Improvements in Flow Rate Measurements by Flumes

Imperfections of the ISO 4359 standard related to the application of a boundary layer concept for predicting flow rates through rectangular and U-shaped flumes are described in detail. The primary equation for a flume flow chart results from a system of equations consisting of the energy equation and two continuity equations. The first equation requires a different modification of the stream width and depth when the boundary layer concept is applied to all three equations. Additionally, modification of the stream dimensions should refer to the cross section in the throat, where the critical depth occurs, instead of at the very end of the flume throat, as suggested by the ISO 4359 standard. To improve the accuracy of flow rate computations, the critical depth position in Venturi and Palmer-Bowlus flumes was predicted numerically by solving an ordinary differential equation, which describes the water surface profile of steady and gradually varied flow in open channels of prismatic and nonprismatic cross sections. Computing the stream modification for the position of the critical depth in a flume throat resulted in the reduction of the highest relative error of flow prediction for the Palmer-Bowlus flume for an inside sewer diameter $D=0.762\mathrm{m}$ from 3.3 to 0.8%, for $D=0.381\mathrm{m}$ from 3.7 to 1.2%, for $D=0.203\mathrm{m}$ from 4.3 to 3.2%, and for $D=0.102\mathrm{m}$ from 5.2 to 3.5%. In addition, a simple algebraic equation for calculating the critical depth position in Venturi flumes was developed. Calculation of the stream modification in the cross section of a flume throat in which the critical depth occurs was proved to improve the accuracy of flow rate computations both for Venturi and for Palmer-Bowlus flumes. However, for the latter type of flume, no such simple algebraic equation for the position of critical depth could be developed successfully. In this case, still some improvements of flow rate calculations could be achieved by modifying the stream dimensions as described by ISO 4359 but for the middle of the throat rather than at its end.