import math
# Calculations and Results
print ("Part(i)");
print ("Absolute unit of viscosity(in C.G.S) is Poise.");
print ("Poise = 1 dyne-sec/cm**2");
print ("Gravitational unit of viscosity is 1 gm-sec/cm**2.");
print ("On equating we get, 1 gm = 981 dyne");
#Let x = 1kg-sec/m**2
x = 1*10.**3/10**4; #g-sec/cm**2
x = x*981; #dyne-sec/cm**2 or Poise(Putting 1gm = 981 dyne)
print "1 kg-sec/m**2 = ",(x)," Poise"
one_Poise = 1./x; #kg-sec/m**2
one_Poise = 1/x*9.81; #N-sec/m**2 or Pa-sec(as 1Pa = 1N/m**2)
print "1 Poise = ",(one_Poise)," N-sec/m**2 or Pa-sec"
print ("Part(ii)");
print ("Kinematic viscosity = viscosity/specific_gravity");
print ("Kinematic viscosity C.G.S unit is cm**2/sec. 1cm**2/sec = 1stoke");
print ("Kinematic viscosity M.K.S unit is m**2/sec");
#let x = 1; #m**2/sec
x = 1.; #m**2/sec
x = x*10**4; #cm**2/sec or stokes
print "1 m**2/sec = ",(x)," cm**2/sec or stoke"
one_stoke = 1/x; #m**2/sec
print "1 stoke = ",(one_stoke)," m**2/sec"
print ("1 stoke = 100 centi-stokes");
import math
# Variables :
mu = 0.009; #kg-sec/m**2
rho = 0.89; #sp. gravity
Q = 4.*10**-3; #m**3/sec
d = 30./1000; #meter
# Calculations and Results
v = mu/rho; #m**2/s
print "Kinematic viscosity in m**2/sec : %.4f"%v
A = math.pi*d**2/4; #m**2
vm = Q/A; #m/s
Rn = vm*d/v; #Reynolds no.
print "Reynolds number for flow : %.1f"%Rn
print ("This is laminar flow because Rn no. is less than 2000.");
import math
# Variables :
d = 200./1000; #meter
Q = 40.*10**-3; #m**3/sec
A = math.pi*d**2/4; #m**2
vm = Q/A; #m/s
v = 0.25*10**-4; #m**2/s
# Calculations and Results
Rn = vm*d/v; #Reynolds no.
print "Reynolds number for flow : %.f"%Rn
print ("This is turbulent flow because Rn no. is greater than 4000.");
print "New Reynolds number for flow : %.f"%(Rn/8)
print ("This is laminar flow because Rn no. is less than 2000.");
import math
# Variables :
D = 30./100; #meter
L = 100.; #meter
v = 0.01*10**-4; #m**2/s
a = 3.; #m/s
g = 9.81; #gravity consmath.tanty
Rn = a*D/v; #Reynolds no.
# Calculations
f = 0.079/Rn**(1./4); #umath.sing blasius formula
hf = 4*f*L/D*a**2/2/g; #meter
# Results
print "Head lost in meter : %.2f"%hf
#Answer in the book is wrong.
import math
# Variables :
D = 30./100; #meter
L = 500.; #meter
Q = 300.*10**-3; #m**2/sec
f = 0.0008; #coeff. of friction
# Calculations
v = Q/(math.pi/4*D**2); #m/s
g = 9.81; #gravity consmath.tanty
hf = 4*f*L*v**2/D/2/g; #meter
# Results
print "Difference in elevation in meter : %.2f"%hf
#Answer in the book is wrong.
import math
# Variables :
D = 20./100; #meter
v = 3.; #m/s
v1 = 0.01*10**-3; #m**2/sec
Re = D*v/v1; #Reynolds number
f = 0.002+0.09/Re**0.3; #coeff. of friction
L = 5.; #meter
g = 9.81; #gravity consmath.tanty
# Calculations
hf = 4*f*L*v**2/D/2/g; #meter
# Results
print "Head lost due to friction in meter : %.3f"%hf
import math
# Variables :
D = 80./1000; #meter
Q = 600.*10**-3/60; #m**3/sec
L = 1.*10**3; #meter
f = 0.02; #coefficient of friction
# Calculations
v = Q/(math.pi/4*D**2); #m/s
g = 9.81; #gravity consmath.tanty
hf = 4*f*L*v**2/D/2/g; #meter
# Results
print "Head lost due to friction in meter : %.3f"%hf
#Answer is wrong in the book.
