# Chapter 10:Open Channel Flow¶

### Example 10.2 Page no.572¶

In [1]:
%matplotlib inline

Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].

In [1]:
#Given
z2=0.5              #ft
q=5.75              #(ft**2)/sec
y1=2.3              #ft
z1=0                #ft
V1=2.5              #ft/sec

#calculation
#bernoulli equation
a=y1+((V1**2)/(2*32.2))+z1-z2   #ft where a=y2+((V**2)/(2*g))
#continuity equation
from scipy.optimize import fsolve
#Calculation
b=(y1*V1)                       #(ft**2/sec) where b=(y2*V2)
#From b and  bernouli eq.  f=y**3-1.90*y**2+0.513
def f(y):
f1=y**3-1.90*y**2+0.513
return(f1)
y=fsolve(f,2)
L=y+z2
print "Surface Elevation is ",round(L,2),"ft"

#Plot
E=[3,2,1.51,2.4,3]
Y=[2.9,1.8,1.01,0.5,0.4]
a=plot(E,Y)
xlabel("E  ft")
ylabel("Y (ft)")
plt.xlim((0,4))
plt.ylim((0,4))
show(a)

Surface Elevation is  2.23 ft


### Example 10.3 Page no.579¶

In [2]:
#Given
y=5.0                       #ft
angle=40.0               #degree
l=12.0                      #ft
rate=1.4                  #ft per 1000 ft of length
K=1.49

#Calculation
import math
A=(l*y)+(y*y/math.tan(angle*math.pi/180))     #ft
P=(l+(2*y/math.sin(angle*math.pi/180)))         #ft
Rh=A/P
S0=rate/10**3
x=K*(A)*(Rh**(0.666667))*(S0**(0.5))             #where Rh=Q*n
n=0.012
Q=x/n                        #cfs

#Result
print "The flowrate=",round(Q,0),"cfs"
V=Q/A                     #ft/sec
Fr=V/(32.2*y)**(0.5)
print "Froude number=",round(Fr,2)

The flowrate= 917.0 cfs
Froude number= 0.8


### Example 10.4 Page no.580¶

In [4]:
y=5                 #ft
angle=40            #degree
l=12                #ft
rate=1.4            #ft per 1000 ft of length
Q=10                #m**3/sec
bw=l*1/3.281        #m where bw=bottom width

#Calculation
import math
from scipy.optimize import fsolve
#A=(l*y)+(y*y/math.tan(angle*math.pi/180)) ft**2
#A=1.19*y**2+3.66*y           area interms of distance depth y, 1.19,3.66  are constant
#Rh=1.19*y**2+3.66*y/((3.11*y+3.66)**2)
#P=bw(2*y/math.sin(angle*math.pi/180)) m
#Rh=A/P
#Q=10=k*A*Rh**2/3*So**0.5/(n)
n=0.03              #From table 10.1

def f(y):
f1=((1.19*y**2+3.66*y)**5-515*(3.11*y+3.66)**2)  #digits used are costants which is used in the area equation.
return(f1)
y=fsolve(f,2)

#Result
print "The depth of the flow=",round(y,1),"m"

The depth of the flow= 1.5 m


### Example 10.7 Page no.583¶

In [26]:
#Given
S0=0.002
n1=0.02
z1=0.6               #ft
n2=0.015
n3=0.03
z2=0.8               #ft
#length of section 1 ,2,3
l1=3.0               #ft
l2=2.0               #ft
l3=3.0               #ft
#Area
A1=l1*(z1)           #ft**2
A2=l2*(y)            #ft**2
A3=l3*(z1)           #ft**2
P1=l1+z1             #ft
P2=l2+(2*z2)         #ft
P3=l3+z1             #ft
Rh1=A1/P1            #ft
Rh2=A2/P2            #ft
Rh3=A3/P3            #ft
y=z1+z2              #ft
K=1.49

#Calculation
Q=K*(S0**(0.5))*((A1*(Rh1**(0.667))/n1)+(A3*(Rh3**(0.667))/n3)+(A2*(Rh2**(0.667))/n2))   #(ft**3)/sec

#Result
print "The flowrate=",round(Q,1),"ft**3/s"

The flowrate= 16.8 ft**3/s


### Example 10.8 Page no.584¶

In [14]:
aspratio=2       #asp ratio=aspect ratio=b/y

#result
print "The aspect ratio=",aspratio,":1"

#Plot
b=[0.5,1.2,2,5]
q=[0.85,0.98,1,0.93]
a=plot(b,q)
xlabel("b/y  ")
ylabel("q/qmax")
plt.xlim((0,5))
plt.ylim((0.80,1.05))
show(a)

The aspect ratio= 2 :1


### Example 10.9 Page no.593¶

In [3]:
#Given
w=100                    #ft
y1=0.6                   #ft
V1=18                   #ft/sec
Fr1=V1/(32.2*y1)**0.5
print "The Froude number before the jump=",round(Fr1,2)
yratio=0.5*(-1+(1+(8*(Fr1**2)))**0.5)         #where yratio=y2/y1
y2=y1*yratio        #ft
print "The depth after the jump=",round(y2,2),"ft"
#Q1=Q2, hence
V2=(y1*V1)/y2              #ft/sec
Fr2=V2/(32.2*y2)**0.5
print "The froude number after the jump=",round(Fr2,2)
Q=w*y1*V1#(ft**3)/sec
hL=(y1+(V1*V1/(32.2*2)))-(y2+(V2*V2/(2*32.2)))       #ft
Pd=62.4*hL*Q/550             #hp
print "Power dissipated within the jump=",round(Pd,3),"hp"

#Plot
b=[1.54,1.2,0.8,0.6,0.4]
P=[0,10,80,277,900]
a=plot(b,P)
xlabel("b (ft)")
ylabel("P  (hp)")
plt.xlim((0,1.6))
plt.ylim((0,1000))
show(a)

The Froude number before the jump= 4.1
The depth after the jump= 3.19 ft
The froude number after the jump= 0.33
Power dissipated within the jump= 277.539 hp