Discussion of 'Discharge Coefficient of Circular-Crested Weirs Based on a Combination of Flow around a Cylinder and Circulation' by Abdorreza Kabiri-Samani and Sara Bagheri

摘要

Based on a combination of flow around a cylinder and circulation, the authors of the original paper derived Eqs. (1) and (2) for the discharge coefficient C_d and crest-sectional velocity distribution of circular-crested weirs where K' = -O.14(H_1/R_b)~(-1.46) + 0.056; H_1 = total upstream head; R_b = radius of circular-crested weir; Rs = free-surface streamline radius; r = radial coordinate measured from the crest center; u = velocity at depth y; and g = gravitational acceleration. Assuming a concentric streamline over the weir crest, they estimated R_s and r as R_s=R_b + Y_2 (3) r = R_b+y (4) where Y_2 = crest flow depth (0.7H_1). Based on the theoretical and experimental analysis of Mohammadzadeh-Habili and Heidarpour (2013), the streamlines over the crest surface of a circular-crested weir (Fig. 1) are not concentric, and Eqs. (3) and (4) incorrectly estimate the values of R_s and r. For flow past circular-crested weir, R_s and r can respectively estimated as (Jaeger 1956) R_s =R_b + mY_2 (5) r = R_b + my (6) where m = experimental parameter. R_s and therefore m can be estimated from the measured water-surface data over the circular crested weir. Defining x and y as the horizontal and vertical axes, respectively, passing through the top point of the weir crest, the functional representation of the free-surface streamline passed over the weir crest surface can be expressed as y=f(x) (7) Using the Eq. (7), the free-surface streamline radius Rs can be estimated as (8) where f'(0) and f"(0) are the first and second derivatives, respectively, of f(x) at x = 0. To estimate R_s, the measured water-surface data of a circular-crested weir is taken from Vo (1992). A polynomial equation is fit to the water-surface data of the each test, and R_s is then estimated from Eq. (8). Replacing the values of R_b, Y_2, and R_s into Eq. (5), m is estimated and the results are then presented against HJR_b (Fig. 2).