import math
# Variables :
m = 2000.; #litre or kg(1litre water = 1kg)
M = m/60; #kg/s
p = 4.5; #bar
p = p*10**5; #N/m**2
g = 9.81; #consmath.tant
w = g*1000; #N/m**3
# Calculations
H = p/w; #m
Power = M*g*H/1000; #kW
# Results
print "Power required in kW : %.f"%Power
import math
# Variables :
v1 = 400.*10**-3; #m/s
d1 = 300./1000; #meter
d2 = 450./1000; #meter
# Calculations and Results
A1 = math.pi*d1**2/4; #m**2
A2 = math.pi*d2**2/4; #m**2
Q1 = A1*v1*100; #litres/sec(1m**3 = 1000litres)
print "Discharge of pipe in litres/sec : %.2f"%Q1
v2 = (Q1/100)/A2; #m/s(Q1 = Q2)
print "Mean velocity of flow in m/s : %.3f"%v2
#Answer of discharge is wrong in the book.
import math
# Variables :
PotentialHead = 2; #meter of fluid
print "Potential Head is ",(PotentialHead)," meter of fluid."
v = 5.; #m/s
g = 9.81; #constant
# Calculations and Results
VelocityHead = v**2/2/g; #m
print "Velocity Head is ",round(VelocityHead,3)," meter of fluid."
w = g*1000; #N/m**3
S = 0.8; #sp. gravity of fluid
p = 200; #kPa
PressureHead = p*10**3/w/S; #meter of fluid
print "Pressure Head is ",round(PressureHead,3)," meter of fluid."
TotalHead = PotentialHead+VelocityHead+PressureHead; #meter of fluid
print "Total Head is ",round(TotalHead,3)," meter of fluid."
import math
# Variables :
p = 0.8/10**-4; #kg/m**2
datumH = 4.; #meter
v = 0.8; #m/s
g = 9.81; #consmath.tant
# Calculations
VelocityH = v**2/2/g; #m
w = 1000; #kg/m**3
PressureH = p/w; #meter of fluid
TotalH = datumH+VelocityH+PressureH; #meter of fluid
# Results
print "Total Energy is ",round(TotalH,4)," meter."
import math
# Variables :
D1 = 800./1000; #m**2
D2 = 600./1000; #m**2
p1 = 100.; #kPa
p2 = 40.; #kPa
v1 = 4000.*10**-3; #m/s
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
Z1 = 4.; #meter
Z2 = 7.; #meter
rho = 1.; #sp. gravity
g = 9.81; #constant
# Calculations
PHeadA = p1/rho/g; #meter of fluid
PHeadB = p2/rho/g; #meter of fluid
v2 = A1*v1/A2; #m/s
VHeadA = v1**2/2/g; #meter
VHeadB = v2**2/2/g; #meter
E1 = Z1+PHeadA+VHeadA; #meter
E2 = Z2+PHeadB+VHeadB; #meter
# Results
if E1>E2:
print "Total Energy at A(",round(E1,4)," meter) is greater than total energy at B(",round(E2,4)," meter). \
\nFlow of water is from A to B."
else:
print "Total Energy at B(",(E2)," meter) is greater than total energy at A(",(E1)," meter). Flow of water is from B to A."
import math
# Variables :
D1 = 1.25; #meter
D2 = 0.625; #meter
slope = 100.;
L = 300.; #/meter
g = 9.81; #consmath.tant
Z12 = L/slope; #meter
Q = 100.; #litres/sec
Q = Q*10**-3; #m**3/sec
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
v1 = Q/A1; #m/s
v2 = Q/A2; #m/s
p1 = 100.; #kN/m**2
#Higher End :
w = 9.81; #kN/m**3
Phead = p1/w; #meter
Vhead = v1**2/2/g; #meter
#Lower End :
w = 9.81; #kN/m**3
#Phead = p1/w; #meter
Vhead = v2**2/2/g; #meter
p2 = (Z12+v1**2/2/g+p1/w-v2**2/2/g)*w; #kN/m**2(By Bernoulli's theorem)
# Results
print "Pressure at the lower end in kN per m**2 : %.2f"%p2
import math
# Variables :
Z1 = 0.; #meter
Z2 = 5.; #meter
Q = 300.*10**-3; #m/s
D1 = 0.3; #meter
D2 = 0.6; #meter
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
v1 = Q/A1; #m/s
v2 = Q/A2; #m/s
p1 = 100.; #kN/m**2
p2 = 600.; #kN/m**2
g = 9.81; #consmath.tant
# Calculations and Results
Vhead11 = v1**2/2/g; #meter
Vhead22 = v2**2/2/g; #meter
Phead11 = p1/g; #meter
Phead22 = p2/g; #meter
E1_11 = Z1+Vhead11+Phead11; #meter
E2_22 = Z2+Vhead22+Phead22; #meter
if E1_11>E2_22:
print "Energy at section 1-1(",round(E1_11,3)," meter) is greater than energy at section 2-2(",(E2_22)," meter). Flow of water is from section 1-1 to 2-2."
