Experimental study of flow over piano key weirs with different plan shapes

ABSTRACT

The piano key weir (PKW) is an evolution with more hydraulic efficiency, compared to labyrinth weir. The studies on this type of weir have shown a significant increase in its discharge efficiency, especially at low heads. In this study, discharge coefficient of various shapes of piano key weir (i.e. rectangular, trapezoidal, and triangular) is investigated experimentally. Also, the aeration process of the studied weirs is described. According to the results, it was found that the discharge coefficient of the triangular PKW is about 28.2% more than the discharge coefficient of the rectangular PKW, and the discharge coefficient of the trapezoidal PKW is about 12.9% more than the discharge coefficient of the rectangular PKW. Also, the discharge capacity of the rectangular, triangular, and trapezoidal PKWs are 3.8, 3.96, and 3.96 times the sharp crest weir, respectively. The equations introduced for the discharge coefficient show good agreement (with R² from 0.968 to 0.988 and average percentage error from 0.82 to 2.6%) between the actual and calculated values.

KEYWORDS:

• Discharge coefficient
• rectangular PKW
• trapezoidal PKW
• triangular PKW
• weir efficiency

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notations

The following abbreviations was used in this study
B	=	Weir length in streamwise direction;
$B_b$	=	Weir base length;
$B_o$	=	Upstream overhang length;
$C_d$	=	Discharge coefficient.
$C_{{\mathit{d}}_{\mathit{computed}}}$	=	Computed discharge coefficient;
$C_{{\mathit{d}}_{\mathit{actual}}}$	=	Measured discharge coefficient;
$C_{{\mathit{d}}_{\mathit{min}}}$	=	Minimum discharge coefficient;
$C_{{\mathit{d}}_{\mathit{max}}}$	=	Maximum discharge coefficient;
$C^{\prime }$	=	Empirical coefficient;
F	=	Functional symbol;
$H_t$	=	Total upstream head;
h	=	Approach flow depth over the weir;
g	=	Gravity acceleration;
L	=	Total length of PKW;
N	=	Number of weir cycles;
n	=	Number of data;
P	=	Weir height;
Q	=	Discharge;
Q*	=	Discharge difference between present rectangular PkW and other researchers;
$S_o$	=	Longitudinal bed slope
$T_s$	=	Thickness of weir wall;
V	=	Average approach flow velocity
W	=	Total weir width;
$W_i$	=	Width of inlet key;
$W_o$	=	Width of outlet key;
$W_u$	=	Width of weir cycle; and
$\mathit{\alpha }$	=	Angle between weir sidewall and the flow direction