​​ MCD4140 Assignment Page 1 of 6 MCD 4140: Computing for Engineers Assignment Trimester 1, 2016 Status: Individual Hurdle: There is no hurdle on assignment Weighting: 10% Word limit: No limit Due date: By 12.00pm on Monday 09/05/2016 via Moodle. INSTRUCTIONS This assignment should be completed INDIVIDUALLY. Plagiarism will result in a mark of zero. Plagiarism includes letting others copy your work and using code without citing the source. If a part of your code is written in collaboration with classmates, say so in your comments and clearly state the contributions of each person. Download template.zip from Moodle and update the M-Files named q1a.m, q2.m, etc. with your assignment code. DO NOT rename the M-Files in the template or modify run_all.m. Check your solutions to Q1 and Q2 by running run_all.m. The teacher will only run the run_all.m file when marking. SUBMITTING YOUR ASSIGNMENT Submit your assignment online using Moodle. You must include the following attachments: A ZIP (NOT .rar or any other format) file named after your student ID containing the following: a. An assignment coversheet with your name and ID b. Solution M-Files for assignment tasks named: q1.m, q2a.m, etc. c. Any additional function files required by your M-Files d. All data files needed to run the code, including the input data provided to you We will extract (unzip) your ZIP file and mark you based on the output of run_all.m. It is your responsibility to ensure that everything needed to run your solution are included in your ZIP file. MCD4140 Assignment Page 2 of 6 MARKING SCHEME This assignment is worth 10% (1 Mark == 1%). Code will be graded using the following criteria: 1) run_all.m produces results automatically (no additional user interaction needed to fix your code) 2) Your code produces correct results (printed values, plots, etc…) and is well written. ASSIGNMENT HELP 1) Hints and additional instructions are provided as comments in the assignment template M-Files 2) Hints may also be provided during Lectures/Labs QUESTION 1 [6 MARKS] Background information The transport of liquids in pipes is ever present in the real world. Examples include transporting drinking water from a dam to a town water supply, pumping oil in an undersea pipeline, transporting milk in a dairy. All of these applications and many others require careful design of the system including choosing the best pipe diameter and the sizing of the pump to ensure both efficient pumping at the same time as having an ability to turn the flow rates up or down during times of high and low demand. Pipe flow is characterised using two derived parameters. First we define a dimensionless group called the Reynolds number (Re) that is defined by Eqn 1 In Eqn 1, ρ is the fluid density, U is the mean fluid velocity in the pipe (given by the volumetric flow rate Q m3s-1 divided by the pipe cross-sectional area πD2/4), D is internal pipe diameter and µ is the dynamic viscosity (measured in Pascal seconds). Second we define the Darcy friction factor that relates the pressure gradient (dP/dx) required to drive the flow to the speed of the flow. The friction factor f is given by Eqn 2 You are going to install a pumping system to transport water from a ground water desalination plant to a small remote community in a 50mm (ID) plastic pipe, but you don't know what pump you need to use. You search your company's internal reports and come up with lots of data where previous research has measured the pressure drop in a smooth-walled pipe as a function of the applied pressure gradient. You have put all this data into a single file called "Pipe_Data.txt". Each line has the result of one measurement and has the following format MCD4140 Assignment Page 3 of 6 Line 1 – Column headers Line 2 – Column units (e.g. mm, seconds, kg, etc.) Line 3 – Pipe diameter, Mean velocity, Fluid density, Fluid viscosity, Pressure gradient Line 3 – Pipe diameter, Mean velocity, Fluid density, Fluid viscosity, Pressure gradient " " " " " " " " " " Line N+2 – Pipe diameter, Mean velocity, Fluid density, Fluid viscosity, Pressure gradient You are not sure how to analyse this data and see in your fluid mechanics text book that the data for smooth walled pipes can be "collapsed" into a form where the friction factor is related to the Reynolds number in the following way Eqn 3 If you can determine appropriate values for "A" and "n" in Eqn 3 from your data, then you will be able to determine the pressure gradient you need. Question 1 NOTE: Where your MATLAB code is required to do something (plot, print, etc.) I have explicitly stated "OUTPUT:" Q1a. Read in the pipe flow data from "Pipe_Data.txt". Then you need to calculate the Reynolds number and the friction factor for each of the measured values in the file. (IMPORTANT NOTE: You MUST ensure that all units in your data are consistent, i.e. S.I. units – you cannot mix units) OUTPUT: Create a figure with two sub-plots (one above the other). In the top sub-plot, plot f vs Re as a linear-linear plot, with each data point as a solid green circle (do NOT join these symbols with a line). In the lower sub-plot plot the same