Hydraulic design of A-type Piano Key Weirs

Abstract

Piano Key Weirs (PKWs) are an alternative to linear overflow structures, increasing the unit discharge for similar heads and spillway widths. Thus, they allow to operate reservoirs with elevated supply levels, thereby providing additional storage volume. As they are relatively novel structures, few design criteria are available. Hence, physical model tests of prototypes are required. This study describes comprehensive model tests on a sectional set-up of several A-type PKWs, in which the relevant parameters were systematically varied. Considering data of former studies, a general design equation relating to the head-discharge ratio is derived and discussed. The latter is mainly a function of the approach flow head, the developed crest length, the inlet key height, and the transverse width. To extend its application range, case study model tests were analysed to provide a design approach if reservoir approach flow instead of channel flow is considered.

Estimation of A-type Piano Key weir rating curve

“…Furthermore, the parameter P i /H is known to be relevant for Labyrinth weirs (Tullis 1995), and also significantly affects the PKW efficiency. The data analysis conducted by Leite Ribeiro et al (2012a) finally let to the principal normalization Figure 3a shows the values r derived from measurements versus δ, including data of Leite Ribeiro et al (2012a) and some data of Machiels et al (2012). Note that the data of Machiels et al (2012) with a bottom slope (P i -R)/(B i + B b ) > 0.7 were not collapsing with the proposed normalization, so that these were ignored and the application of Eq.…”

“…(4) and are specified herein, by introducing four correction factors. The latter are equivalent to individual factors between 0.92 and 1.20, for the geometries tested by Leite Ribeiro et al (2012a). The individual correction factors are defined as given below, namely for the ratio between inlet and outlet key width as …”

“…the 'dry' key for the latter reservoir level. The developed crest length L is defined as Mainly two approaches are common to describe the PKW discharge Q P : by (1) deriving a specific discharge coefficient using the Poleni equation (Kabiri-Samani and Javaheri 2012, Anderson and Tullis 2011, Ouamane et al 2006), or (2) comparing the PKW discharge Q P with that of a linear sharp-crested weir Q S (Leite Ribeiro et al 2012a). The second option is chosen herein as it seems better physically based (Falvey 2003, Schleiss 2011.…”

“…The Poleni equation was taken as reference, and the rating curve expressed in terms of the discharge coefficient. Leite Ribeiro et al (2012a) performed systematic model tests in a channel of 3 m length and 0.5 m width. In total, 380 tests were conducted, considering 49 different PKW geometries of type A, with cylindrical weir crests.…”

“…In the frame of the study conducted by Leite Ribeiro et al (2012a), systematic physical model tests were carried out at the Laboratory of Hydraulic Constructions (LCH) of EPFL. A straight rectangular channel with a length of 40 m, a width of 2 m and a height of 1 m was used.…”