Example Fixed Point Method, Fluid Flow

import numpy as np

def fp(g, x, tol=1E-5, maxit=10000):
    for k in range(1, maxit+1):
        xnew = g(x)
        if np.linalg.norm(xnew-x)/np.linalg.norm(x) <= tol:
            return xnew, k
        x = xnew
    print(f"No convergence it {maxit} iterations")
    return x, k

def gfluids(vF):
    v = vF[0]
    F = vF[1]

    rho = 1000.   # kg/m3
    mu  = 1E-3    # Pa*s = kg/m*s
    D   = 0.1     # m
    L   = 100.    # m
    eps = D/100.  # m
    dP  = 101325. # Pa

    Re = rho*D*v/mu
    F  = -np.log10(eps/D/3.7 + 2.51*F/Re)
    v  = np.sqrt(2*D*dP/rho/L)*F

    return np.array([v, F])

vFguess = np.array([1.0, 1.0])
vF, nit = fp(gfluids, vFguess)
print(f"v = {vF[0]:.4f} (m/s)")
print(f"f = {1.0/vF[1]**2:.4f}")
print(f"iterations = {nit}")