1377 Words6 Pages

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*…show more content…*

Notice that the Reynolds number is given in logarithmic scale. Then, we exit the diagram horizontally, starting from the point defined above, towards the left of the diagram. Page 1 of 4 The Colebrook-White formula was proposed in the first half of last century, and allows for the computation of f . It is expressed as follows: 1 = − 2 log10 f ε 2.51 + 3 .7 D ℜ f (1) where ε or ks indicates the pipe equivalent roughness, D is the pipe diameter, and ℜ is the Reynolds number. The main characteristic of Equation (1) is that it is implicit. It can be observed that the Darcy-Weisbach coefficient appears at both sides in (1), and there is no way of obtaining it solely as a function of known variables. Therefore, a numerical method needs to be applied to compute that coefficient. Equation (1) can be expressed as: ε 1 2.51 + 0.869 ln + 3.7 D ℜ f f =0 (2) where the logarithm on base 10 has been converted to the "natural" logarithm. Multiplying by f , Equation (2) yields: ε 2.51 f 0.869 ln + 3.7 D ℜ f =0 F =1+ (3) which is still an implicit equation. Problem 1 You are asked to: 1. Please, develop a code for the bisection method to obtain the value of f in the following 12 points, well distributed on the Moody diagram: ℜ =3 x 106ε D =0.0008; ℜ =3 x 106- ε D =0.00005; ℜ =3 x 107- ε D =0.00001; ℜ =3 x 107ε D =0.002; ℜ =3 x 107- ε D =0.015; ℜ =3 x 105- ε D =10-10; ℜ =3 x 105ε D =0.002; ℜ

Notice that the Reynolds number is given in logarithmic scale. Then, we exit the diagram horizontally, starting from the point defined above, towards the left of the diagram. Page 1 of 4 The Colebrook-White formula was proposed in the first half of last century, and allows for the computation of f . It is expressed as follows: 1 = − 2 log10 f ε 2.51 + 3 .7 D ℜ f (1) where ε or ks indicates the pipe equivalent roughness, D is the pipe diameter, and ℜ is the Reynolds number. The main characteristic of Equation (1) is that it is implicit. It can be observed that the Darcy-Weisbach coefficient appears at both sides in (1), and there is no way of obtaining it solely as a function of known variables. Therefore, a numerical method needs to be applied to compute that coefficient. Equation (1) can be expressed as: ε 1 2.51 + 0.869 ln + 3.7 D ℜ f f =0 (2) where the logarithm on base 10 has been converted to the "natural" logarithm. Multiplying by f , Equation (2) yields: ε 2.51 f 0.869 ln + 3.7 D ℜ f =0 F =1+ (3) which is still an implicit equation. Problem 1 You are asked to: 1. Please, develop a code for the bisection method to obtain the value of f in the following 12 points, well distributed on the Moody diagram: ℜ =3 x 106ε D =0.0008; ℜ =3 x 106- ε D =0.00005; ℜ =3 x 107- ε D =0.00001; ℜ =3 x 107ε D =0.002; ℜ =3 x 107- ε D =0.015; ℜ =3 x 105- ε D =10-10; ℜ =3 x 105ε D =0.002; ℜ

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