Chapter 11 : Flow Measurement

Example 11.1 Page No : 321

In [1]:
import math 
			
# Variables :
staticPHead = 5.;			#meter
stagnationPHead = 6.;			#meter

# Calculations
h = stagnationPHead-staticPHead;			#meter
g = 9.81;			#consmath.tant
Cv = 0.98;			#Coeff of pilot tube
V = Cv*math.sqrt(2*g*h);			#m/s

# Results
print "Velocity of flow in m/sec : %.2f"%V

Velocity of flow in m/sec : 4.34

Example 11.2 Page No : 321

In [2]:
import math 
			
# Variables :
Cv = 0.975;			#Coeff of pilot tube
h = 100./1000;			#meter
g = 9.81;			#consmath.tant
Sm = 13.6;			#Sp. gravity
S = 0.86;			#gravity of turpinre

# Calculations
V = Cv*math.sqrt(2*g*h*(Sm/S-1));			#m/s

# Results
print "Velocity in m/sec : %.3f"%V

Velocity in m/sec : 5.256

Example 11.3 Page No : 325

In [3]:
import math 


# Variables :
l = 2.;			#meter
d0 = 0;			#meter
d1 = 0.3;			#meter
d2 = 1.0;			#meter
d3 = 1.2;			#meter
d4 = 1.6;			#meter
d5 = 2.0;			#meter
d6 = 1.4;			#meter
d7 = 1.0;			#meter
d8 = 0.4;			#meter
d9 = 0.3;			#meter
d10 = 0.2;			#meter
V0 = 0;			#meter
V1 = 0.5;			#meter
V2 = 0.7;			#meter
V3 = 0.8;			#meter
V4 = 1.0;			#meter
V5 = 1.2;			#meter
V6 = 0.9;			#meter
V7 = 0.8;			#meter
V8 = 0.6;			#meter
V9 = 0.5;			#meter
V10 = 0.3;			#meter

# Calculations
Q = l/3*(d0*V0+4*d1*V1+2*d2*V2+4*d3*V3+2*d4*V4+4*d5*V5+2*d6*V6+4*d7*V7+2*d8*V8+4*d9*V9+2*d10*V10+d0*V0);			#cum/sec

# Results
print "Rate of discharge in cum/sec : ",Q

Rate of discharge in cum/sec :  17.04

Example 11.4 Page No : 329

In [4]:
import math 
			
# Variables :
Cd = 0.62;			#consmath.tant
H = 0.12;			#meter
L = 0.3;			#meter
g = 9.81;			#consmath.tant

# Calculations
Q = 2./3*Cd*math.sqrt(2*g)*L*H**(3./2);			#m**3/s

# Results
print "Discharge in m**3/sec : %.4f"%Q

Discharge in m**3/sec : 0.0228

Example 11.5 Page No : 329

In [5]:
import math 
			
# Variables :
Cd = 0.66;			#consmath.tant
H = 0.15;			#meter
L = 0.40;			#meter

# Calculations
g = 9.81;			#consmath.tant
Q = 2./3*Cd*math.sqrt(2*g)*L*H**(3./2);			#m**3/s

# Results
print "Discharge in m**3/sec : %.5f"%Q
print "Discharge in litres/sec : %.2f"%(Q*10**3)

Discharge in m**3/sec : 0.04529
Discharge in litres/sec : 45.29

Example 11.6 Page No : 331

In [7]:
import math 
			
# Variables :
Cd = 0.62;			#consmath.tant
H = 200./1000;			#meter
theta = 90.;			#degree
g = 9.81;			#consmath.tant

# Calculations
Q = 8./15*Cd*math.sqrt(2*g)*math.tan(math.radians(theta/2))*H**(5./2);			#m**3/s
Q = Q*1000*60;			#litres/minute

# Results
print "Discharge in litres/minute : %.f"%Q

Discharge in litres/minute : 1572

Example 11.7 Page No : 331

In [9]:
import math 
			
# Variables :
Cd = 0.62;			#consmath.tant
Q = 250;			#litres/sec
Q = Q*10**-3;			#m**3/s
theta = 90;			#degree
g = 9.81;			#consmath.tant
d = 1.3;			#meter

# Calculations
H = (Q/8*15/Cd/math.sqrt(2*g)/math.tan(math.radians(theta/2)))**(2./5);			#m
h = d-H;			#meter

# Results
print "Position above the bed in meter : %.3f"%h

Position above the bed in meter : 0.807

Example 11.8 Page No : 335

In [11]:
import math 
from scipy.integrate import quad 
			
# Variables :
Cd = 0.65;			#consmath.tant
A = 220;			#m**2
g = 9.81;			#consmath.tant
l = 30./100;			#meter
H1 = 16.8/100;			#meter
H2 = 6.8/100;			#meter

# Calculations
def f1(h): 
	 return h**(-3./2)

T = A/(2./3*Cd*l*math.sqrt(2*g))* quad(f1,H2,H1)[0]

# Results
print "Time taken is ",(math.floor(T/60))," minute ",round((T/60-math.floor(T/60))*60)," sec."

# note : answer might be vary because of quad function.

Time taken is  17.0  minute  46.0  sec.

