Newtonian fluids Navier-Stokes equations for

It has become quite popular to optimize the manifold design using computational fluid dynamic codes, ie, FID AP, Phoenix, Fluent, etc, which solve the full Navier-Stokes equations for Newtonian fluids. The effect of the area ratio, on the flow distribution has been studied numerically and the flow distribution was reported to improve with decreasing yiR. 

The solution of the system produces a time series of the value of x in time t with the initial value of X given at time t = 0 or x(f = 0) = xq. The space x R") with t as a parameter is termed a phase space. The function/determines the time evolution of the system. The dynamic system is nonlinear with nonlinear term in the function/. One example in fluid dynamics is the Navier-Stokes equations for Newtonian fluids. The nonlinearity of the system comes mainly from the convective motion of the fluid flow. The fluid motion can develop unpredictable, yet observable, behavior with the proper choice of the initial conditions. 

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