Technical Note: The effect of the ratio of length to width of rectangular orifices on discharge coefficient

Rectangular orifices are considered as a common structure for discharge measurement in hydraulics. The purpose of the present research is to investigate the effect of the ratio of length to width of rectangular orifices with same surface area on discharge coefficient. Different rectangles are examined as orifice while the aspect ratio in one of them is equal to 1.618 (golden ratio). Golden ratio is a special number which can be frequently existed in nature and this study attempts to find the probable specialty of this ratio in hydraulics. So, the experiments were carried out on five rectangle orifices that the ratio of length to width of ones varied from 1 to 16. Also, a comparison between the discharge coefficient of rectangular and circular orifices is performed. Therefore, the number of 94 tests was conducted on the orifices in the discharge range of 0.136 - 0.637 L/s. A mathematical relation is developed as pressure distribution coefficient in order to account the effect of non-hydrostatic pressure distribution under low head condition. Results of the experiments showed that the increasing of aspect ratio generally leads to increase discharge coefficient so that discharge coefficient of orifices with variation of the ratio of length to width changes about 11.7%. Furthermore, it is illustrated that golden ratio doesn’t have any specialty in flow evacuation and the discharge coefficient of circular orifices is equal to minimum discharge coefficient of rectangular orifices.