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SECTION 2: TRAPEZOIDAL AND CIRCULAR CHANNEL ANALYSIS PROGRAMS <br /> 2.4.2.7 Circular Channel Diameter <br /> If the channel is a circular pipe, then the channel diameter is simply the <br /> inside diameter of the pipe. If the channel is a semicircular flume, then the <br /> channel diameter is the diameter of the circle circumscribing the flume. <br /> 2.4.3 Description of Results of Normal Depth Procedure <br /> 2.4.3.1 Normal Depth <br /> 2.4.3.1.1 Normal Depth in a Trapezoidal Channel <br /> For both trapezoidal and circular channels, the program computes Normal Depth <br /> using an iterative approach to arrive at a value which satisfies Manning's <br /> Equation: <br /> (2/3) (1/2) <br /> Q — 1.486 AR S <br /> n <br /> in which: <br /> Q — Flow Rate in the channel (cfs) <br /> n — Manning's Roughness Coefficient <br /> A — Area of Flow (square feet) <br /> R — Hydraulic Radius (feet) — (Flow Area)/(Wetted Perimeter) <br /> S — Slope of Energy Grade Line (feet per foot) <br /> For a trapezoidal channel, the equation is re-arranged in terms of the depth <br /> of flow. An initial flow depth estimate of 1 foot is substituted into the <br /> equation, and a new approximation is computed for the flow depth. The new <br /> value is compared with the previous approximation, and if the difference is <br /> less than 0.001 feet, the depth is assumed to be the Normal Depth. If not, a <br /> new approximation for Normal Depth is computed as the geometric mean of the <br /> previous two approximations. This method quickly gives a very precise and <br /> reliable value for the Normal Depth of flow in a trapezoidal channel. <br /> 2.4.3.1.2 Normal Depth in a Circular Channel <br /> The first step in determining the Normal Depth in a circular channel is to <br /> compute the maximum flow capacity of the channel. This capacity occurs at a <br /> flow depth of 0.9382 times the channel diameter. (Note: one of the example <br /> problems for the Rating Curve Procedure demonstrates that this is the case.) <br /> If this capacity is less than the required flow rate, then it is not possible <br /> to compute a Normal Depth of flow, and the program gives you a message to that <br /> effect. <br /> Assuming that the channel has sufficient capacity to convey the required flow <br /> rate, this program computes Normal Depth using the same method as the Normal <br /> Depth procedure except that the initial flow depth is assumed to be one-half <br /> of the channel diameter. <br /> This method quickly gives very precise and reliable values for the Normal <br /> DODSON & ASSOCIATES, INC. THE DODSON HYDRAULICS LIBRARY, PAGE 16 <br />