Discharge Coefficient of a C-Type Piano Key Side Weir at 30° and 120° Sections of a Curved Channel

Yaser Mehri, Jaber Soltani, Mojtaba Saneie, Mohhamad Rostami


A piano key side weir (PKSW) is a non-linear weir that discharge exceeds linear weirs by increasing the length in width. PKSW can be used in side weirs with space limitation. As side weirs are extensively used in flood control, water level control in rivers, and water supply channels, it is necessary to use PKSW as side weirs. This research discusses the discharge coefficient of a PKSW by assessing a C-type PKSW at 30° and 120° sections of a channel with a longitudinal curve. Dimensional analysis was used for identifying the parameters effective in the discharge coefficient. The effects of these parameters are examined by analysing the effective parameters. Finally, an empirical relationship has been proposed for determining the discharge coefficient based on the dimensionless parameters for calculating the discharge coefficient with the correlation coefficient of 0.88 and the mean error of 0.091. The influence of the parameter on the PKSW is more than that of the remaining parameters: With an increase in the value of this parameter, considering decreases in the length of the deviation and a lack of submerged inlet keys, the coefficient of discharge increases.


Non-Linear Weir; Piano Key Side Weir (PKSW); Curved Channel; Empirical Equation; Dimensional Analysis.


Mahmodinia, S., M. Javan, and Afshin Eghbalzadeh. "The flow field and free surface pattern of the submerged side weir with different lengths." Arabian Journal for Science and Engineering 39.6 (April 2014): 4461-4472. doi: 10.1007/s13369-014-1058-y.

Emin Emiroglu, M., M. Cihan Aydin, and Nihat Kaya. "Discharge characteristics of a trapezoidal labyrinth side weir with one and two cycles in subcritical flow." Journal of Irrigation and Drainage Engineering 140.5 (February 2014): 04014007. doi: 10.1061/(ASCE)IR.1943-4774.0000709.

Lemperiere, F, and Ahmed Ouamane. "The Piano Keys weir: a new cost-effective solution for spillways." International Journal on Hydropower & Dams 10.5 (2003): 144-149.

Kabiri-Samani, A, and Amir Javaheri. "Discharge coefficients for free and submerged flow over Piano Key weirs." Journal of Hydraulic Research 50.1 (August 2012): 114-120. doi: 10.1080/00221686.2011.647888.

Agaccioglu, Hayrullah., M. Emin Emiroglu, and Nihat Kaya. "Discharge coefficient of side weirs in curved channels." Proceedings of the Institution of Civil Engineers-Water Management. Vol. 165. No. 6. Thomas Telford Ltd, (August 2012). doi: 10.1680/wama.11.00007.

Agaccioglu, H, and Yalcin Yuksel. "Side-weir flow in curved channels." Journal of irrigation and drainage engineering 124.3 (May 1998): 163-175. doi:10.1061/(ASCE)0733-9437(1998)124:3(163).

Cosar, A, and Hayrullah Agaccioglu. "Discharge coefficient of a triangular side-weir located on a curved channel." Journal of irrigation and drainage engineering 130.5 (October 2004): 410-423. doi: 10.1061/(ASCE)0733-9437(2004)130:5(410).

Agaccioglu, H., F. Onen, and Fuat Toprak. "Scour around a side-weir at a 30 DG section of a 180 DG alluvial curved channel." Irrigation and Drainage 56.4 (June 2007): 423-438. doi: 10.1002/ird.304.

Kaya, N., M. Emin Emiroglu, and Hayrullah Agaccioglu. "Discharge coefficient of a semi-elliptical side weir in subcritical flow." Flow Measurement and Instrumentation 22.1 (March 2011): 25-32. doi:10.1016/j.flowmeasinst.2010.11.002.

Emiroglu, M, and Nihat Kaya. "Discharge coefficient for trapezoidal labyrinth side weir in subcritical flow." Water resources management 25.3 (December 2011): 1037-1058. doi: 10.1007/s11269-010-9740-7.

