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KKKQ 3013 PENGIRAAN BERANGKA

KKKQ 3013 PENGIRAAN BERANGKA. Assignment #4 – Numerical Derivatives & Integrals 05 September 2007 8.00 pm – 10.00 pm. Assignment #4 (adapted courtesy of ref. [1]).

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KKKQ 3013 PENGIRAAN BERANGKA

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  1. KKKQ 3013PENGIRAAN BERANGKA Assignment #4 – Numerical Derivatives & Integrals 05 September 2007 8.00 pm – 10.00 pm

  2. Assignment #4 (adapted courtesy of ref. [1]) In an experiment, the internal flow through a 30 cm diameter pipe was measured at several radial distance from its center. The measurement of the fully developed flow is summarised in the following table (r is measured outward from the center of the pipe): a) Fit a quadratic polynomial curve to the velocity data b) Find the volumetric flow rate (Q) of the pipe based on the best fit curve for velocity per (a) above. Estimate the flow rate using (i) 3/8 Simpson’s rule (with 3 segments) and (ii) 4-point Gauss quadrature (R is radius of pipe) c) Assumming the velocity profile in (a) is accurate, find the exact flow rate and determine the relative true error of both numerically estimated flow rate. Is a 4-point gauss quadrature more accurate than a 2-point gaus quadrature ? [1] Chapra, S.C & Canale, R.P, Numerical Methods for Engineers, McGraw-Hill 5th ed. (2006) Week 9

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