Assessment of Equivalence of Small and Large Orifice Computational Models

Abstract

The aim of this paper was to analyze theoretical aspects of calculating steady water flow through unsubmerged circular orifices. Theoretical analysis shows that the values of discharge obtained by using formulas intended for small orifices are greater than those calculated using formulas for large orifices. These differences attain a maximum value when the water level reaches the upper edge of the orifice, and decrease when water head increases. It has been proven that the volumetric flow rate for circular unsubmerged orifices can be calculated by formulas for small orifices when the water level above the center of gravity is at least four times as high as the diameter of the orifice.

Flow Measurements Using a Sluice Gate; Analysis of Applicability

“…In Figure 11, only exemplary points of Cd and Cdcc were given (as a function of H/a) from selected experiments in the V2 variant. All discharge coefficients determined on the basis of measurements and calculated from relationship (5), with a correction (13), show a satisfactory agreement. The percentage deviation of the Cd discharge coefficients determined directly by the measurements of those calculated using relationship (13)(14), with correction Cdcc in cases V1 and V2, as function h/a, is presented in Figure 12.…”

“…All discharge coefficients determined on the basis of measurements and calculated from relationship (5), with a correction (13), show a satisfactory agreement. The percentage deviation of the Cd discharge coefficients determined directly by the measurements of those calculated using relationship (13)(14), with correction Cdcc in cases V1 and V2, as function h/a, is presented in Figure 12. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18H/a The percentage deviation of the C d discharge coefficients determined directly by the measurements of those calculated using relationship (11,12), with correction C dcc in cases V1 and V2, as function h/a, is presented in Figure 12.…”

“…Thus, the H/a ratio increases, as a result of which the determined discharge coefficient values are higher than in variant V2 (Figure 14). The percentage deviation of the Cd discharge coefficients determined directly by the measurements of those calculated using relationship (13)(14), with correction Cdcc in cases V1 and V2, as function h/a, is presented in Figure 12 As previously stated, the percentage deviations of the discharge coefficients determined from the Cd measurements and relationship (5) given by Swamee [15] Cdc are in the range of (−5÷40)% ( Figure 10). The values of the Cdcc discharge coefficients calculated from Equation (5) with the correction ΔCdcc differ from the discharge coefficients Cd obtained from measurements by ± 9% (Figure 12)…”

“…The discharge coefficients obtained from the measurements and calculated using relationship (5) with correction (13)(14) for both cases are shown in Figure 13.…”

“…The values of the discharge coefficient µ for free flow (unsubmerged) are µ = εφ, where ε-contraction coefficients, defined as the ratio of a final cross-sectional area of the gate opening, if only normal stresses act, the magnitude of this coefficient will depend entirely on the boundary geometry (H/a); φ-velocity coefficients defined as the ratio between the actual velocity of a water stream at vena-contracta and theoretical velocity of the stream and depth in cross-section 1-1 given by h 1 = εa. The values of contraction coefficients ε for the free flow conditions are determined on the basis of hydraulic experiments, which can be found in the literature [12,13]. In a one-dimensional description of the submerged sluice gate flow, the location of cross-section 1-1, where the depth h z necessary in Equation (1) should be measured, is not clearly defined.…”