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<br />, <br />, <br />~--<, <br /> <br />co,~"i <br />---~l: <br /> <br />(V2/29)2 + P2/y + Y02 = (V2/29)1 + Plly + YOl + HL (2-8) <br /> <br />~ <br /> <br />The significance of the terms in equation 2-8 is illustrated in <br /> <br />I <br />'. <br /> <br />fig. 2.01 for a streamtube along a channel bottom. <br />The foregoing manipulations are not a rigorous development of <br />Bernoulli's law, but rather they illustrate the relationship be~/een <br />the familiar form of. the equation which appears to have units of feet <br />or meters and the basic physical principles involved. Actually, the <br />units in this equation are ft-lbs/lb (or mkgflkg ) of fluid flowing. <br /> <br />In practice. unit total energy is usually referred to in units of feet <br />or meters. Subsequently, it will be designated by the symbol H for <br />total head. The kinetic energy component is referred to as velocity <br /> <br />head. <br /> <br />The Bernoulli equation is equally applicable to each streamtube <br />in a flow field. A basic assumption in developing this equation was <br />that everywhere in the hypothetical streamtube, velocity vectors were <br />equal in magnitude and parallel in direction. However, when integrat- <br />ing over all streamtubes in a flow field of finite cross sectional <br />area for the general case, neither are velocity vectors parallel nor <br />do they have equal magnitudes. Consequently. three energy equations <br />result--one for each spatial direction. Each equation requires a <br />velocity distribution correction factor, a, to produce a representative <br />velocity head from the distribution of magnitudes. A complete solution <br />of these equations is not necessary for fluid flow problems having a <br />predominant velocity in one direction, and most water surface profile <br />calculations fall into this category. As a result, the equations <br /> <br />2.05 <br />