The Nash cascade is a sequence of $N$ linear stores in series, each having a residence time of $K$ time units. The resulting mathematical form of the Nash-cascade is:

$$h(t) = (t/K)^{N-1}*{exp(-t/K)}/{K \gamma (N)}$$

where $h(t)$ is the unit hydrograph in terms of a unit discharge and $\gamma$ is the gamma function $\gamma(N)=(N-1)!$ for integer values $N$. $N$ can also have rational values.

|Nash.py

from pylab import *
from math import *
def Nash(t):
    K = 2.0
    N =  4
    Q = 1/(K*math.factorial(N-1))*(t/K)**(N-1)*exp(-t/K)
    return Q
t = arange(0.0, 35.0, 0.1)
plot(t, Nash(t))
ytext = ylabel('Q (l/s)')
xtext = xlabel('Time (t)')
setp(xtext, size='medium', name='courier', weight='bold', color='g')
setp(ytext, size='medium', name='helvetica', weight='light', color='b')
show()