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<br />_n ____~_ <br />~--~= <br />------~.- <br /> <br />Section 5.05. The Velocity Distribution Factor <br /> <br />Textbooks on open channel flow often associate the velocity <br />distribution factor, a, with the shape of the velocity profile in <br />the vertical direction. Typical values range from 1.03 to 1.36 for <br />straight prismatic channels. This is insignificant relative to all <br /> <br />the other uncertainties in calculating water surface profiles. How- <br />ever, as illustrated in fig. 5.01, the horizontal distribution of <br />velocity in complex cross sections is quite a different problem and <br />can result in a values greater than 2 or even 20. Analytical pro- <br />cedures account for this horizontal distribution by utilizing the <br />following equation for the velocity distribution factor. <br /> <br />a = <br /> <br />ridQ <br />V2Q <br /> <br />(5-15) <br /> <br />where <br /> <br />dQ = discharge associated with v <br />Q = total discharge <br />V = average velocity for cross section <br />v = point velocity <br />Applying this equation to the horizontal direction requires knowledge <br />about the horizontal distribution of discharge which can be inferred <br />from the horizontal distribution of conveyance as follows: <br /> <br />a = <br /> <br />I 2 <br />.J: Ki(Ki/Ai) <br />1=1 <br />2 <br />Kt<Kt/At) <br /> <br />(5-16) <br /> <br />5.12 <br />