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    <p>This works fine. I've done a few things here. First, I've used a simpler definition of the function using the global variables you've defined anyway. I find this a little nicer than passing the args= to the solvers, it also enables easier use of your own custom solvers if you ever need something like that. I've used the generic <code>root</code> function as an entry point rather than using a particular algorithm - this is nice because you can simply pass a different method later. I've also fixed up your spacing to be as recommended by <a href="http://www.python.org/dev/peps/pep-0008/" rel="nofollow">PEP 8</a> and fixed your erronious rewriting of the equation. I find it more intuitive simply to write LHS - RHS rather than manipulate as you did. Also, notice that I've replaced all the integer literals with 1.0 or whatever to avoid problems with integer division. 0.02 is regarded as a pretty standard starting point for the friction factor.</p> <pre><code>import numpy from scipy.optimize import root w = 10.0 d = 0.22 rho = 1.18 ni = 18.2e-6 Re = w*d*rho/ni k = 0.2e-3 def f(x): return (-2*numpy.log10((2.51/(Re*numpy.sqrt(x))) + (k/(3.71*d))) - 1.0/numpy.sqrt(x)) print root(f, 0.02) </code></pre> <p>I must also mention that fixed point iteration is actually faster than even Newton's method for this problem. You can use the built-in fixed point iteration routine by defining <code>f2</code> as follows:</p> <pre><code>def f2(x): LHS = -2*numpy.log10((2.51/(Re*numpy.sqrt(x))) + (k/(3.71*d))) return 1/LHS**2 </code></pre> <p>Timings (starting further from the root to show speed of convergence):</p> <pre><code>%timeit root(f, 0.2) 1000 loops, best of 3: 428 µs per loop %timeit fixed_point(f2, 0.2) 10000 loops, best of 3: 148 µs per loop </code></pre>
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    1. POsolving colebrook (nonlinear) equation in python
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    1. COHello chthonicdeamon, and thank you for your input. I have some questions. 1.Can you please elaborate this "I've used the generic root function as an entry point rather than using a particular algorithm - this is nice because you can simply pass a different method later." 2. Yes, thank you, my equation was dumb. 3. So if I understand correctly, fixed-point method is pretty much what I would do manually, like I said in the first post? 4. I will edit if I have more. You have been a great help. Thank you
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    2. CO1. If you look at [the documentation for scipy.optimize.root](http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.root.html), you will see that the various algorithms are selectable from a parameter, rather than having to change the actual function name. 3. Pretty much, but the function wraps the convergence procedure.
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