### A new equation for calculating the uniform flow in hydraulically smooth and rough channels

Tarciso Cabral da Silva, Emerson Farias Salvado de Lima, Sara Almeida de Figueiredo

Tuesday 30 june 2015

9:00 - 9:15h at Europe 1 & 2 (level 0)

Themes: (T) Water engineering, (ST) Computational methods

Parallel session: 4E. Engineering - Computational

Since the early decades of the twentieth century, after the advent of the theory of turbulence and equations deduced by Theodore von Kármán, researchers try to standardize the equations for the steady uniform flow in open channels and for the pressurized pipes. A rational procedure to get better approaches is the modification of the friction factor for the flow in open channels, increasing it to include the effects of additional head loss due to circulating currents. Later, in the end of the last century, was suggested that the friction factor for channels with noncircular cross sections could be corrected by a shape factor greater than a unity and the Colebrook-White formula could be used. More recently, other authors have deduced a new format for the Colebrook-White formula with a combination with the Darcy-Weisbach one, and the resultant equation, in this way, do not need of interactive calculations for the friction factor f. In this work, the main expression of the Kazemipour method, which was developed in the last century, and considers the shape effects on resistance in the calculating the average velocity of the uniform flow, is used for the correction of the friction factor. Then, it is inserted in the modified Colebrook-White equation to produce another expression applicable for narrow and wide channels and hydraulically smooth or rough channels. An additional advantage of this new equation is the consideration of the value of the cinematic viscosity of the water, which makes it appropriated to be used to different values of the temperatures. The new equation is then applied to experimental data of uniform flow in triangular rough channel and a smooth rectangular channel. Comparisons were made between the results obtained from the new equation and the Manning formula. It was concluded that the results obtained from the use of the new equation were better.