An attempt at using the entropy approach to predict the transverse distribution of boundary shear stress in open channel flow

Abstract

This paper highlights the similarities between a number of studies which have applied the concept of Shannon's entropy to Hydraulic Engineering. The entropy concept is further developed in an attempt to predict the transverse distribution of boundary shear stress in circular open channels. The approach is also extended and applied to circular channels with a flat bed and trapezoidal channels, and the Lagrange multipliers, k, found by recourse to empirical equations. Doubts are expressed concerning the value of the entropy approach to such problems.

Comparison of five different models in predicting the shear stress distribution in straight compound channels

“…Sterling and Knight [12] used the Lagrange coe cient to maximize the Shannon entropy and introduce an equation to predict shear stress. Based on this method, the shear stress distribution in a compound channel with the section shown in Figure …”

“…where w (y) and w (y 1 ) are shear stress at the wall of the main channel and oodplain, respectively; b (z) and b (z 1 ) are the shear stress on the bed of the main channel and oodplain, respectively; max(wfp) , max(bfp) , max(wm) , and max(bm) are the maximum shear stress at the wall and bed of the oodplain and main channel; and y c and z c are constant values of 5 mm [12]. Eqs.…”

“…Studies have shown that it is di cult to determine the boundary shear stress distribution in an open channel [4][5][6][7][8][9]. To overcome this di culty, empirical, analytical, and simpli ed computational methods have been conducted by several researchers [10][11][12][13][14][15][16][17][18][19][20][21]. Still, even with sophisticated turbulence models, it is challenging to accurately calculate local shear stress values.…”

“…In this method, the impact of secondary ow structures and the transfer of momentum between the main channel and its oodplains are neglected. The Shannon entropy concept has been applied by several researchers to predict the shear stress distribution in open channels [12,[21][22][23]. Sterling and Knight [12] developed a new approach to predict the distribution of boundary shear stress in open channels (SKM) based on Shannon entropy.…”

“…The Shannon entropy concept has been applied by several researchers to predict the shear stress distribution in open channels [12,[21][22][23]. Sterling and Knight [12] developed a new approach to predict the distribution of boundary shear stress in open channels (SKM) based on Shannon entropy. Although their proposed method has limitations in re ecting the hydraulic behaviour of open channels, the results indicated that the method could estimate shear stress distribution reasonably well, but it must be developed for practical applications.…”