ENGR Socolofsky

Transcription

1 ENGR Socolofsky Date : due 9/3/2018 at 12:40 p.m. Engineering Lab I - Computation Lab Assignment #01b Writing Your Own Programs Return your solution (one per group) as outlined in the activities below by the date and time shown above. Please show all your work and follow the rules outlined in the course syllabus. The work for this part of the Lab assignment is expected to be done individually and both in Lab and at home. This lab assignment is adapted from the assignment created by Dr. John Keyser for the pilot version of this course. In this lab, you will continue practicing how to create Python programs using the PyCharm IDE, how to find documentation for new Python commands through online resources, and to become flexible with the print statement. After you complete all parts of this assignment, you should create a single.zip archive of your three program files and submit it. For each of your programs, be sure that you: Include a comments block at the top of each program that list the name of the program, a short description of the program, and your authorship details List all import statements as the first line of executable code For several of the items below, you will have to find equations on the internet or in books. In the comments in your program before each equation is used, list the reference. For instance, you may have: # Compute the volume of a pyramid. Use the equation given at # print( The volume of a pyramid of base 2.5 units squared and height 4 units is: ) print( V = 1/3 b^2 h ) print(1 / 3 * 2.5 * 2.5 * 4) 1. Program 1: Engineering Formulas Write a program that outputs each of the following items on subsequent lines. You will probably need to look up some of the formulas for some of these items online (it is fine to do so!). In each case, your program should print out a description of the problem, the mathematical expression used to calculate the value, and the result obtained. You should not just print the final value. We will ignore units in these equations. Write a program to print the following:

2 1. Your name, UIN, and section number of ENGR 102 that you are enrolled in 2. A sentence giving some interesting fact about yourself 3. A sentence about your expectations for this course and about programming in general 4. The voltage across a conductor with resistance 20 and a current of 5. Ohms Law states that the current through a conductor between two points is directly proportional to the voltage across the two points. 5. The kinetic energy of an object with mass 100 and velocity 21 The Kinetic Energy of an object is the energy that it possesses due to its motion. standard unit of kinetic energy is the joule. The 6. The Reynolds number for a fluid with velocity 0.5 and kinematic viscosity , with characteristic linear dimension 2.5. The Reynolds Number is an important dimensionless quantity in fluid mechanics that is used predict flow patterns in different fluid flow situations. It is the ratio of inertial forces to viscous forces. 7. The energy radiated per unit surface area (across all wavelengths) for a black body with temperature Use for the Stefan-Boltzmann constant. The Stefan-Boltzmann Law describes the power radiated from a black body in terms of its temperature. Specifically, the total energy radiated per unit surface area of a black body across all wavelengths per unit time is proportional to the fourth power of the black body s thermodynamic temperature 8. The production of a well after 20 days, if it had an initial production rate of 100, an initial decline rate of 2/day, and a hyperbolic constant of 0.8. Arps equation is a mathematical model to forecast future production rates of oil and gas wells. 9. The average length of an M/M/1 queue with an arrival rate of 20 and a service rate of 35. An M/M/1 Queue represents the queue length in a system having a single server, where arrivals are determined by a Poisson process and job service times have an exponential distribution. The model is the most elementary of queueing models. 10. The shear stress when a normal stress of 20 is applied to a material with cohesion 2 and angle of internal friction 35 degrees The Mohr-Coulomb Failure Criterion represents the linear envelope that is obtained from a plot of the shear strength of a material versus the applied normal stress. More generally, the MohrCoulomb theory is a mathematical model that describes the response of brittle materials, like concrete or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials somehow follow this rule in at least a portion of their shear failure envelope. 2

