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SECTION 2: TRAPEZOIDAL AND CIRCULAR CHANNEL ANALYSIS PROGRAMS <br /> requires that you supply the following items of input data: <br /> 1) The Flow Rate in the channel. <br /> 2) The Manning's Roughness Coefficient for the channel. <br /> 3) The Channel Side Slopes and Channel Bottom Width for Trapezoidal Channels. <br /> 4) The Channel Diameter for Circular Channels. <br /> Each of these items is described in connection with the Normal Depth procedure <br /> earlier in this manual. <br /> 2.5.3 Description of Results of Critical Depth Procedure <br /> 2.5.3.1 Critical Depth <br /> This program computes the critical depth by an iterative procedure, which <br /> arrives at a value which satisfies the following equation: <br /> 2 3 <br /> Q = A <br /> g T <br /> in which <br /> Q - Flow Rate in the channel, in cfs <br /> g - Acceleration due to gravity (32.2 ft/sec/sec) <br /> A - Cross-sectional area of flow (square feet) <br /> T - top width of flow (feet) <br /> For trapezoidal channels, the Newton-Raphson method of locating roots of a <br /> polynomial equation is used to solve the equation for the Critical Depth.. This <br /> method gives a quick and efficient solution which is accurate to within 0.001 <br /> foot. <br /> For circular channels, the Critical Depth is initially assumed to be at the <br /> midpoint of the pipe. A binary search algorithm is then used to converge to <br /> the actual Critical Depth. Successively smaller steps are used to adjust the <br /> estimated critical depth to the actual value to within 0.0001 foot. This <br /> method of solution is very stable and is highly accurate even for Critical <br /> Depths of 99% or more of the pipe depth. <br /> 2.5.3.2 Critical Slope <br /> Critical Slope is the channel slope at which Normal Depth equals Critical <br /> Depth. Critical Slope is computed by inserting the Critical Depth in Manning's <br /> Equation, which is re-arranged as follows: <br /> (1/2) On <br /> S (2/3) <br /> 1.486AR <br /> DODSON & ASSOCIATES, INC. THE DODSON HYDRAULICS LIBRARY, PAGE 21 <br />