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<br />: ~ <br /> <br />12 <br /> <br />an extent that the streamlines are no longer parallel and acceleration <br /> <br />. <br /> <br />effects predominate. In this area, the assumption of uniform flow <br /> <br />. <br /> <br />(hydrostatic pressure distribution) needed for solution of the equation <br /> <br />of gradually varied flow, does not apply. Therefore, comments on <br /> <br />application of the various methods of water surface profile solution <br /> <br />are limited to cases outside the influence of the critical depth line. <br /> <br />The determination of a flow profile can be accomplished by use of <br /> <br />three baaic methoda. These include the graphical integration method, <br /> <br />the direct integration method, and the step method. As its name <br /> <br />implies, the graphical integration method uses a graphical procedure <br /> <br />for integration of the dynamic equation of gradually varied flow. If <br /> <br />Xl snd x2 are two stations in a channel separated by distance x, then <br /> <br />x - x2 - xl <br /> <br />JX2 <br />~ dx <br />Xl <br /> <br />=Jfx2 <br /> <br />Xl <br /> <br />dx <br />-~ <br />~ <br /> <br />(2-5) <br /> <br />. <br /> <br />. <br /> <br />By assuming values of y and computing corresponding values of dx/dy <br /> <br />from the reciprocal of the right hand side of an equation such as <br /> <br />Eq. (2-4), a plot of y versus dx/dy can be constructed and then the <br /> <br />area under the plot graphically integrated to solve for x <br /> <br />The direct integration method of the dynamic equation of gradually <br /> <br />varied flow applies to special cases or simplified conditions, or both, <br /> <br />for integration of the equation. Chow (2) summarizes existing methods <br /> <br />dating from 1848-1954. The summary includes fifteen methods, at least <br /> <br />. <br /> <br />one of which has been adapted to computer solution. Bakhmeteff's method <br /> <br />(1), published in 1912, used a varied flow function to carry out inte- <br /> <br />. <br /> <br />gration by short-range steps. Improvements attempted on Bakhmeteff's <br /> <br />method assumed hydraulic exponents for expressing the section factor <br />