Fully Developed Fluid Velocity Profiles in Regular Polygon Ducts

23-2 FULLY DEVELOPED FLUID VELOCITY PROFILES IN REGULAR POLYGON DUCTS 

In this case, the flow cross section is 2a in the x direction by 2b in the y direction. A series solution has been obtained by Boussinesq (1868) in the following form  

TABLE 23-1 Effect of Aspect Ratio on the Ratio of Maximum to Average Fluid Velocity  

This Euler-Lagrange equation reduces to the following second-order partial differential equation for v x, y)  

The triangular cross section is equilateral when m = 1 / v. In this case, the flow cross section S = H ly/3, and the final result for the average velocity is 

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