Unformatted text preview: HOMEWORK – 5 SUBROUTINES 1. Three circular subdivisions need to be cleared for construction. The XYZ tree cutting company charges $100 per square feet to clear trees and to stabilize the area, and would charge $5 per linear ft to install fence in that area. Approximate radii of the sites are estimated to be 50, 75, and 100 ft. This problem will be solved as a part of the lab work. 5 2
2. Develop a visual basic program with subroutine to evaluate the integral I x ln( x)dx using the 1 trapezoidal rule. Use n = 10. This is your lab problem 2. Refer to lab for further details. The formula for computing an integral using trapezoidal rule is given by (check the class notes for derivation): n 1 f ( x0 ) 2 f ( xi ) f ( xn ) ba
i 1 Use the following pseudo code to write the program: I 2 n . Get the inputs a, b and n Calculate the interval, h = (b‐a)/n Write a subroutine which takes the values of x as input and outputs fx Sub myfunction(x as Single, fx as Single) fx=x^2*log(x) End Sub Call the subroutine “myfunction” to evaluate the value of the function at x0 (a) and xn (b) Compute the value of f(x) at every xi (=a+h*i) and compute their sum (use loop) Compute I = h*(f(a)+2*sum+f(b))/2 Output result. 3. Develop a visual basic program for the above problem using a function to evaluate the integral 5 I x 2 ln( x)dx using trapezoidal rule. This is your lab problem 4. Also, see ppt slides for details. 1 4. Modify the above code with subroutine to solve the following problem: 1 x 0.1 (1.2 x)(1 e20( x 1) )dx . Try your program for n = 10, 20, 30. Compare your answer with the 0
analytical solution (true value = 0.602297) and calculate percentage error for each n. 1 5. The permutation, P(n,r) and combination, C(n,r) are given by the following formulae: P (n, r ) n!
n!
, C (n, r ) (n r )!
r !(n r )! Write a Visual Basic program that evaluates the permutation and combination for a given n and r. The program should contain a subroutine that evaluates the factorial. Check your program for n = 10 and r = 4. 5 2
6. Develop a visual basic program with subroutine to evaluate the integral I x ln( x)dx using 1 Simpson’s rule. Check your program for n = 10, 16, 20 and calculate the percentage error. The formula for computing an integral using Simpson’s rule is given by (check the class notes for derivation): f ( x0 ) 4 f ( x1 ) f ( x2 ) f ( x2 ) 4 f ( x3 ) f ( x4 ) I 2h 2h ... 6
6 f ( xn 2 ) 4 f ( xn 1 ) f ( xn ) 2h 6 Use the following pseudo code to write the program: a) Get the inputs a, b and n b) Calculate the interval, h = (b‐a)/n c) Start a FOR loop from i =1 to n‐1 with step 2 d) Compute xi‐1 = a + h * (i ‐ 1), xi = a + h * i, xi+1 = a + h * (i + 1) e) Compute the value of function f(x) at xi‐1 ,xi ,xi+1. f) Compute the term= h * (f(xi‐1) + 4 * f(xi) + f(xi+1)) / 3 g) Compute the sum of the terms. h) Output the result. 7. Develop a visual basic program for Richardson integration using subroutines for the integral
5 I x 2 ln( x)dx . Check your program for n = 10, and calculate the error percentage. Your program 1 should contain one subroutine to evaluate the function and one subroutine to evaluate the area using the trapezoidal rule. Use the following logic in the main program: n1 = n
n2 = 2 * n
Call traprule(a, b, n1, area1)
Call traprule(a, b, n2, area2)
integration = (area2 * 4  area1) / 3 Your traprule subroutine should have the logic to calculate the trapezoidal rule: 2 h = (bb  aa) / nn
Call myfunction(aa, fa)
Call myfunction(bb, fb)
For i = 1 To nn  1
x = aa + h * i
Call myfunction(x, fx)
fxSum = fxSum + fx
Next i
area = h * (fa + 2 * fxSum + fb) / 2 8. The electric company charges its customers according to the following rate schedule: 8 cents a kilowatt‐hour(kwh) for electricity used up to the first 300 kwh; 6 cents a kwh for the next 300 kwh (up to 600 kwh) 5 cents a kwh for the next 400 kwh (up to 1000 kwh) 3 cents a kwh for all electricity used over 1000 kwh Write a subroutine to calculate the total charge for each customer. Develop a visual basic program that calls this subroutine for the following data: Customer number 123 205 464 596 601 9. The head loss in a pipe is given by: H loss KWH used 47
1015
600
327
915 fLV 2 2 gD Where L is the length of the pipe, V is the velocity in the pipe, g is the gravitational constant, D is the diameter and f is the friction factor. The friction factor for laminar flow (Re <=2300) is given by: f 64 Re The friction factor for turbulent flow (Re>4000) is given by the following explicit approximation (Haaland equation): 6.9 / D 1.11 1 1.8log10 f Re 3.7 Where Re is the Reynolds number, ε is the roughness and D is the diameter of the pipe. a) Develop a visual basic program to calculate the head loss using subroutines. The subroutine should calculate the friction factor. (Note: log10 x 0.43429*ln x ). b) Run your program for Re = 500,000 and ε/D=0.004, D = 1.2ft, g = 32ft/s2, V=4.17ft/s; L = 100ft. c) Run your program for Re = 1200, D = 0.5ft, V = 0.024 ft/s, L = 50ft, g=32ft/s2 3 ...
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This note was uploaded on 11/14/2011 for the course CE 3010 taught by Professor Clement during the Fall '09 term at Auburn University.
 Fall '09
 Clement

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