# Chapter 6 : Orifices¶

## Example 6.1 Page No : 178¶

In [1]:
import math

# Variables :
Do = 25.;			#mm
Dc = 20.;			#mm
H = 85.;			#mm
x = 335.;			#mm
y = 350.;			#mm

# Calculations and Results
a = math.pi/4*Do**2;			#m**2
ac = math.pi/4*Dc**2;			#m**2
Cc = ac/a;
print "Coefficient of contraction : ",Cc

Cv = math.sqrt(x**2/4/H/y);
print "Coefficient of velocity : %.3f"%Cv

Cd = Cc*Cv;
print "Coefficient of discharge : %.2f"%Cd

Cr = (1/Cv**2-1);
print "Coefficient of Resistance : %.2f"%Cr

Coefficient of contraction :  0.64
Coefficient of velocity : 0.971
Coefficient of discharge : 0.62
Coefficient of Resistance : 0.06


## Example 6.2 Page No : 179¶

In [2]:
import math

# Variables :
Do = 0.125;			#m
H = 10.5;			#mm
Q = 6500.;			#litres/minute
Q = Q/60./1000;			#cumec
x = 6.;			#m
y = 1.;			#m
g = 9.81;			#gravity consmath.tant

# Calculations and Results
a = math.pi/4*Do**2;			#m**2
Qth = a*math.sqrt(2*g*H);			#cumec
Cd = Q/Qth;			#
print "Coefficient of discharge : %.2f"%Cd
Cv = math.sqrt(x**2/4/H/y);
print "Coefficient of velocity : %.3f"%Cv

Cc = Cd/Cv;
print "Coefficient of contraction : %.3f"%Cc

Cr = (1/Cv**2-1);
print "Coefficient of Resistance : %.3f"%Cr

Coefficient of discharge : 0.62
Coefficient of velocity : 0.926
Coefficient of contraction : 0.664
Coefficient of Resistance : 0.167


## Example 6.3 Page No : 181¶

In [3]:
import math

# Variables :
g = 9.81;			#consmath.tant
h = 102.;			#mm
H = 105.;			#mm

# Calculations
Cv = math.sqrt(2*g*h)/math.sqrt(2*g*H);

# Results
print "Coefficient of velocity : %.2f"%Cv

Coefficient of velocity : 0.99


## Example 6.4 Page No : 181¶

In [4]:
import math

# Variables :
Q = 180./62;			#litres/sec
Q = Q/1000;			#cumec
Dc = 25./1000;			#m
H = 1.9;			#m

# Calculations
ac = math.pi/4*Dc**2;			#m**2
g = 9.81;			#consmath.tant
Cv = Q/math.sqrt(2*g*H)/ac;

# Results
print "Coefficient of velocity : %.2f"%Cv

Coefficient of velocity : 0.97


## Example 6.5 Page No : 181¶

In [5]:
import math

# Variables :
g = 9.81;			#consmath.tant
d = 30./1000;			#meter
wl = 2;			#kgm
w1 = 148.6/60;			#kg/sec
y = 1.65;			#meter
H = 1.3;			#meter

# Calculations and Results
Cv = wl/w1/y*math.sqrt(g)/math.sqrt(2*H);
print "Coefficient of velocity : %.3f"%Cv

Q = w1/1000;			#Cumec
a = math.pi/4*d**2;			#meter**2
Qth = a*math.sqrt(2*g*H);			#Cumec
Cd = Q/Qth;			#coeff. of discharge
print "Coefficient of discharge : %.3f"%Cd

Cc = Cd/Cv;			#coeff. of contraction
print "Coefficient of contraction : %.3f"%Cc

#Answer in the book are not accurate.

Coefficient of velocity : 0.951
Coefficient of discharge : 0.694
Coefficient of contraction : 0.730


## Example 6.6 Page No : 183¶

In [6]:
import math

# Variables :
g = 9.81;			#consmath.tant
a = 9*10**-4;			#m**2
H = 3;			#meter
x = 2.5;			#meter
y = 54./100;			#meter
Qactual = 250*10**-3/60;			#Cumec

# Calculations and Results
Qth = a*math.sqrt(2*g*H);			#Cumec
Cd = Qactual/Qth;			#coeff. of discharge
print "Coefficient of discharge : %.3f"%Cd

Cv = math.sqrt(x**2)/math.sqrt(4*H*y);			#velocity
print "Coefficient of velocity : %.3f"%Cv

Cc = Cd/Cv;			#coeff. of contraction
print "Coefficient of contraction : %.3f"%Cc

#Answer in the book are not accurate.

