltiness of the water and somewhat by the surface area A of the plates but by not that much. The static (no water movement) input resistance R is between 290 to 400 ohms at about T= 35 degrees celsius water temperature. Variable T is the temperature of the brine water between the electrodes 4 and 5. Coefficient "a" is determined by the electrical conductivity of the electrolyte at T=25 degrees celsius. Imaginary example: V=+30 volts, B=0.02 tesla, x=0.026 metre, T=1 to 30 degrees celsius.

        
Vectors and Water Propulsion Device
Magnetic Water Propulsion Experiment
                      Figure 2.

Figure 3 shows a photograph of the water propulsion experiment of figure 2 design.

    Photograph of Water Propulsion Experiment

              Figure 3.

The magnetic force F on the electrolyte causes the brine electrolyte to flow at a velocity v the water propulsion motor at a mass flow rate M. The combined magnetic force F on the brine between electrodes 4 and 5 is assumed to be: F=Mv+xh(Pf-Pi). Where Pi is the brine static pressure just before the motor and Pf the brine pressure just after the motor. The x is the distance between the electrodes 4 and 5 which is the horizontal dimension of the electrolyte 7 in the motor. The h is the height of the electrodes 4 and 5 which is also the height of the electrolyte 7 in the motor. Then wh is the flow area of the electroltyte 7 in the motor between electrodes 4 and 5. Another way to calculate the thrust force of the magnetohydrodynamic motor is with equation: F=HI, (3);  where H is the magnetic field strength of the stator magnet 5. The magnetic field strength H is:
H=BA, (4); or H=BAz, (5);
where A=wD is the surface area of the magnet which is on a plane perpendicular to magnetic field direction or axis of B. Variable D is the length of electrode 5 or depth magnet 2 which is perpendicular to w and in the same plane as w. Varible z is the length of magnet along the direction of the magnetic field axis or centre. The variable A is also the surface area of the electrolyte exposed to the magnetic field of magnet 2. This says the larger the magnet, the stronger the magnetic field strength H. The magnetic field intensity B is also independent on the size of the stator magnet like 2 or 3. Magnetic field strength H is also dependent on the length z of the magnet along the magnetic field axis or centre. For example, if the length z of the magnet is longer, the magnet 2 can pull other magnets to it with a stronger magnetic pull. The dynamic input impedance Z of the magnetohydrodynamic motor should be: Z=vBw, (6);
where v is the velocity of the electrically conducting fluid or propellant 4
which is in the same direction as force F. The dynamic impedance Z is caused by the flow speed v of the fluid with magnetic field intensity B. The w can be the distance between the electrodes 2 and 3 in the electrolyte 4 which is also the width of the electrolyte 4 exposed to the magnetic field of magnet 5. The increase in magnet 5 magnetic field strength H results in an increase of force F and motor input impedance   Z. The required electric supply voltage V to produce the force F should then be: V=I(R+Z), (7).
The magnetic force F on the electrolyte is more accurately:      F=BI, (8).
The thrust power is assumed to be: Fv=BVI, because increasing magnetic field intensity B should increase the propellant (brine water) speed v and reduce input current I. I=(V-Vco)R. Counter electromotive force Vco=Bv.

  Demonstration Video 1. Figure 1    Water Propulsion Design Experiment:
  ../magnetohydrodynamics/.WMV ,
  file size:  kilobytes, (not available yet).

  Figure 4 shows a picture of the magnetohydrodynamic water propulsion motor experiment. The electrolyte which is the propellant flows in a circular path.

     Magnetohydrodynamic Motor Experiment

                       Figure 4.

Magnetohydrodynamically Propelled Submarine


References
1. Patent: Propulsion System; 3,106,058.

January 14, 2004; page was revised: on March 8, 2013.