The discharge coefficient Cd, defined as the ratio of the experimental flow rate to the ideal flow rate, is an important parameter. It is the ultimate correction factor for the theoretical stage-discharge relationship when it is determined on the basis of simplifying assumptions. To understand the behavior of the flow rate Q, the plot of Q as a function of the stage h is insufficient because the influence parameters are not detected. Plotting the experimental discharge coefficient against the relative upstream flow depth, related to the width of the approach channel, is the best way to know which are the parameters that influence the flow rate and hence the stage-discharge relationship. This can sometimes reveal the existence of unsuspected influential phenomena.

Regarding the SMBF flume, the literature does not report any relationship likely to govern the discharge coefficient of the device. Studies have focused on the stage-discharge relationship without alluding to the discharge coefficient. The stage-discharge relationships available in the literature are of two types. There are formulas of complex form, totally locked, which do not allow any possibility of development or expansion to extract the discharge coefficient relationship hidden inside. There are formulas that are rather simple in form but require transformations to highlight the unapparent discharge coefficient relationship.

It is the last type of formula that will be addressed in this study. For each stage-discharge relationship proposed in the literature, the main objective is to associate it with the relationship that governs the discharge coefficient and to highlight the influential parameters.

The different models describing the discharge coefficient of the device will be compared with the observations available in the literature, and interesting conclusions will be drawn.


SMBF flume, Flow measurement, Stage-discharge, Discharge coefficient.

Full Text:



ACHOUR B., AMARA L. (2022). Accurate discharge coefficient relationship for the Crump weir, Larhyss Journal, No 52, pp. 93-115.

ACHOUR B., AMARA L. (2022b). Theoretical and experimental investigation of a lateral broad-crested contraction as a flow measurement device, Flow Measurement and Instrumentation, Vol. 86, Paper 102175.

ACHOUR B., BOUZIANE M.T., NEBBAR K. (2003). Broad-crested triangular flowmeter in rectangular channel, Larhyss Journal, No 2, pp. 7-43. (In French)

BAIAMONTE G., FERRO V. (2007). Simple flume for flow measurement in sloping open channel, Journal of Irrigation and Drainage Engineering, Vol. 131, Issue 1.

BOS M.G. (1976). Discharge Measurement Structures, Laboratorium Voor Hydraulica AanAfvoerhydrologie, Landbouwhogeschool, Wageningen, the Netherlands, Report 4, May.

BOS M.G. (1989). Discharge Measurement Structures, third ed., Publication 20, Int. Institute for Land Reclamation and Improvement, Wageningen, Netherlands.

BURCHARTH H.F., HAWKINS S.J., ZANUTTIGH B., LAMBERTI A. (2007). Environmental Design Guidelines for Low Crested Coastal Structures, Chapter 13-Design tools related to engineering, Elsevier, pp. 203-333.

CAROLLO F.G., DI STEFANO C., FERRO V., PAMPALONE V. (2016). New stage–discharge relationship for the SMBF flume, Journal of Irrigation and Drainage Engineering, Vol. 142, Issue 5, Paper 04016005.

CAROLLO F.G., PAMPALONE V. (2021). Testing the Stage-Discharge Relationship in Sloping SMBF Flumes, Journal of Irrigation and Drainage Engineering, Vol. 147, Issue 5.

CONE V.M. (1917). The Venturi Flume, Journal of Agricultural Research, Washington D.C., Vol. IX, Issue 4, pp. 115-130.

DI STEFANO C., DI PIAZZA G.V., FERRO V. (2008). Field testing of a simple flume (SMBF) for flow measurement in open channels, Journal of Irrigation and Drainage Engineering, Vol. 134, Issue 2, pp. 235–240.

FERRO V. (2002). Discussion of ‘Simple flume for flow measurement in open channel’ by Zohrab Samani and Henry Magallanez, Journal of Irrigation and Drainage Engineering; Vol. 128, Issue 2, pp. 129–131.

HAGER W.H. (1986). Discharge Measurement Structures, Communication 1, Department of Civil Engineering, Federal Polytechnic School of Lausanne, Switzerland.

HENDERSON F.M. (1966). Open Channel Flow, the McMillan Company, New York, N.Y, USA.

KULKARNI K.H., HINGE G.A. (2021). Performance enhancement in discharge measurement by compound broad crested weir with additive manufacturing, Larhyss Journal, No 48, pp. 169-188.

PARSHALL R.L. (1926). The improved Venturi flume, Transactions ASCE, Vol. 89, pp. 841–880

SAMANI Z., MAGALLANEZ H. (2000). Simple flume for flow measurement in open channel, Journal of Irrigation and Drainage Engineering, Vol. 126, Issue 2, pp. 127-129.

TADDA M.A., AMIMUL I.A., MONZUR A., SHITU A., DANHASSAN U.A., ALIYU I.M. (2020). Operation and maintenance of hydraulic structures, Part of the edited volume Hydraulic Structures, Eds Amimul Ahsan, Swinburne University of Technology, 80 p.

VATANKHAH A.R. (2017). Discussion of “new stage–discharge equation for the SMBF flume, by Francesco Giuseppe Carollo, Costanza Di Stefano, Vito Ferro, and Vincenzo Pampalone, Journal of Irrigation and Drainage Engineering, Vol. 143, Issue 8, Paper 07017011.

VATANKHAH A.R., MOHAMMADI M. (2020). Stage–discharge equation for simple flumes with semi‑cylinder contractions, SN Applied Sciences, No 2, Article number 510.

WESTESEN G.L. (1992). Montana (Short Parshall) Flume (Part 1), Water meas. MT 9121 (AG).


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.