  Following the work on Shannon entropy together with the principle of maximum
entropy, Luo & Singh (J. Hydrol. Eng., 2011, 16(4): 303-315) and Singh & Luo
(J. Hydrol. Eng., 2011, 16(9): 725-735) explored the concept of non-extensive
Tsallis entropy for modelling velocity in open channels. Later, the idea was
extended by Cui & Singh (J. Hydrol. Eng., 2013, 18(3): 331-339; 2014, 19(2):
290-298) by hypothesizing an accurate cumulative distribution function (CDF).
However, these studies estimated the entropy index through a data-fitting
procedure and the values of the index were different for different studies. The
present study investigates the role of Tsallis entropy index for modelling
velocity in open channels using the method of moments, based on conservation of
mass and momentum. It is found that the entropy index depends on the normalized
mean velocity and the momentum coefficient. In addition to the physical meaning
of the index, it is also found that the modified velocity profile significantly
improves for both wide and narrow channels, as shown by small predicted
velocity errors. The proposed approach may be further employed for other open
channel flow problems, such as sediment concentration, and shear stress
distribution.
