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<br />dealing with vertical and lateral velocity vectors are neglected yield- <br /> <br /> <br />ing the so-called One-Dimensional Energy Equation upon which water <br /> <br /> <br />surface profile calculations are based. <br /> <br />2 <br />0.2V2 <br />--- + <br />2g <br /> <br />P <br />-1.+y <br />y O2 <br /> <br />. 2 <br />0.1 V 1 <br />= - + <br />2g <br /> <br />Pl <br />- + Y + HL <br />y 01 <br /> <br />(2-9) <br /> <br />The One-Dimensional Energy Equation has the same form as the <br />Bernoull i equation and the same terms are present. In addition, an <br />0. term has been added to correct for velocity distribution. The terms <br />in the above equation represent average conditions in the cross section <br />rather than conditions for a single streamtube. <br />The proper application of this equation is left to the judgment <br />of the engineer who must visualize the flow field and insure that it <br />is, in fact, one dimensional. For example, two- and three-dimensional <br />flow occurs at all expansions and contractions. When one-dimensional <br />theory is being used. additional coefficients are often required to <br />account for the increased rate of energy loss in such cases. <br /> <br />Section 2.02. Necessary Independent Conditions and Equations <br /> <br />At this point in its development, equation 2-9 applies equally <br />well to water flowing under pressure (pipe or confined) or in an open <br />channel (surface free to atmosphere). However, the nine unknowns re- <br />quire that eight more independent conditions be specified in order to <br />obtain a solution. These are obtained from functions, constraints or <br />initial conditions which depend upon classification of flow as either <br /> <br />2.06 <br />