08 August 2007 KKKQ 3013 PENGIRAAN BERANGKA Assignment #2 – Systems of Nonlinear Equations 08 August pm – pm

08 August 2007 Week 5 Page 2 Assignment #2 (adapted courtesy of ref. [1]) [1] Chapra, S.C & Canale, R.P, Numerical Methods for Engineers, McGraw-Hill 5th ed. (2006) A fluid is pumped into a network of pipes shown in the figure below. At steady state, flow rate (Q i ) balance must hold. In addition, the pressure drop AROUND the right hand loop must equal zero. The pressure drop in each circular pipe can be computed by where the friction factor f could be approximated by Given fluid density  = 1.23 kg/m 3, dynamic viscosity  = 1.79 x Ns/m 2 and flow rate in pipe 1, Q 1 = 1 m 3 /s. All pipes have diameter D = 500 mm. Determine the flow rates in the remaining pipes using a) False position method and b) Newton-Raphson method. Note: (i) for circular pipe, velocity V = 4Q/  D 2 (ii)  P is –ve if against the flow and (iii) terminate iteration if relative error < 0.1% Hint: Q2 and Q3 should lie between [0,1] m 3 /s

08 August 2007 Week 5 Page 3 Assignment #2 (adapted courtesy of ref. [1]) [1] Chapra, S.C & Canale, R.P, Numerical Methods for Engineers, McGraw-Hill 5th ed. (2006) f(Q 2 ) Q2Q2 f(Q 2 ) = AL 3 (1-Q 2 ) AL 2 Q