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<br />The value of the velocity-head coefficient, k, in equation 6 depends <br /> <br />on whether the subreach is hydraulically contracting or expanding. <br /> <br />Because al I cross sections were of simple trapezoidal shape and there- <br /> <br />fore required no subdivision, it was assumed that no adjustment to the <br /> <br />velocity head was required to compensate for the variation of point <br /> <br />velocities within the cross section. Consequently, whether a subreach <br /> <br />was considered to be hydraul ical ly contracting or expanding depended <br /> <br />entirely on the relative size of the upstream and downstream cross- <br /> <br />sectional areas. If the area of the upstream cross section was equal <br /> <br />to, or greater than, that of the downstream section, k was assumed to <br /> <br />equal 0; if the upstream area was smaller than the downstream area, k <br /> <br />was assumed equal to 0.5. <br /> <br />. The friction slope, 5, to be used in the Manning equation is thus <br /> <br />5 = ~ = <br />L <br /> <br />~h+~h -k(~h ) <br />v v <br /> <br />(7) <br /> <br /> <br />defined as: <br /> <br />L <br /> <br />where ~h is the difference in water-surface elevation at the two sections <br /> <br />and L is the length of the reach. <br /> <br />I <br /> <br />,;t/ <br />