information in log-log coordinates (using the MATLAB plot command loglog). Plot each data point as a solid red circle (again, do NOT join these symbols with a line). MCD4140 Assignment Page 4 of 6 Q1b. Write a MATLAB function that will undertake a non-linear least squares fit to a set of data points (xi ,yi). You can use polyfit inside this function or write your own least squares code as you wish, but you will need to choose which type of non-linear model fit is appropriate. Use this MATLAB function and fit a curve to ALL of your data in order to estimate the coefficients "A" and "n" in Eqn 3 and return these two values as the output arguments of the function. OUTPUT: Write the kind of non-linear regression you are using to the command window. OUTPUT: Create a figure. Plot your best fit function (using a solid black line with a line width 2) AND the data points with solid green circles. OUTPUT: Write the coefficients "A" and "n" that your model predicts, and the coefficient of determination (r2) of the fit into the top sub-plot. Q1c. The Colebrook equation is a different correlation that relates the friction factor to the Reynolds number for turbulent flow (we will define turbulent flow here as being Re > 2,500). It is usually regarded as more accurate than the power law expression you found in the previous equation. For a smooth pipe it is written Eqn 4 This is an implicit equation that cannot be solved analytically for the friction factor, f. However, you can use a root finding algorithm to find f if you know Re. Write a function called FrictionFactor that calculates the friction factor using the Colebrook equation and an input value of Re in the turbulent region. If Re is in the laminar regime (i.e. Re<=2500), the function should print an error message (i.e., there should be error checking INSIDE the function). You may use any root finding method you like (including in-built MATLAB functions). OUTPUT: In script Q1c, put the friction factor calculation inside a while loop that asks for an input Reynolds number and then prints to the screen the friction factor from your function "FrictionFactor.m" and also the percentage difference between your power law fit in Q1b and the value from the Colebrook equation. You will also need to implement a sensible criteria to stop the while loop so that the run_all.m script can continue to execute and do Question 2. NOTE: The values you calculated in Q1a and Q1b will needed to be used in Q1b and Q1c. You can pass these as output/input parameters or use the "global" command. MCD4140 Assignment Page 5 of 6 QUESTION 2 [3 MARKS] Assuming that you are part of a project team in a Telecom company, your project is focusing on the following wireless communications between a base station and a mobile handset. Assuming the Base station is transmitting a set of binary bits x = [0 0 0 0 1] to the mobile handset, what you expect is to receive the same signal x at the mobile handset. However, due to surrounding noise, the recovered message in mobile handset is y = [1 0 1 0 0] ≠ x. Comparing transmitted signal x and received signal y, they are different in 3 digits (marked in red), or we can say that there are 3 bits in error in y. Hence the error rate in this wireless communication is 0.6 (i.e., 5 bits are transmitted and 3 bits are in error). Q2a) Now we transmit a set of 100 bits from the base station to mobile handset, and the transmitted data is saved to the file transmitted_bits.txt. The recovered signal in the mobile handset is stored in the file received_bits.txt. Now, write a MATLAB code to load both transmitted_bits.txt and received_bits.txt data into MATLAB. Then compute the error rate in this wireless communication. OUTPUT: Using the command 'fprintf' to print out the error rate as a floating point number with two decimals and start a new line after this print out. Q2b) Now we consider the scenario that the Base station communicates with many mobile users, say 10 users. ) ) ) ... ) ) ) ) ) ) MCD4140 Assignment Page 6 of 6 Then we measure the received signal-to-noise ratio (SINR) at each mobile receiver. Normally the SINR data is measured in dB (decibel). If the SINR is greater than or equal to a given Threshold T, we say this mobile is in coverage and can work properly. Otherwise, we say that this mobile is in outage and cannot work properly. We have measured the received SINRs at those 10 mobile terminals, and we saved the SINR values in the text file SINR.txt. Assuming that our threshold T is 1 dB, write a MATLAB code to load SINR.txt. OUTPUT: Create a figure where the x-axis is the mobile number (i.e. 1, 2, etc.) and the y-axis is the mobile SINRs. The plot will use red circles as data markers with no line in between. Add the title 'Received SINRs' to the figure. Label the x-axis as 'User number' and the y-axis as 'SINR'. Then find out how many users are in Outage and how many users are in Coverage. OUTPUT: Print out both results using 'fprintf' and '%d'. NOTE: After completing parts (a) and (b), you should end up with only ONE M-file for question 2. Good Programming Practices (Coding style and Comments) [1 Mark] (END OF ASSIGNMENT)