import math
# Variables :
g = 9.81; #gravity consmath.tanty
f = 0.02; #coefficient of friction
Cc = 0.62; #coefficient of contraction
# Calculations
#Portion AB
Q1 = 50.*10**-3; #m**3/sec
D1 = 150./1000; #meter
v1 = Q1/(math.pi/4*D1**2); #m/s
hr = 0.5*v1**2/2/g; #meter
L1 = 200.; #meter
hf1 = 4*f*L1*v1**2/2/g/D1; #meter
D2 = 200./1000; #meter
v2 = Q1/(math.pi/4*D2**2); #m/s
hc1 = (v1-v2)**2/2/g; #meter
L2 = 500.; #meter
hf2 = 4*f*L2*v2**2/2/g/D2; #meter
d = 75./1000; #meter
ho = ((math.pi/4*D2**2)/Cc/((math.pi/4*D2**2)-(math.pi/4*d**2))-1)**2*v2**2/2/g; #meter
D3 = 120./1000; #meter
v3 = Q1/(math.pi/4*D3**2); #m/s
hc2 = v3**2/2/g*(1/Cc-1)**2; #meter
L3 = 500.; #meter
hf3 = 4*f*L3*v3**2/2/g/D3; #meter
Kb = 0.25; #assumed
hb1 = Kb*v3**2/2/g; #meter
D4 = 120./1000; #meter
v4 = Q1/(math.pi/4*D4**2); #m/s
L4 = 500.; #meter
hf4 = 4*f*L4*v4**2/2/g/D4; #meter
hb2 = Kb*v3**2/2/g; #meter
L5 = 500.; #meter
hf5 = 4*f*L5*v4**2/2/g/D4; #meter
h_outlet = v3**2/2/g; #meter
h_total = hr+hf1+hc1+hf2+ho+hc2+hf3+hb1+hf4+hb2+hf5+h_outlet; #meter
# Results
print "Total loss of head in meter : %.f"%h_total
import math
# Variables :
g = 9.81; #gravity consmath.tanty
Cc = 0.62; #coefficient of contraction
D1 = 150./1000; #meter
D2 = 100./1000; #meter
Q = 2.7/60; #m**3/sec
p1 = 0.8*10**4; #kg/m**2
# Calculations
v1 = Q/(math.pi/4*D1**2); #m/s
v2 = Q/(math.pi/4*D2**2); #m/s
hc = v2**2/2/g*(1/Cc-1)**2; #meter
w = 1000; #kg/m**3
p2 = (v1**2/2/g+p1/w-v2**2/2/g-hc)*w; #kg/m**2(Z1 = Z2)
p2 = p2*10**-4; #kg/cm**2
# Results
print "Intensity of pressure in kg/cm**2 : %.4f"%p2
import math
# Variables :
g = 9.81; #gravity consmath.tanty
L = 3.*1000; #meter
hf = 20.; #meter
Q = 1.; #m**3/sec
f = 0.02; #coeff. of friction
# Calculations
#v = math.sqrt(hf*2*g/4/f/L/D); #it is v**2*D
D2v = Q/(math.pi/4); #it is D**2*v
D = (Q/(math.pi/4)/math.sqrt(hf*2*g/4/f/L))**(2./5); #meter
D = D*1000; #mm
# Results
print "Diameter of pipe in mm : %.f"%D
import math
# Variables :
g = 9.81; #gravity consmath.tanty
D1 = 100./1000; #meter
D2 = 200./1000; #meter
PQ = 100.; #meter
QR = 100.; #meter
slope = 1./100; #upward slope
Q = 0.02; #cumec
p1 = 2.; #kg/cm**2(Pressure in 100 mm dia pipe)
f = 0.02; #unitless
Q_P = 100./100; #meter(Point Q hight respect to point P)
Q_R = 200./100; #meter(Point Q hight respect to point R)
# Calculations and Results
v1 = Q/(math.pi/4*D1**2); #m/sec
v2 = Q/(math.pi/4*D2**2); #m/sec
hf1 = 4*f*PQ*v1**2/(2*g*D1); #meter
hf2 = 4*f*QR*v2**2/(2*g*D2); #meter
hse = (v1-v2)**2/2/g; #meter(loss due to sudden enlargement)
#Section PQ
Z1P = 0; #meter(Datum Head)
H1P = v1**2/2/g; #meter(velocity Head)
