Warning of Application of the Chezy-Manning Formula Regardless of Channel Shape

Abstract

The way of the Chezy formula derivation implies a straight uniform channel with an identical velocity distribution along cross-section, i.e. a wide uniform rectangular channel with uniform lining. However to apply it for natural river channels this restriction are relaxed. The reasons for that is the lack of alternative for depth-discharge rating curve derivation applicable for any channel shape in case of a small number of flow discharge measurements and an encouragement from authors of hydrologic books stating lack of definite evidence about the shape of a channel as an important factor affecting the value of n Manning coefficient. In fact the influence of shape may be overshadowed by other factors usually existing in natural channels like irregularities along their length, nonuniform lining,…

From human knowledge got during the ages of irrigation practice comes that for steady state in a channel with uniform lining and without flow obstruction:

• (1) any increase of water level is related with increase of flow discharge;

• (2) an increase of channel width above any level causes an increase in flow capacity for any other level above it.

The scope of the paper is a mathematical analysis of the Chezy formula for steady flow in an uniform symmetric channel with constant slope-friction factor focused on investigation of both axioms. A channel is assumed to be filled up to a certain level called an initial level and the analysis is made above this level with the corresponding initial shape defined by flow area, wetted perimeter and width of water surface. The problem of determination of the channel shape above initial level for given rating curve of stage-flow discharge or flow area-flow discharge, i.e. an inverse solution of the Chezy formula, is posed and then solved for selected forms of rating curves and of initial shapes. It is demonstrated that the Manning roughness shall be dependant on channel shape and on flow depth if both axioms are to be fulfilled by the formula.

The paper is addressed as a warning of unlimited in channel shape use of the Chezy formula and it may explain one of the reasons of difficulties faced in an interpretation of the roughness coefficient n — gauge height relationship in natural river channels.