Pandas - Operations between rows - distance between 2 points

If we have a table with a column with xy coordinates, for example:

We can get the difference between consecutive rows by using  Pandas SHIFT function on columns.
".shift(-1)" will roll the rows 1 position backwards, and ".shift(1)" or simply ".shift()" will roll down your column by 1 position of the rows.

In our example, df1['x'].shift() will return:

0              NaN
1    455395.996360
2    527627.076641
3    536278.269190
4    553932.441097
5    568699.553239
6    569709.130272
7    573016.302437
8    575141.096777
9    580107.934566

if we want to calculate the euclidean distance between consecutive points, we can use the shift associated with numpy functions numpy.sqrt and numpy.power as following:

df1['diff']= np.sqrt(np.power(df1['x'].shift()-df1['x'],2)+
   np.power(df1['y'].shift()-df1['y'],2))

Resulting in:

0              NaN
1     89911.101224
2     21323.016099
3    204394.524574
4     37767.197793
5     46692.771398
6     13246.254235
7      2641.201366
8     15153.187527
9     15853.974422

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)