p1BYw = p1*10**4/1000; #meter(Pressure Head at P)
Z1Q = 1; #meter(Datum Head)
H1Q = v2**2/2/g; #meter(velocity Head)
#Applying bernaullis theorem
p2BYw = Z1P+p1BYw+H1P-Z1Q-H1Q-hf1; #meter(Pressure Head at Q)
print "Pressure Head at point P(m)",p1BYw
print "Velocity Head at point P(m) %.3f"%H1P
print "Pressure Head at point Q(m) : %.3f"%p2BYw
#Section QR
#Applying bernaullis theorem
p2dashBYw = p2BYw+H1P-H1Q-hse; #meter(Pressure Head at Q)
Z2 = 1; #meter(Datum Head)
H1Q = v2**2/2/g; #meter(velocity Head)
Z3 = 2; #meter(Datum Head at R)
H1R = v2**2/2/g; #meter(velocity Head at R)
#Applying bernaullis theorem
p3BYw = Z2+p2dashBYw+H1Q-Z3-H1R-hf2; #meter(Pressure Head at R)
print "Velocity Head at point Q after enlargemant(m) : %.2f"%H1Q
print "Pressure Head at point Q after enlargemant(m) : %.3f"%p2dashBYw
print "Pressure Head at point R(m) : %.3f"%p3BYw
print "Velocity Head at point R(m) : %.3f"%H1R
#Answer in the book is wrong for some calculations.
import math
# Variables :
g = 9.81; #gravity consmath.tanty
D1 = 400./1000; #meter
D2 = 300./1000; #meter
D3 = 200./1000; #meter
v1 = 3; #m/s
v2 = 2; #m/s
# Calculations and Results
A1 = math.pi/4*D1**2; #m**2
A2 = math.pi/4*D2**2; #m**2
A3 = math.pi/4*D3**2; #m**2
Q1 = A1*v1; #cumec
print "Discharge in pipe 1 in cumec : %.4f"%Q1
Q2 = A2*v2; #cumec
Q3 = Q1-Q2; #cumec
v3 = Q3/A3; #m/s
print "Velocity of water in 200mm pipe in m/s : ",v3
import math
# Variables :
g = 9.81; #gravity consmath.tanty
D1 = 100./1000; #meter
D2 = 300./1000; #meter
# Calculations
Q1 = 0.01; #m**3/sec
A1 = math.pi/4*D1**2; #m**2
A2 = math.pi/4*D2**2; #m**2
#hf1 = hf2
Q2 = math.sqrt(D2/(D1)*(Q1/A1)**2*A2**2); #cumec
# Results
print "Discharge throough 300mm pipe in cumec : %.3f"%Q2
import math
# Variables :
g = 9.81; #gravity consmath.tanty
f = 0.02; #coeff. of friction
PQ = 500.; #meter
QR = 1000.; #meter
RS = 500.; #meter
# Calculations
hf = 10+PQ/62.5+QR/125-RS/100-2; #meter
l = 500+1000+500; #/meter
D = 250./1000; #meter
v = math.sqrt(hf*2*g*D/4/f/l); #m/s
Q = math.pi/4*D**2*v; #m**3/sec
Q = Q*1000; #litres/sec
# Results
print "Discharge in pipe line in litres/sec : %.f"%Q
import math
# Variables :
g = 9.81; #gravity consmath.tant
slope = 1./125; #slope
hA = 12.; #meter(level of water in reservoir A)
hB = 1.5; #meter(level of water in reservoir B)
L1 = 500.; #meter
D1 = 250./1000; #meter
L2 = 1000.; #meter
D2 = 200./1000; #meter
L3 = 500.; #meter
D3 = 150./1000; #meter
# Calculations
f = 0.02; #coeff. of friction
fall_level = (L1+L2+L3)*slope; #meter
H = hA+fall_level-hB; #meter(Head available for flow)
v2BYv1 = (D1/D2)**2;
v3BYv1 = (D1/D3)**2;
#H = hf = hf1+hf2+hf3
