解决隐式函数并传入三个参数 [英] Solving implicit function and passing in three arguments

问题描述

在上面的等式中，我想求解 f 并传入 Re、D 和 epsilon.这是我的代码如下:

In the equation above I want to solve for f and pass in Re, D, and epsilon. Here is my code below:

import math
from scipy.optimize import fsolve

# Colebrook Turbulent Friction Factor Correlation
def colebrook(Re, D, eps):
    return fsolve(-(1 / math.sqrt(f)) - 2 * math.log10(((eps / D) / 3.7) + (2.51 / Re * math.sqrt(f))), f)

我会使用 fsolve() 还是 solve()?我在 Python 的主站点上阅读了 fsolve() ，但是我不明白它想要的一些输入.先感谢您！

Would I use fsolve() or solve()? I read up on fsolve() on Python's main site, however I don't understand some of the inputs it wants. Thank you in advance!

另外，我使用的是 Spyder (Python 3.6)

Also, I am using Spyder (Python 3.6)

推荐答案

维基百科页面上的达西摩擦"因子公式" 有一个关于Colebrook 方程的部分a>，并展示了如何使用 Lambert W 函数以其他参数表示 f>.

The wikipedia page on "Darcy friction factor formulae" has a section on the Colebrook equation, and shows how f can be expressed in terms of the other parameters using the Lambert W function.

SciPy 实现了 Lambert W 函数，因此您可以使用它来计算 f 而不使用数值求解器:

SciPy has an implementation of the Lambert W function, so you can use that to compute f without using a numerical solver:

import math
from scipy.special import lambertw


def colebrook(Re, D, eps):
    """
    Solve the Colebrook equation for f, given Re, D and eps.

    See
        https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae#Colebrook%E2%80%93White_equation
    for more information.
    """
    a = 2.51 / Re
    b = eps / (3.7*D)
    p = 1/math.sqrt(10)
    lnp = math.log(p)
    x = -lambertw(-lnp/a * math.pow(p, -b/a))/lnp - b/a
    if x.imag != 0:
        raise ValueError('x is complex')
    f = 1/x.real**2
    return f

例如

In [84]: colebrook(125000, 0.315, 0.00015)
Out[84]: 0.019664137795383934

为了进行比较，https://www.engineeringtoolbox.com/colebrook 上的计算器-equation-d_1031.html 给出 0.0197.

For comparison, the calculator at https://www.engineeringtoolbox.com/colebrook-equation-d_1031.html gives 0.0197.

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