For fully developed laminar incompressible flow through a straight noncircular duct, as in Sec. 6.8, the Navier-Stokes Equation (4.38) reduce to where (y, z) is the plane of the duct cross section and x is along the duct axis. Gravity is neglected. Using a non-square rectangular grid (Δx, Δy), develop a finite-difference model for this equation, and indicate how it may be applied to solve for flow in a rectangular duct of side lengths a and b.

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Il it it up const < 0 i-1.j+1 i+1j+1 Az 1.J i+1.j Ay Ay i-1j-1 ij-1 i+1j-1