Discharge Equation for Round Gates in Turnout Pipes: Dimensional Analysis and Theoretical Approaches

Abstract

Meter gates are widely used in California and all over the world for both flow control and discharge measurement. The calibration data of the popular round Armco meter gates are available in tabular form for gate diameters varying from 0.2 to 1.22 m. The net gate opening area acts as a crescent-shaped submerged orifice that controls the flow discharge through the turnout pipe. The available discharge equations for these gates are not dimensionally homogeneous; however, a general valid equation in physics must be dimensionally homogeneous. In this study, using dimensional analysis and 10,500 data points on the 14 Armco gates, different dimensionally homogeneous equations are proposed to calculate the flow discharge values through the round Armco gates. The dimensional analysis approach was improved using a standard orifice equation and by applying net gate opening area. The results showed that the turnout pipe diameter, D, the gate opening, w, the gate head loss, H, and Reynolds number, R, are key parameters for deducing a generic flow discharge equation. This study resulted in a calibration discharge equation for the submerged round Armco gates for any gate size in the range of the 14 Armco gates (D=0.2–1.22 m; and w=0.051 m to fully open, that is, D). The proposed generic equation also makes it possible to compute the flow discharge of the gates with custom and intermediate sizes. The average error in the estimated discharge by the proposed continuous discharge equation for all gate sizes is 2.03% compared with original Armco calibration tables.