Discussion of “Discharge Coefficients for Orifices Cut into Round Pipes” by Alex J. McLemore, John S. Tyner, Daniel C. Yoder, and John R. Buchanan

Abstract

The authors are appreciated for a useful contribution regarding the discharge coefficient for flow into orifices cut with a circular bit perpendicular to and along the centerline of a round pipe, and the discusser would like to draw attention to some points. As mentioned by the authors, the orifice area is generally defined as the area of the bit used to cut the hole, but the true orifice area is larger than the bit due to the curvature of the riser pipe. Prohaska et al. (2010) studied flow into a riser while assuming the orifice area equal to the bit area. McLemore et al. (2011) provided several descriptions for the orifice area. The authors conducted an excellent investigation of the discharge through orifices in riser pipes, but the area used to calculate discharge in the orifice equation is considered as an ellipse area, Ae, due to the complexity of the solutions for the actual area. In this research, the actual orifice area, Ao, is considered equivalent to the area of pipe removed by the bit (Fig. 1), and a near exact solution for Ao is presented using the two-point Gauss quadrature rule (Vatankhah 2011). As orifice depth decreases, the error due to assuming a single h (head at center of orifice) increases. This error can be removed by integrating the head across the area. A simple accurate approximation for this case is also presented. Because the orifice area encountered by water entering a riser is described more accurately by Ao, it is interesting to ponder whether the fits to discharge coefficient in the original paper might be further improved by using this area. Area of Pipe Removed by the bit, Ao