Prepare a pipe network system that transfers water from the upper pipe to the lower pipe. Note that Figure is a plan view and the elevation is constant across all pipes. The static pressure difference between points A and D is designed to be PA - PD = 3 atm (1 atm = 1 standard atmospheric pressure = 101.3 kPa). It is required to make sure that the speed of the flow through every pipe is at least 2 m/s so that there is no sediment build-up.

A square-wave pulse is given in Figure (a) with its corresponding Fourier transform in Figure (b).

The analytical result for the Fourier transform is

If a particular signal has the property a = 5, use a numerical method to evaluate a from the signal F(ω). (This sounds perverse, but pretend you have data for a signal and you don't know the value: at least you know whether your code is any good!) To attempt this, you should calculate a value of ω where either ω is a known function of a or F(ω) is a known function of a. The main numerical method you use should not rely on complex MATLAB functions. You should validate your code using another numerical method and verify your code by using the same numerical method but solving by hand for 3 iterations.

Requirements

You must produce MATLAB code which:

1. Finds the value of a using a numerical method that has been taught in the content.

2. Validates the numerical method using any other numerical method available to you and reports the result to the Command Window.

3. Validates both numerical methods by computing the relative error compared to the analytical solution and reports the result to the Command Window.