Example 11.9 Page No : 337

In [13]:
import math 
			
# Variables :
H = 0.40;			#meter
L = 5;			#meter
print ("(i) End contractions are Suppressed : ");

# Calculations and Results
Q = 1.84*L*H**(3./2);			#m**3/s
print "Discharge in m**3/sec : %.4f"%Q
print "Discharge in litres/sec : %.1f"%(Q*1000)

print ("(ii) End contractions are Considered : ");
n = 2;
Q = 1.84*(L-0.1*n*H)*H**(3./2);			#m**3/s
print "Discharge in m**3/sec : %.5f"%Q
print "Discharge in litres/sec : %.2f"%(Q*1000)

(i) End contractions are Suppressed : 
Discharge in m**3/sec : 2.3274
Discharge in litres/sec : 2327.4
(ii) End contractions are Considered : 
Discharge in m**3/sec : 2.29020
Discharge in litres/sec : 2290.20

Example 11.10 Page No : 339

In [14]:
import math 
			
# Variables :
Cd = 0.62;			#Coeff of discharge
H = 250./1000;			#meter
L = 400./1000;			#meter

# Calculations
g = 9.81;			#gravity acceleration
Q = 2./3*Cd*math.sqrt(2*g)*L*H**(3./2);			#m**3/s or cumec

# Results
print "Discharge in cumec : %.4f"%Q

Discharge in cumec : 0.0915

Example 11.11 Page No : 339

In [16]:
import math 
			
# Variables :
g = 9.81;			#consmath.tant
Cd = 0.6;			#Coefficient of discharge
B = 1.3;			#meter
H1 = 6-(1.8+1.5);			#meter
H2 = 6-1.5;			#meter

# Calculations
Q = 2./3*Cd*B*math.sqrt(2*g)*(H2**(3./2)-H1**(3./2));			#m**3/sec

# Results
print "Discharge through the orifice in m**3/sec : %.1f"%Q

# note : answer is in m**3/sec.

Discharge through the orifice in m**3/sec : 11.8

Example 11.12 Page No : 342

In [17]:
import math 
			
# Variables :
Cd = 0.60;			#Coeff of discharge
L = 36.;			#meter
H = 1.1;			#meter
A = 50.;			#m**2
g = 9.81;			#gravity acceleration

# Calculations and Results
Qmax = 1.705*Cd*L*H**(3./2);			#m**3/s
print "Maximum Discharge in m**3/sec : %.3f"%Qmax

Va = Qmax/A;			#m/s(velocity of approach)
Q = 1.705*Cd*L*((H+Va**2/2/g)**(3./2)-(Va**2/2/g)**(3./2));			#m**3/s
print "New discharge considering velocity of approach in m**3/sec : %.2f"%Q

Maximum Discharge in m**3/sec : 42.488
New discharge considering velocity of approach in m**3/sec : 44.38

Example 11.13 Page No : 346

In [18]:
import math 
			
# Variables :
w = 1.5;			#m
d = 0.75;			#m
Cd = 0.64;			#Coeff of discharge
QT = 45.;			#cumec
h = 8.;			#meter
A = w*d;			#m**2
g = 9.81;			#gravity acceleration

# Calculations
Q = Cd*A*math.sqrt(2*g*h);			#m**3/sec
n = QT/Q;			#no. of spillways

# Results
print "No. of spillways : ",round(n)

No. of spillways :  5.0

Example 11.14 Page No : 348

In [19]:
import math 
			
# Variables :
B = 1;			#meter
b = 0.4;			#meter
H = 0.57;			#meter
h = 0.5;			#meter
A = B*H;			#m**2
g = 9.81;			#gravity consmath.tant
a = b*h;			#m**2

# Calculations
Q = A*a/math.sqrt(A**2-a**2)*math.sqrt(2*g*(H-h));			#m**3/sec

# Results
print "Discharge in m**3/sec : %.2f"%Q

Discharge in m**3/sec : 0.25