HeadLoss = E1_11-E2_22; #meter
print "Head Loss in meter : ",HeadLoss
else:
print "Energy at section 2-2(",round(E2_22,3)," meter) is greater than energy at section 1-1(",round(E1_11,3)," meter). Flow of water is from section 2-2 to 1-1."
HeadLoss = E2_22-E1_11; #meter
print "Head Loss in meter : %.3f"%HeadLoss
import math
# Variables :
D = 400./1000; #meter
v1 = 20.; #m/s
Z1 = 28.; #meter
Z2 = 31.; #meter
p1 = 4./10**-4; #kg/m**2
p2 = 3./10**-4; #kg/m**2
g = 9.81; #consmath.tant
w = 1000.; #kg/m**3
# Calculations
Vhead1 = v1**2/2/g; #meter
Phead1 = p1/w; #meter
Vhead2 = Vhead1; #meter
Phead2 = p2/w; #meter
E1 = Z1+Vhead1+Phead1; #meter
E2 = Z2+Vhead2+Phead2; #meter
HL = E1-E2; #meter
# Results
print "Loss of head between P & Q in meter : ",HL
import math
# Variables :
Z1 = 0.; #meter
Z2 = 4.; #meter
rho = 0.8; #sp. gravity
# Calculations and Results
Q = 250.*10**-3; #m/s or cumec
D1 = 250./1000; #meter
D2 = 500./1000; #meter
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
v1 = Q/A1; #m/s
v2 = Q/A2; #m/s
p1 = 0.1*10**3; #N/m**2
p2 = 0.06*10**3; #N/m**2
g = 9.81; #consmath.tant
Vhead1 = v1**2/2/g; #meter
Phead1 = p1/rho/g; #meter
Vhead2 = v2**2/2/g; #meter
Phead2 = p2/rho/g; #meter
H1 = Z1+Vhead1+Phead1; #meter
H2 = Z2+Vhead2+Phead2; #meter
if H1>H2 :
print "Total head at A(",round(H1,3)," meter) is greater than total head at B(",round(H2,3)," meter). Flow will take place from A-B."
HeadLoss = H1-H2; #meter
print "Head Loss in meter : %.3f"%HeadLoss
else:
print "Total head at B(",(H2)," meter) is greater than total head at A(",(H1)," meter). Flow will take place from B-A."
HeadLoss = H2-H1; #meter
print "Head Loss in meter : ",HeadLoss
import math
# Variables :
Q = 200.*10**-3; #m**3/s
D1 = 250./1000; #meter
D2 = 200./1000; #meter
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
v1 = Q/A1; #m/s
v2 = Q/A2; #m/s
Z1 = 2.; #meter
Z2 = 8.; #meter
g = 9.81; #consmath.tant
w = 1000; #kg/m**3
# Calculations
p1 = w*(Z1-v1**2/2/g); #kg/m**2
p2 = v1**2/2/g*w+p1+Z2*w-v2**2/2/g*w-4*w; #kg/m**2(by Bernolli's theorem)
p1 = p1*g; #N/m**2
p2 = p2*g; #N/m**2
# Results
print "Pressure intensity at point P in N/m**2 : ",p1
print "Pressure intensity at point Q in N/m**2 : ",p2
# Note :Answer in the book is not accurate.
import math
# Variables :
slope = 1./10;
Z1 = 0.; #meter
Z2 = 40.*slope; #meter
p1 = 1.5/10**-4; #kg/cm**2
v2 = 4.1; #m/s
D1 = 600./1000; #meter
D2 = 300./1000; #meter
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
v1 = A2*v2/A1; #m/s
g = 9.81; #consmath.tant
w = 1000; #kg/m**3
p2 = (p1/w+v1**2/2/g+Z1-v2**2/2/g-Z2)*w; #kg/m**2(by Bernolli's theorem)
p2 = p2*10**-4; #kg/cm**2
Q1 = A1*v1; #m**3/sec
Q1 = Q1*1000; #litre/sec
# Results
print "Pressure intensity at point Q in kg/cm**2 : %.3f"%p2
print "Discharge of pipe in litres/sec : %.3f"%Q1
#Answer in the book is not accurate. calculation for A1 & A2 is wrong.
