Applied Numerical Engineering Assignment-

You have to show your m-files and printing output.

The discharge coefficient (C) of an orifice (shown in Fig. 1) as you will learn in Fluid Mechanics is defined as the ratio of actual mass flow rate and theoretical mass flow rate and is given by Eq. (1)

C = 0.5959 + 0.0312β^2.1 - 0.184β⁸ +  91.71β^2.5/Re^0.75           (1)

where  β = d/D denotes the ratio of diameters and Re indicates Reynolds number. 

You are required to determine the value of β at a Reynolds number of Re=10⁴ that yields a discharge coefficient of C = 0.5N where N is 9 So C = 0.59.

Use (a) a graphical method to locate the initial estimate and (b) the Bisection method with tolerance (accuracy) of 10^-4 and (c) Newton Raphson method with tolerance 10^-4.

To do this you are required to perform the following tasks:

1. To use a graphical method you need to create a function in Matlab. Run this function and create a plot which allows you to find a good starting point for β_ans.

2. To use the Bisection method you need the code bisect.m. Verify that the number of iterations you obtained  for the Bisection method  from  Matlab  can be obtained using the  formula N = log2(E_i/E_r). Using hand calculations perform 3 iterations with the Bisection method using the same initial range as in Matlab. What accuracy is achieved after 3 iterations?

3. To use Newton Raphson you need the code newtraph.m. Using hand calculations perform 3 iterations with one of the initial range value. Compare your answer with Bisection method.

Matlab code + calculation (can be hand written) + 2 pages report.

Attachment:- Assignment Files.rar