human
I am working on the file ".ipynb_checkpoints/barriere-capillaire-checkpoint.ipynb".
The first task is:
Profile de succion dans une colonne de matériau poreux soumis à un débit unitaire
Une démonstration similaire a d'abord été publiée parKisch (1959).
\begin{align}
q = k(\psi) \frac{dh}{dz} \
h = z + p = z - \psi \
q = k(\psi) \frac{dz - d\psi}{dz} \
q = k(\psi) (1 - \frac{d\psi}{dz}) \
\frac {q}{k(\psi)} = 1 - \frac{d\psi}{dz} \
\frac{d\psi}{dz} = 1-\frac {q}{k(\psi)} \
dz = \frac{d\psi}{1-\frac {q}{k(\psi)}} \
z(\psi) = \int_{\psi_{min}}^{\psi} \frac{1}{1-\frac {q}{k(\psi)}}d\psi
\end{align}
L'intégrale peut être approximée par:
\begin{align}
z(\psi) = \sum_{i=1}^{n} \frac{\Delta\psi}{1-\frac {q}{k_n(\psi)}}
\end{align}
Can you write Python program for it?
 What is a the Python program you requested?
assistant
#Here is the Python program you requested.

class VerticalFlow(object):
    """
    This class uses the vertical flow model presented by Kisch (1959).
    """
    def __init__(self, model, q, psiMin = 1e-3, zMin = 0, perc = 0.999):
        self.model = model
        self.q = q
        self.psiMin = psiMin
        self.zMin = zMin
        self.perc = perc
        
    def kisch(self):
        # suction vector
        self.psiModel = self.model.hcf()[0]
        self.kModel = self.model.hcf()[1]
        
        #Find the maximal succion that can be found in a column of a por. mat. described by model under flow q
        interpFuncModel = interp1d(np.log10(self.kModel[::-1]), np.log10(self.psiModel[::-1]))
        
        # succion varies from the minimum succion in the model to the maximal succion value psiMax by deltaPsi
        self.psiMax = 10**interpFuncModel(np.log10(self.q))
        
        # recompute the model between psiMin and psiMax
        self.psiNewMod = np.logspace(start = np.log10(self.psiMin), stop = np.log10(self.psiMax),
                                     num = self.model.npoints, endpoint = True)
        newModel = VanGenuchten(thR = self.model.thR, thS = self.model.thS, 
                                aVG = self.model.aVG, nVG = self.model.nVG, mVG = self.model.mVG, 
                                lVG = self.model.lVG, ksat = self.model.ksat, psi = self.psiNewMod)
        
        self.psiKisch = newModel.hcf()[0] # suction vector
        self.kKisch = newModel.hcf()[1] # hydraulic conductivity vector
                
        # delta psi
        self.psiKischB = np.append(self.psiMin, self.psiKisch)
        self.deltaPsiKisch = []
        for i in range(1, len(self.psiKischB)):
            d = self.psiKischB[i] - self.psiKischB[i-1]
            self.deltaPsiKisch.append(d)
        self.deltaPsiKisch = np.array(self.deltaPsiKisch)
        
        # kisch
        zPieces = self.deltaPsiKisch / (1 - self.q/self.kKisch) # pieces to sum
        self.z = []
        for i in range(0, len(self.deltaPsiKisch)):
           ...