Essay on Engineering

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UNIVERSITY OF CALIFORNIA, DAVIS DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING COURSE: WATER RESOURCES SIMULATION (ECI 146)
CRN 29727; 4 units INSTRUCTOR: Fabián A. Bombardelli (fabombardelli@ucdavis.edu, fabianbombardelli2@gmail.com, bmbrdll@yahoo.com) OFFICE: 3105, Ghausi Hall Class: Tuesdays and Thursdays-12:10 PM to 1:30 PM (Olson 118) Computer lab: Fridays-1:10 PM to 2:00 PM (Academic Surge 1044) READER: Mr. Kaveh Zamani (kzamani@ucdavis.edu) TEACHING ASSISTANT: Ms. Kate Hewett (kmhewett@ucdavis.edu)

COMPUTER PROBLEM 1: Solution of the Colebrook-White equation via three different methods. Assigned on: Friday, January 13, 2012 Due on: Tuesday, January 24, 2012

Introduction The Moody diagram is the most reliable source of
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Start the iterations with an interval [0,0.1], and determine the number of iterations needed to achieve a tolerance of 10-2. To stop the computations, please compare two successive values of f , as follows: f j +1 − f j f j +1

100 < tolerance

(4)

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2. Indicate the regimes to which the above points pertain (fully rough, smooth or transition), by determining where the points fall on the Moody chart. 3. Please, redo part 1. using the Newton-Raphson method. For this part, it is better to solve for X = 1 f (this will be your new variable; start from Eq. (2), not with Eq. (1), and re-arrange it in terms of X ) and then to back-calculate the resistance coefficient f for each iteration (this will ease the analytical determination of the derivative). As an initial guess, please start with f =0.05. Please, determine the number of iterations needed to achieve a tolerance of 10-2, defined in the same way as in point 1. 4. Compare your results in 1. and 3. with the explicit formula, proposed by Swammee and Jain (1976):

f =

0.25  − log10    ε 5.76    +  3.7 D (ℜ )0.9    
2

(5)

5. Please, redo part 1. using the fixed-point, or iteration- of-a-point method for the first five points in 1. Determine the number of iterations needed to achieve a convergence of 10-2, defined in the same way as in point 1. Start with a guessed value of f =0.05. 6. Please re-do computations of part 1., using tolerances of 10-1, 10-3, and 10-4. 7.