import math
# Variables :
D1 = 180./1000; #meter
D2 = 90./1000; #meter
g = 9.81; #gravity consmath.tant
S = 0.8; #sp. gravity of oil
Sm = 13.6; #sp. gravity of mercury
x = 300./1000; #meter
K = 0.97; #coeff. of meter
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
C = A1*A2*math.sqrt(2*g)/math.sqrt(A1**2-A2**2)
h = x*(Sm/S-1); #meter of oil
Q = K*C*math.sqrt(h); #m**3/sec
Q = Q*1000; #litre/sec
# Results
print "Discharge of oil in litres/sec : %.2f"%Q
import math
# Variables :
D1byD2 = 1/0.7;
D1 = 320./1000; #meter
D2 = 320.*0.7/1000; #meter
g = 9.81; #gravity consmath.tant
Q = 30.6/60; #m**3/sec
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
C = A1*math.sqrt(2*g)/math.sqrt((D1byD2)**4-1);
h = 1.2; #meter of water
K = Q/C/math.sqrt(h); #Coeff. of meter
# Results
print "Coefficient of meter : %.3f"%K
#Answer in the book is wrong.
import math
# Variables :
D1 = 320./1000; #meter
D2 = 224./1000; #meter
g = 9.81; #gravity consmath.tant
Q = 25000./1000./60; #m**3/sec
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
C = 0.4984; #venturi consmath.tant
K = 0.92; #Coeff. of meter
h = (Q/K/C)**2
S = 1; #sp. gravity
Sm = 13.6; #sp. gravity
x = h/(Sm/S-1); #meter of water
# Results
print "Deflection in manometer(mm) : %.1f"%(x*1000)
import math
# Variables :
D1 = 120./1000; #meter
D2 = 120*0.55/1000; #meter
g = 9.81; #gravity consmath.tant
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
Q = 30./1000; #m**3/sec
# Calculations
C = A1*math.sqrt(2*g)/math.sqrt((D1/D2)**4-1); #venturi consmath.tant
K = 0.94; #Coeff. of meter
h = (Q/K/C)**2; #meter
Z1 = 0; #meter
Z2 = 0.3; #meter
S = 0.79; #sp. gravity
w = 1000*S; #kg/m**3
delta_p = (h+Z1-Z2)*w; #kg/m**2
delta_p = delta_p*g; #N/m**2
# Results
print "Pressure difference in N/m**2 : %.3f"%delta_p
#answer is wrong in the book.
import math
# Variables :
D1 = 160./1000; #meter
D2 = 60./1000; #meter
g = 9.81; #gravity consmath.tant
S = 0.8; #sp. gravity
Sm = 13.6; #sp. gravity of mercury
Q = 0.05; #m**3/sec
K = 0.98; #Coeff. of meter
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
C = A1*math.sqrt(2*g)/math.sqrt((A1/A2)**2-1); #venturi consmath.tant
h = (Q/K/C)**2; #meter
x = h/(Sm/S-1); #meter
# Results
print "Deflection in meter : %.2f"%x
import math
# Variables :
D1 = 200./1000; #meter
D2 = 100./1000; #meter
x = 220./1000; #meter
g = 9.81; #gravity consmath.tant
K = 0.98; #Coeff. of meter
S = 1.; #sp. gravity
Sm = 13.6; #sp. gravity of mercury
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
C = A1*math.sqrt(2*g)/math.sqrt((A1/A2)**2-1); #venturi consmath.tant
h = x*(Sm/S-1); #meter
Q = K*C*math.sqrt(h); #m**3/sec
Q = Q*1000; #litres/sec
# Results
print "Rate of flow in litres/sec : %.f"%Q
import math
# Variables :
D1 = 40./100; #meter
D2 = 15./100; #meter
x = 25./100; #meter
g = 9.81; #gravity consmath.tant
K = 0.98; #Coeff. of meter
S = 1.; #sp. gravity
Sm = 13.6; #sp. gravity of mercury
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
C = A1*A2*math.sqrt(2*g)/math.sqrt(A1**2-A2**2); #venturi consmath.tant
h = x*(Sm/S-1); #meter
Q = K*C*math.sqrt(h); #m**3/sec
Q = Q*1000*3600; #litres/hour
# Results
print "Flow of water in litres/hour : %.f"%Q
#Answer in the book is wrong.