Coefficient of discharge : 0.603
Coefficient of velocity : 0.982
Coefficient of contraction : 0.614


## Example 6.7 Page No : 184¶

In [7]:
import math

# Variables :
g = 9.81;			#consmath.tant
d = 20./1000;			#meter
a = math.pi/4*d**2;			#m**2
H = 1;			#meter

# Calculations
Qactual = 0.85*10**-3;			#m**3/sec
v = math.sqrt(2*g*H);			#m/sec
Qth = a*v;			#Cumec
Cd = Qactual/Qth;			#coeff. of discharge

# Results
print "Coefficient of discharge : %.2f"%Cd

Coefficient of discharge : 0.61


## Example 6.8 Page No : 185¶

In [8]:
import math

# Variables :
g = 9.81;			#consmath.tant
d = 1.5;			#meter
h = 1.;			#meter
Volume = math.pi/4*d**2*h;			#m**3
time = 25.;			#sec
Qactual = Volume/time;			#Cumec
H = 10.;			#meter
do = 10./100;			#meter
x = 4.3;			#meter
y = 0.5;			#meter

# Calculations and Results
ao = math.pi/4*do**2;			#m**2
Qth = ao*math.sqrt(2*g*H);			#cumec
Cd = Qactual/Qth;			#Coeff. ofdischarge
print "Coefficient of discharge : %.3f"%Cd

Cv = math.sqrt(x**2)/math.sqrt(4*H*y);			#Coefficient of velocity
print "Coefficient of velocity : %.3f"%Cv

Cc = Cd/Cv;			#coeff. of contraction
print "Coefficient of contraction : %.2f"%Cc

Cr_dash = (1/Cv**2-1);			#coeff. of Resistance
print "Coefficient. of Resistance : %.2f"%Cr_dash

Coefficient of discharge : 0.643
Coefficient of velocity : 0.962
Coefficient of contraction : 0.67
Coefficient. of Resistance : 0.08


## Example 6.9 Page No : 187¶

In [9]:
import math

# Variables :
g = 9.81;			#consmath.tant
do = 2.5/100;			#meter
H = 75./100;			#meter
x = 30./100;			#meter
y = 3.2/100;			#meter

# Calculations and Results
Qactual = 1.186*10**-3;			#Cumec
ao = math.pi/4*do**2;			#m**2
Qth = ao*math.sqrt(2*g*H);			#cumec
Cd = Qactual/Qth;			#Coeff. ofdischarge
print "Coefficient of discharge : %.2f"%Cd

Cv = math.sqrt(x**2)/math.sqrt(4*H*y);			#Coefficient of velocity
print "Coefficient of velocity : %.4f"%Cv

Cc = Cd/Cv;			#coeff. of contraction
print "Coefficient of contraction : %.3f"%Cc

Cr_dash = (1/Cv**2-1);			#coeff. of Resistance
print "Coefficient. of Resistance : %.3f"%Cr_dash

#Answers in the book are not accurate.

Coefficient of discharge : 0.63
Coefficient of velocity : 0.9682
Coefficient of contraction : 0.651
Coefficient. of Resistance : 0.067


## Example 6.10 Page No : 187¶

In [10]:
import math

# Variables :
g = 9.81;			#consmath.tant
H1 = 4-1;			#meter
H2 = 4.;			#meter
Cv1 = 0.9;			#Coefficient of velocity
Cv2 = 0.9;			#Coefficient of velocity

# Calculations
#Cv1 = Cv2 & x1 = x2 at meeting point
#x1/math.sqrt(4*H1*y1) = x2/math.sqrt(4*H2*y2)
y1BYy2 = H2/H1;
#y1 = 1+y2;
y2 = 1/(y1BYy2-1);			#meter
y1 = y1BYy2*y2;			#meter
x1 = Cv1*math.sqrt(4*H1*y1);			#meter

# Results
print "Meeting point horizontal & vertical co-ordinates are(x1 & y1 in meter) : %.2f"%x1,y1

#Answer in the book are not accurate.

Meeting point horizontal & vertical co-ordinates are(x1 & y1 in meter) : 6.24 4.0


## Example 6.11 Page No : 191¶

In [11]:
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 : %.4f"%Q

Discharge through the orifice in m**3/sec : 11.7685


## Example 6.12 Page No : 192¶

In [12]:
import math

# Variables :
g = 9.81;			#consmath.tant
Cd = 0.62;			#Coefficient of discharge
B = 2.;			#meter
H1 = 3.;			#meter
H2 = 3+1.5;			#meter

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

# Results
print "Discharge through the orifice in cumec : %.3f"%Q

Discharge through the orifice in cumec : 15.928


## Example 6.13 Page No : 194¶

In [14]:
import math

# Variables :
g = 9.81;			#consmath.tant
Cd = 0.6;			#Coefficient of discharge
B = 1.6;			#meter
H1 = 1500./1000;			#meter
H2 = (1500.+1250)/1000;			#meter

# Calculations and Results
Q = 2./3*Cd*B*math.sqrt(2*g)*(H2**(3./2)-H1**(3./2));			#m**3/sec or cumec
print "Discharge through the opening in cumec : %.3f"%Q
#For small opening
H = 1.5+1.25/2;			#meter
D = 1.25;			#meter
Qdash = Cd*(B*D)*math.sqrt(2*g*H);			#cumec
Error = (Qdash-Q)/Q*100;			#%
print "%% of error : %.3f"%Error

#Answer is wrong in the book.