Vatankhah, Ali R. "Analytical solution for water surface profile along a side weir in a triangular channel." Flow Measurement and Instrumentation 23.1 (March 2012): 76-79. doi: 10.1016/j.flowmeasinst.2011.10.001.

Vatankhah, Ali R. "Water surface profile along a side weir in a parabolic channel." Flow Measurement and Instrumentation 32 (August 2013): 90-95. doi: 10.1016/j.flowmeasinst.2013.04.010.

Azimi, H, and Saeid Shabanlou. "The flow pattern in triangular channels along the side weir for subcritical flow regime." Flow Measurement and Instrumentation 46 (December 2015): 170-178. doi: 10.1016/j.flowmeasinst.2015.04.003

Aydin, M. Cihan, and Muhammet Emin Emiroglu. "Numerical analysis of subcritical flow over two-cycle trapezoidal labyrinth side weir." Flow Measurement and Instrumentation 48 (April 2016): 20-28. doi: 10.1016/j.flowmeasinst.2016.01.007.

Tiwari, H, and Nayan Sharma. "Turbulent kinetic energy in the upstream of Piano Key Weir." Arabian Journal for Science and Engineering 41.10 (March 2016): 4147-4152. doi: 10.1007/s13369-016-2118-2.

Ghasemzadeh, F., B, Parsa, and Mojtaba Noury. "Numerical study of overflow capacity of spillways (with an emphasis on PK-weirs)." E-proceedings of the 36th IAHR World Congress, Hague, The Netherlands. 2015.

Hu, H., Z, Qian., W, Yang., D, Hou, and Dongmei Hou. "Numerical Study of Characteristics and Discharge Capacity of Piano Key Weirs." Flow Measurement and Instrumentation (August 2018). doi: 10.1016/j.flowmeasinst.2018.05.004.

Al-Shukur, A, K., and Ghufraan H. Al-Khafaji. "Experimental study of the hydraulic performance of piano key weir." International Journal of Energy & Environment 9.1 (2018).

Mehboudi, A., J. Attari, and seyyedamirhossein Hosseini. "Experimental study of discharge coefficient for trapezoidal piano key weirs." Flow Measurement and Instrumentation 50 (August 2016): 65-72. doi:10.1016/j.flowmeasinst.2016.06.005.

De Marchi, G. "Essay on the performance of lateral weirs." L'Energia Elettrica, Milan, Italy 11 (1934): 849-860.

Borghei, S. M., M. R. Jalili, and Masoud Ghodsian. "Discharge coefficient for sharp-crested side weir in subcritical flow." Journal of Hydraulic Engineering 125.10 (October 1999): 1051-1056. doi: 10.1061/ (ASCE) 0733-9429(1999)125:10(1051).

Subramanya, K, and Subhash Chandra Awasthy. "Spatially varied flow over side-weirs." Journal of the Hydraulics Division 98.1 (1972): 1-10.

Nandesamoorthy, T., and A. Thomson. "Discussion of spatially varied flow over side weir." ASCE Journal of the Hydraulics Division 98.12 (1972): 2234-2235.

Hager, W. H. "Lateral outflow over side weirs." Journal of Hydraulic Engineering 113.4 (April 1987): 491-504. doi: 10.1061/(ASCE)0733-9429 (1987)113:4(491).

Ranga Raju, K., S. K. Gupta, and Baidyanath Prasad. "Side weir in rectangular channel." Journal of the Hydraulics Division 105.5 (1979): 547-554.

Singh, R., D. Manivannan, and Tsnarayana Satyanarayana. "Discharge coefficient of rectangular side weirs." Journal of irrigation and drainage engineering 120.4 (July 1994): 814-819. doi:10.1061/(ASCE)0733-9437(1994)120:4(814).

Full Text: PDF

DOI: 10.28991/cej-03091106


  • There are currently no refbacks.

Copyright (c) 2018 Jaber Soltani, Yaser Mehri, Mojtaba Saneie, Mohhamad Rostami

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.