import math
# Variables :
D1 = 15./100; #meter
D2 = 7.5/100; #meter
g = 9.81; #gravity consmath.tant
p1 = 4*g*10**4; #N/m**2
p2 = 1.5*g*10**4; #kg/cm**2
w = 9.81; #kg/m**2
# Calculations
A1 = math.pi*D1**2/4; #m**2
A2 = math.pi*D2**2/4; #m**2
v1BYv2 = A2/A1;
#v1**2/2/g+p1/w = v2**2/2/g+p2/w
#v1**2 = v2**2-50*g
v2 = math.sqrt(50*g/(1-v1BYv2**2)); #m/s
Q = A2*v2; #m**3/sec
Q = Q*1000; #litres/sec
# Results
print "Flow of water in litres/sec : %.f"%Q
#Answer is wrong in the book.
import math
# Variables :
D1 = 20./100; #meter
D2 = 15./100; #meter
A1 = math.pi/4*D1**2; #m**2
A2 = math.pi/4*D2**2; #m**2
# Calculations and Results
v1 = 2; #m/s
v2 = A1*v1/A2; #m/s
print "Velocity at another section in m/s : %.2f"%v2
FlowRate = A1*v1; #m**3/s
FlowRate = FlowRate*1000; #litres/s
print "Flow Rate in litres/sec : %.1f"%FlowRate
#Answer of velocity in the book is not accurate.
import math
# Variables :
rd = 0.75; #relative density
D = 12.5/100; #meter
p = 1.; #bar
p = p*1.02; #kg/cm**2
# Calculations
p = p*9.81*10**4/1000; #kPa
g = 9.81; #gravity consmath.tant
w = g*rd; #N/m**3
pH = p/w; #meter
Z = 2.5; #meter
Et = 20; #Nm
v = math.sqrt((Et-p/w-Z)*2*g); #m/s
A = math.pi/4*D**2; #m**2
Q = A*v; #m**3/sec
Q = A*v*1000; #litres/sec
# Results
print "Flow Rate of oil in litres/sec : %.f"%Q
import math
# Variables :
rd = 0.75; #relative density
d1 = 0.3; #meter
d2 = 0.1; #meter
Q = 50./1000; #m**3/sec
# Calculations
A1 = math.pi/4*d1**2; #m**2
A2 = math.pi/4*d2**2; #m**2
v1 = Q/A1; #m/s
v2 = A1*v1/A2; #m/s
p1 = 200; #kN/m**2
p2 = 100; #kN/m**2
w = 9.81; #kN/m**3
g = 9.81; #gravity consmath.tant
Z1 = 0; #meter
Z2 = Z1+p1/w+v1**2/2/g-p2/w-v2**2/2/g; #meter
# Results
print "Z in meter : %.2f"%Z2
import math
# Variables :
D1 = 300./1000; #meter
D2 = 150./1000; #meter
Q = 50./1000; #m**3/sec
# Calculations
A1 = math.pi/4*D1**2; #m**2
A2 = math.pi/4*D2**2; #m**2
delpBYw = 3; #p1/w-p2/w = 3; #m
v1BYv2 = A2/A1;
Z1 = 0; #meter
Z2 = 0; #meter
g = 9.81; #gravity consmath.tant
#HeadLoss = 1/8*v**2/2/g
#Z1+p1/w+v1**2/2/g = Z2+p2/w+v2**2/2/g+HeadLoss
v2 = math.sqrt((Z1-Z2+delpBYw)/(1./2/g-v1BYv2**2/2/g+1/8/2/g)); #m/s
Q = A2*v2; #m**3/s
Q = Q*1000; #litres/sec
# Results
print "Discharge in pipe in litres/sec : %.1f"%Q
# note : rounding off error