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<br />\ <br />~j, <br />i <br />~d <br />i <br />, <br /> <br />Equation 2-12 contains one independent variable, Q, and seven dependent <br /> <br /> <br />variables. For a given cross section geometry, the area terms are <br /> <br />functions of the water surface elevation: the a terms are functions <br /> <br />\ <br />I, <br />I, <br />I, <br />I, <br />1 <br />I' <br />{ <br /> <br />of WS and hydraulic roughness across the section; and the energy loss <br />term is calculated with the Manning Equation and equations for other <br />losses (e.g., expansion, contraction, weir and bridge). The sixth <br />independent equation comes from a functional relationship between WS <br />and Q for starting conditions. The final independent condition re- <br />quired to solve equation 2-12 is the constraint, critical depth. <br />Critical depth is that depth of flow that would prOduce the minimum <br />total energy head. and it depends on cross section geometry and water <br /> <br />, <br />~ <br />" <br /> <br />, <br />" <br /> <br />" <br />, <br />; <br /> <br />discharge. Flow is classified as either subcritical or supercritical <br />depending upon whether the starting water surface elevation is above <br />or below critical depth. All subsequent calculations are confined <br />to the same side of critical depth as the initial value. The depth- <br />energy relationship is discussed in section 3.02 under "Effect of <br />Gravtty. on state of flow and in section 5.12 under "Critical Depth <br />Calculations." <br /> <br />, <br />, <br />i <br />, <br /> <br />! <br />i <br /> <br />It <br />t <br />. <br /> <br />2.09 <br /> <br />t <br />