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The Agarwal-Okpara-Bao equation is a new form of AVA evaluation equation named after Ramesh K. Agarwal, Emmanuel c Okpara, and Guangyu Bao. [4] [5] It was derived from curve fitting of CFD simulation results and 80 clinical data obtained by Minners, Allgeier, Gohlke-Baerwolf, Kienzle, Neumann, and Jander [6] using a multi-objective genetic ...
A continuity equation is the mathematical way to express this kind of statement. For example, the continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries.
Using the velocity of the blood through the valve, the pressure gradient across the valve can be calculated by the continuity equation or using the modified Bernoulli's equation: Gradient = 4(velocity)² mmHg. A normal aortic valve has a gradient of only a few mmHg.
In the analysis of a flow, it is often desirable to reduce the number of equations and/or the number of variables. The incompressible Navier–Stokes equation with mass continuity (four equations in four unknowns) can be reduced to a single equation with a single dependent variable in 2D, or one vector equation in 3D.
() then provides the governing equation for pressure computation. The idea of pressure-correction also exists in the case of variable density and high Mach numbers, although in this case there is a real physical meaning behind the coupling of dynamic pressure and velocity as arising from the continuity equation
This solution will not depend upon the function . If this is used for the above equation consisting of Navier stokes equation and continuity equations with time derivative of pressure, then the solution will be same as the stationary solution of the original Navier Stoke problem. This process also introduce the new term artificial time as t→∞.
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In fluid dynamics, the Taylor–Green vortex is an unsteady flow of a decaying vortex, which has an exact closed form solution of the incompressible Navier–Stokes equations in Cartesian coordinates. It is named after the British physicist and mathematician Geoffrey Ingram Taylor and his collaborator A. E. Green. [1]