3 11. The scattering angle for maximum interference for light of wavelength hitting a crystalline lattice with planes separated by a distance Braggs Law is a relationship describing the angles for coherent and incoherent scattering from a crystal lattice. Specifically, it describes the condition for maximum constructive interference. 2. Program 2: Undefined Function Values You are to write a program that produces several evaluations. Later in the course, we will see other ways of doing this more efficiently, but for now, you should perform these evaluations by simply creating a sequence of print statements that output the desired numbers. Certain functions might be difficult to evaluate at particular values, where infinity or division by 0 are involved, but their values at these extremes can be understood by evaluating them at a number of values that approach 0 or approach infinity. You are going to investigate three of these. Important: You are to think about each of these briefly, and guess what values they will come to before writing your code! Test whether your Python code output is correct by comparing to hand calculations with your calculator for a few test points. You should write a program that, for each of these functions: 1. First prints out a line of text at the beginning, stating what is being shown in the following lines. 2. Next, prints out a line of text saying what you are guessing the final value you calculate will be. There is not a wrong answer here as long as you make a guess the point is to get you to think about the value first, and then see whether your guess was close or not. 3. Finally, prints out a sequence of 8 numbers, representing evaluating the function at 8 different values that approach the undefined limits of the function. 2.1 Function 1 f(x) = sin(x) x is not defined at the value x = 0 since sin(0) = 0 and, thus, we would be evaluating 0/0. You should show successive calculations for f(x) for values of x ranging from 1 to For each evaluation, decrease the value of x by 1/10 of the previous value, hence, x = 1, 0.1, 0.01, etc. 2.2 Function 2 g(x) = 1 cos(x) x 2 is not defined at the value x = 0 since cos(0) = 1 and, thus, we would be evaluating 0/0. Show evaluations for the same sequence of x-values as for f(x). (1) (2) 3

4 2.3 Function 3 h(x) = ( ) x x (3) cannot be evaluated directly at infinity because infinity is not defined. You should show successive calculations for h(x) for values of x ranging from 1 to For each evaluation, increase the value of x by a factor of 10 over the previous value, hence, x = 1, 10, 100, etc. 3. Program 3: A Mathematical Wall Clock One geek item that you can buy are wall clocks where, in place of the standard numbers, the hours of the clock are labeled by some sort of mathematical formula. As a simple example, instead of the number 12, there might be the expression 3(4) printed on the clock face. To see examples of these clocks, perform an internet search for Math Wall Clock or something similar. You are to write a program with expressions that will evaluate to each of the numbers from 1 to Your program should be a sequence of print statements, where each statement contains some mathematical formula. 2. Running your program should output the formula for each number on the clock followed by the numerical values from 1 to 12, in order. Printing 1.0 instead of 1, 2.0 instead of 2, etc. is acceptable. 3. Formulas should be non-trivial, and you should not zero-out sections of formulas. For example, the following would not be good formulas for the number 2: a. 1+1 b. (<complicated mess>) * Your formulas should be different from each other. That is, you should not have the same formula with just a number changed to generate the next number. For example while these might be individually acceptable formulas for 4 and 5, they are not appropriate to be used together: a. 4, evaluated from 3**2-(3+2) b. and 5, evaluated from 3**2-(3+1) 5. Among your 12 formulas, you should make sure to use the following at least once (you may certainly use other functions, or use these more than once): Built in operations: +, -, *, /, **, //, % Parentheses to override order of operations Trig functions: e.g., sin(), cos(), tan() Square root and absolute value: sqrt() and fabs() Logarithm and exponential functions: log() and/or log10() and exp() 4

5 4. Challenge Problem This part of the assignment is optional and is worth extra credit of 10% of the Lab 1b score. Remember to follow all rules for programming assignments in the course syllabus. In Part 2 above, we wrote a print statement eight different times to evaluate each function at eight different x-vales. When we did this, we had to copy our function eight times. If we later found an error in our function, we had to correct that error on eight different lines of the program. In general, this is very bad programming practice and should be avoided. For the challenge problem, write a new version of the code for Part 2 that has each formula written only one time. Python provides several programming tools to do this. As a hint, you can look at the Python keyword for. You may break your forumla into multiple lines, e.g.: x = 0.01 fx = sin(x) / x print(fx) You just should not repeat any of these lines by copy-and-paste. You will have to add some operation to the first line to make the value of x change. The clear advantage of this new approach is that the equation is much more readable than: print(sin(0.1) / 0.1) print(sin(0.01) / 0.01)... print(sin( ) / ) and it is much easier to find and correct a mistake since your formula occurs once. If you choose to complete this activity, include your modified program in your zip files when you turn in your Lab 1b assignment. 5