Iteration using while loop

Hi i am struggling with the question below, can someone help please?

For pressure drop in pipe flow the pipe friction factor, Cf, is an important parameter. To use software to solve problems graphical forms relating Re to Cf are not that helpful. Coulson & Richardson Vol 1 give some equations relating Re to Cf, some of them are implicit (rather than explicit)

THE EQUATION ------ Sigma^(-0.5)=2.5*ln(Re*(Sigma^0.5))+0.3

The equation is implicit as it cannot be rearranged to get Φ = f(Re). However if we can get the equation in a form Φ = f(Re, Φ), then can try to find Φ by a substitution and iteration method (basically guessing the answer).

Procedure (i) manipulate the eqn to get Φ = f(Re, Φ) - SYMBOL IS SIGMA

(ii) guess a value of Φ, Φi

(iii) the next guess of Φ, Φi+1= f(Re, Φi)

(iv) repeat until Φi+1= Φi to a desired accuracy

Ex 6.3 For a Reynolds Number of 10000, what is the value of Φ?

Hints:

manipulate equation (3) into the form required by (i) above and create a function file to describe it. NB Matlab uses ‘log’ for the natural logarithm (not ‘ln’) and ‘log10’ for base 10 logarithms (not ‘log’).

you will need to think of a logic statement to control your loop – it is probably easiest to use a ‘while’ loop, an adequate desired accuracy is 1e-8 (1 x 10-8).

Answer 1

[Walter Roberson]

Example:

error = -inf;
x = -1;
while error < 0
    x = x + 0.1
    error = x.^3 - 3.*x.^2 + 1
end

x = -0.9000

error = -2.1590

x = -0.8000

error = -1.4320

x = -0.7000

error = -0.8130

x = -0.6000

error = -0.2960

x = -0.5000

error = 0.1250

That is, you initialize your error, and while your error is outside the bounds you want. You change your trial value somehow (the way to determine the new value is important!!), and you update your estimate of the error.

[Walter Roberson]

Note: more common by far would be error would be determined as an absolute value or a value certain not to be negative, and you would normally loop while error > tolerance.

I did not use that approach because I was keeping it simple to show the effect of using a while loop.

[Torsten]

I think somehow the original question got lost.

[Walter Roberson]

The question is about how to do iteration using a while loop, and I show how to do iteration using a while loop.