Solve Manning's Equation with Python Scipy library

from scipy.optimize import root

def manningC(d, args):
    Q, w,h,sSlopeL,sSlopeR,nMann,lSlope = args
    #left side slope can be different from right side slope
    area = ((((d*sSlopeL)+(d*sSlopeR)+w)+w)/2)*d
    # wet perimeter
    wPer = w+(d*(sSlopeL*sSlopeL+1)**0.5)+(d*(sSlopeR*sSlopeR+1)**0.5)
    #Hydraulic Radius
    hR = area/ wPer
    # following formula must be zero
    # manipulation of Manning's formula
    mannR = (Q*nMann/lSlope**0.5)-(area*hR**(2.0/3.0))
    return mannR
    
###### MAIN CODE
# the following are input data to our open channel manning calculation
# flow, width, height, left side slope, right side slope, 
# Manning coefficient, longitudinal slope
args0 = [2.5,2,.5,1.0,1.0,.015,.005]
initD = .00001  # initial water depth value

# then we call the root scipy function to the manningC
sol =root(manningC,initD, args=(args0,))    
# print the root found
print(sol.x)

Calculate the centroid of a polygon with python

In this post I will show a way to calculate the centroid of a non-self-intersecting closed polygon.

I used the following formulas,







as shown in https://en.wikipedia.org/wiki/Centroid#Centroid_of_a_polygon .

In the following code, the function receives the coordinates as a list of lists or as a list of tuples.

from math import sqrt

def centroid(lstP):
    sumCx = 0
    sumCy = 0
    sumAc= 0
    for i in range(len(lstP)-1):
        cX = (lstP[i][0]+lstP[i+1][0])*(lstP[i][0]*lstP[i+1][1]-lstP[i+1][0]*lstP[i][1])
        cY = (lstP[i][1]+lstP[i+1][1])*(lstP[i][0]*lstP[i+1][1]-lstP[i+1][0]*lstP[i][1])
        pA = (lstP[i][0]*lstP[i+1][1])-(lstP[i+1][0]*lstP[i][1])
        sumCx+=cX
        sumCy+=cY
        sumAc+=pA
        print cX,cY,pA
    ar = sumAc/2.0
    print ar
    centr = ((1.0/(6.0*ar))*sumCx,(1.0/(6.0*ar))*sumCy)
    return centr