Discharge through the opening in cumec : 7.720
% of error : 0.368


## Example 6.14 Page No : 195¶

In [15]:
import math

# Variables :
g = 9.81;			#consmath.tant
Cd = 0.6;			#Coefficient of discharge
B = 1600./1000;			#meter
D = 1250./1000;			#meter
ao = 1.6*1.25;			#m**2
H1 = 2+1.25/2;			#meter
H2 = 0.8+1.25/2;			#meter
H = H1-H2;			#meter

# Calculations
Q = Cd*ao*math.sqrt(2*g*H);			#m**3/sec or Cumec

# Results
print "Discharge in Cumec : %.3f"%Q

#Answer is wrong in the book.

Discharge in Cumec : 5.823


## Example 6.15 Page No : 196¶

In [16]:
import math

# Variables :
g = 9.81;			#consmath.tant
Cd = 0.6;			#Coefficient of discharge
B = 1600./1000;			#meter
D = 1250./1000;			#meter
ao = 1.6*1.25;			#m**2
H1 = 2+1.25;			#meter
H2 = 2;			#meter
H = H1-0.8;			#meter

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

# Results
print "Discharge through the orifice in Cumec : %.2f"%Q

Discharge through the orifice in Cumec : 8.18


## Example 6.16 Page No : 198¶

In [17]:
import math

# Variables :
g = 9.81;			#consmath.tant
d = 4;			#meter
d0 = 0.5;			#meter
H1 = 5;			#meter
H2 = 2;			#meter
Cd = 0.6;			#Coefficient of discharge
ao = math.pi/4*d0**2;			#m**2
A = math.pi/4*d**2;			#m**2

# Calculations and Results
t = 2*A/Cd/ao/math.sqrt(2*g)*(math.sqrt(H1)-math.sqrt(H2))
print "Time taken to fall from 5m to 2m(in seconds) : %.1f"%t
#For emptying H2 = 0;
H2 = 0;			#meter
t = 2*A/Cd/ao/math.sqrt(2*g)*(math.sqrt(H1)-math.sqrt(H2))
print "Time taken for completely emptying(in seconds) : %.1f"%t

Time taken to fall from 5m to 2m(in seconds) : 39.6
Time taken for completely emptying(in seconds) : 107.7


## Example 6.17 Page No : 199¶

In [19]:
import math

# Variables :
g = 9.81;			#consmath.tant
d = 1.2;			#meter
do = 50./1000;			#meter
H = 3.;			#meter
Cd = 0.6;			#Coefficient of discharge

# Calculations
ao = math.pi/4*do**2;			#m**2
A = math.pi/4*d**2;			#m**2
t = 2*A*math.sqrt(H)/Cd/ao/math.sqrt(2*g);			#sec

# Results
print "Time taken for emptying the tank is ",math.floor(t/60)," minute %.1f"%((t/60-math.floor(t/60))*60)," seconds."

Time taken for emptying the tank is  12.0  minute 30.8  seconds.


## Example 6.18 Page No : 200¶

In [20]:
import math

# Variables :
g = 9.81;			#consmath.tant
A = 3.2;			#m**2
a = 10*10**-4;			#m**2
H1 = 5;			#meter
H2 = 2.5;			#meter
Cd = 0.6;			#Coefficient of discharge

# Calculations
t = 2*A*(math.sqrt(H1)-math.sqrt(H2))/Cd/a/math.sqrt(2*g);			#sec

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

Time taken is  26.0  minute  17.0  seconds.


## Example 6.19 Page No : 200¶

In [24]:
import math
import datetime

# Variables :
g = 9.81;			#consmath.tant
A = 3.2;			#m**2
a = 10*10**-4;			#m**2
H = 5;			#meter
Cd = 0.6;			#Coefficient of discharge

# Calculations
t = 2.*A*math.sqrt(H)/Cd/a/math.sqrt(2*g);			#sec

# Results
print "Time taken is : in hours, minutes, seconds", datetime.timedelta(seconds=t)
#(math.floor(t/3600))," hour ",round((t/3600-math.floor(t/3600))*60)," minute ",(((t/3600-t/3600)*60-(t/3600-t/3600)*60)*60)," seconds."

Time taken is : in hours, minutes, seconds 1:29:44.733625