A New Quadrature for Determining the Mean Duct Velocity

Abstract

The mean velocity in circular ducts is often determined by a traverse in which the cross section of the pipe is divided into equal annular areas and a center circle, and the velocity determined at some point within each. This process can be improved by integration (quadrature) procedures that either optimize the spacing of the sampling points and/or incorporate weighting factors into the quadrature. New quadrature formulae are proposed here for the purpose of determining the average velocity in a duct. These formulae include, as a boundary condition, a value of zero at the boundaries of the function being integrated. Thus the fact that the flow velocity is zero at the surface of the duct is automatically included in each quadrature. The sampling points and weighting factors needed for each quadrature are presented, along with a sample calculation illustrating the use of a quadrature procedure.