TY - JOUR
T1 - A Reformed Empirical Equation for the Discharge Coefficient of Free-Flowing Type-A Piano Key Weirs
AU - Kadia, Subhojit
AU - Pummer, Elena
AU - Kumar, Binit
AU - Rüther, Nils
AU - Ahmad, Zulfequar
N1 - Publisher Copyright:
© 2023 American Society of Civil Engineers.
PY - 2023/4/1
Y1 - 2023/4/1
N2 - The existing equations for the discharge coefficient of Piano key weirs (PKWs) use a limited range of experimental data, which means that they are inappropriate for wide parametric ranges that might lead to significant errors. This study aimed to propose a reformed empirical equation using a wide range of data points gathered from previous experimental studies. Further, the appropriateness to use the existing equations for the collected data points, and the related errors, were investigated in detail using graphical and statistical analyses. The proposed equation predicted the discharge coefficients with <5% absolute errors for 83.5% data points and with <10% absolute errors for 100% data points, and the mean absolute error was 2.9%. Such variations may be attributed to the differences in experimental conditions that exist among the previous studies. The correlation indices were higher for the proposed equation as compared to the same for the existing equations, whereas the error indices were lowest for the proposed one. For some very specific parametric ranges, the existing equations still hold better accuracy. Overall, the proposed equation can precisely estimate the discharge coefficient of the basic geometry of Type-A PKWs for a wide parametric range and will be handy in the hydraulic design of such PKWs.
AB - The existing equations for the discharge coefficient of Piano key weirs (PKWs) use a limited range of experimental data, which means that they are inappropriate for wide parametric ranges that might lead to significant errors. This study aimed to propose a reformed empirical equation using a wide range of data points gathered from previous experimental studies. Further, the appropriateness to use the existing equations for the collected data points, and the related errors, were investigated in detail using graphical and statistical analyses. The proposed equation predicted the discharge coefficients with <5% absolute errors for 83.5% data points and with <10% absolute errors for 100% data points, and the mean absolute error was 2.9%. Such variations may be attributed to the differences in experimental conditions that exist among the previous studies. The correlation indices were higher for the proposed equation as compared to the same for the existing equations, whereas the error indices were lowest for the proposed one. For some very specific parametric ranges, the existing equations still hold better accuracy. Overall, the proposed equation can precisely estimate the discharge coefficient of the basic geometry of Type-A PKWs for a wide parametric range and will be handy in the hydraulic design of such PKWs.
KW - Discharge coefficient
KW - Empirical equation
KW - Graphical analysis
KW - Piano key weir (PKW)
KW - Statistical analysis
UR - http://www.scopus.com/inward/record.url?scp=85148647200&partnerID=8YFLogxK
U2 - 10.1061/JIDEDH.IRENG-9886
DO - 10.1061/JIDEDH.IRENG-9886
M3 - Article
AN - SCOPUS:85148647200
SN - 0733-9437
VL - 149
JO - Journal of Irrigation and Drainage Engineering
JF - Journal of Irrigation and Drainage Engineering
IS - 4
M1 - 04023003
ER -