Discharge coefficient for rectangular notch using a dimensional analysis technique

Abstract

The rectangular weir (notch) is a common device used to regulate and measure discharge in irrigation projects. The current research was based mainly on laboratory experiments studying the hydraulic characteristics of rectangular notches. Four rectangular notches were used in this research in different models. Notches for all models were designed with the same shape, arrangement, and width (4 cm), but differed in height, with examples at 6, 8, 10, and 12 cm. The main objective of this research was to study the influence of rectangular notch dimensions and upstream water depth on discharge coefficients. The results obtained from this research indicate that the relationship between the discharge coefficient and the upstream water depth is a power function. The values of the discharge coefficient increase with increases in the values of the upstream water depth. The relationship between the discharge coefficient and the Reynolds number is also a power function, and an increase in the Reynolds number leads to a decreased discharge coefficient. In addition, when the value of the Reynolds number is high (turbulent flow), the values of the discharge coefficient converge to an approximately constant value. The flow in all runs was subcritical and the relationship between discharge coefficient and Froude number was also found to be a power function. An increase in Froude number thus leads to a decrease in discharge coefficient. The slope of the discharge coefficient-Froude number curve values gradually decreases until the value the discharge coefficient reaches an approximately constant value. A dimensional analysis technique was used to estimate the values of the discharge coefficient for various rectangular notch dimensions, and an empirical equation for discharge coefficient estimating was derived using regression procedure. This equation has a coefficient of determination R 2 of 0.955.