OPTIMIZATION TECHNIQUES ASSIGNMENT

Jun 17th, 2015
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Consider flow through an open rectangular channel. Using Maning’s formula, the various relationships for the flow can be combined to produce this equation

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OPTIMIZATION TECHNIQUES ASSIGNMENTSubmitted by: Group Members:Name: Nitesh Kumar Suresh Kumar Jat (2011UCE1155)ID: 2011UCE1131 Nitesh Kumar (2011UCE1131)Group: A1. NEWTON RAPHSON (EXCEL):Considering the following function as our problem:f(x) = - 12 - 21x + 18x2 24 x3Differentiating with respect to x:f(x) = - 21 + 36x -72x2Now, xi+1 = xi f(x)/f(x)xi+1= xi (- 12 - 21xi + 18xi2 24 xi3) / ( - 21 + 36xi -72xi2)Error can be calculated as {(xi+1 - xi)/ xi} * 100 %Using theseformulas in excel as shown in figure: The value comes out to be -0.382299009 after 7 iterations.2. CASE STUDY (CIVIL):Consider flow through an open rectangular channel. Using Manings formula, the various relationships for the flow can be combined to produce this equation:Q = { S1/2 (BH)5/3 } / { n (B+2H)2/3}Where,Q = DischargeS = Slope of channel bottomB = Width of the channelH = Depth of water in the channeln = Manings Coefficient.Thus, the equation now contains a single unknown H along with the given value for Q and the channel parameters (n, S, and B). Although we have one equation with an unknown, it is impossible to solve explicitlyfor H. However, the depth can be determined numerically by reformulating the equation as:f(H) = { S1/2 (BH)5/3 } / { n (B+2H)2/3} Q = 0Consider the following values: Q = 5 m3/sB = 20 mn = 0.03S = 0.0002f(H) = 0.471405 { (20H)5/3 } / {20+2H}2

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