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TWEET # Untitled a guest May 15th, 2019 80 Never
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1. Q = 1.2;
2. g = 9.81;
3. b = 1.8;
4. h0 = 6;
5. H = 0.075;
6. c0 = 1;
7. c1 = H - h0 -(Q .^ 2 / (2 * g * (b * h0).^2))
8. c2 = 0
9. c3 = (Q .^2 /(2 * g * b .^ 2)
10. %f(x) - the function of the polynomil
11. f=@(x) c0 * x .^ 3 + c1 * x .^ 2 + c3;
12. %function to find the derivative of the polynomial
13. function d = derivative(x)
14.     h = 0.000001;
15.     d = (f(x + h) - f(x)) / h
16.
17. newton_raphson = @(x) x - (f(x) / derivative(x))
18.
19. funcion x = iterate(p, n)
20.     x = p;
21.     for i in 1:n
22.         x = newton_raphson(x)
23.     end
24. fprintf('Approximate head is %.15f',x)
25. end
26. iterate(80, 100)
27.
28. %{ another solution:
29. p = [c0 c1 c2 c3];
30. r = roots(p);
31. h = r(1);
32. fprintf('Approximate head is %.15f',h)
33. %}
34.
35.
36. x = 0:0.1:10;
37. plot(x,f(x))
38. ylim([-10 10])
39. xlabel('The head over pump')
40. ylabel('Bernoulli equation')
41. grid on
42. hold on
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