Authors: A. A. Frempong
Coincidences. The US Supreme Court consists of nine members, one of whom is the Chief Justice of the Court. So also, a one-direction Navier-Stokes equation consists of nine members, one of which is the indispensable gravity term, without which there would be no incompressible fluid flow as shown by the solutions of the N-S equations (viXra:1512.0334). Another coincidence is that numerologically, the number, 9, is equivalent to the 1800's (1 + 8 + 0 + 0 = 9) time period during which the number of the members of the Supreme Court became fixed at 9, while the formulation of the nine-term N-S equations was completed. Also, another coincidence is that the solutions of the N-S equations were completed (viXra:1512.0334) by the author in the year, 2016 (2 + 0 +1+ 6 = 9). Using a new introductory approach, this paper covers the author's previous solutions of the N-S equations (viXra:1512.0334). In particular, the N-S solutions have been compared to the equations of motion and liquid pressure of elementary physics. The N-S solutions are (except for the constants involved) very similar or identical to the equations of motion and liquid pressure of elementary physics. The results of the comparative analysis show that the N--S equations have been properly solved. It could be stated that the solutions of the N-S equations have existed since the time the equations of motion and liquid pressure of elementary physics were derived. A one-direction Navier-Stokes equation has also been derived from the equations of motion and liquid pressure of elementary physics. Insights into the solutions include how the polynomial parabolas, the radical parabolas, and the hyperbolas interact to produce turbulent flow. It is argued that the solutions and methods of solving the N-S equations are unique, and that only the approach by the author will ever produce solutions to the N-S equations. By a solution, the equation must be properly integrated and the integration results must be tested in the original equation for identity before the integration results are claimed as solutions
Comments: 19 Pages. Copyright © by A. A. Frempong
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