#H = (4*f*L1*v1**2/(2*g*D1)+4*f*L2*v2**2/(2*g*D2)+4*f*L3*v3**2/(2*g*D3))
v1 = math.sqrt(H/(4*f*L1/(2*g*D1)+4*f*L2*v2BYv1**2/(2*g*D2)+4*f*L3*v3BYv1**2/(2*g*D3))); #m/s
Q = math.pi*D1**2/4*v1; #m**3/sec
Q = Q*1000; #litres/sec
# Results
print "Discharge in pipe line in litres/sec : %.1f"%Q
import math
# Variables :
g = 9.81; #gravity consmath.tant
l = 4.; #km
n = 5000.; #habimath.tants
Ch = 200.; #litres/day(habimath.tant capacity)
t = 10.; #hour(daiy supply time)
hf = 20.; #meter(Head loss)
f = 0.008; #coeff. of friction
# Calculations
Qty = n*Ch/2; #litres(Water supplied in 10 hours)
Q = Qty/(t*60*60); #litres/sec
Q = Q/1000; #m**3/sec
d = (f*l*1000*Q**2/3.0257/hf)**(1./5); #meter
# Results
print "Diameter of pipe(mm) : %.f"%(d*1000)
import math
# Variables :
g = 9.81; #gravity consmath.tant
D1 = 50./1000; #meter
D2 = 100./1000; #meter
l1 = 100.
l2 = 100.; #meter
hf1 = 10.; #meter(level difference)
f = 0.008; #coeff. of friction
# Calculations and Results
Q2BYQ1 = math.sqrt((l1/l2)*(D2/D1)**5); #as hf1 = hf2
Q1 = math.sqrt(hf1/f/l1*(3.0257*D1**5)); #m**3/sec
Q2 = Q2BYQ1*Q1; #m**3/sec or cumec
print "Rate of flow of pipe 1(m**3/sec) : %.2e"%Q1
print "Rate of flow of pipe 2(m**3/sec) : %.3f"%Q2
Q = Q1+Q2; #m**3/sec(Total Discharge)
d = (f*l1*Q**2/3.0257/hf1)**(1./5); #meter
print "Diameter of math.single pipe(mm) : %.1f"%(d*1000)
#Answer in the book is not accurate.
import math
# Variables :
g = 9.81; #gravity consmath.tant
D = 30./100; #meter
l = 400.; #meter
Q = 300.; #litres/sec
f = 0.008; #coeff. of friction
Q = Q*10**-3; #m**3/sec
# Calculations
A = math.pi*D**2/4; #m**2
v = Q/A; #m/s(velocity of flow)
h1 = 0.5*v**2/2/g; #meter(Head loss at entrance to a pipe)
h2 = 4*f*l*v**2/(2*g*D); #meter(Head loss due to friction)
h3 = v**2/2/g; #meter(Head loss at entrance of reservoir)
H = h1+h2+h3; #meter(Difference of water level)
# Results
print "Difference of water level between two reservoir(meter) : %.3f"%H
#Answer in the book is not accurate as h2 is calculated wrong.
import math
# Variables :
g = 9.81; #gravity consmath.tant
D = 150./1000; #meter
l = 70.; #meter
H = 2.6; #meter(head of water)
f = 0.01; #coeff. of friction
# Calculations
#Applyong Bernoullis theorem
v = math.sqrt(H*(2/g*(1+0.5+4*f*l/D))/4); #m/s
Q = math.pi*D**2/4*v; #m**3/sec
Q = Q*1000; #litres/sec
# Results
print "Discharge through the pipe(litres/sec) : %.1f"%Q
import math
# Variables :
g = 9.81; #gravity consmath.tant
Cv = 0.97; #coeffiecient of velocity
Cc = 0.95; #coeffiecient
Dn = 50./1000; #meter(Nozzle diameter)
D = 100./1000; #meter(Pipe diameter)
p = 6.867; #N/cm**2(Pressure at the base of nozzle)
# Calculations and Results
Hb = p*10**4/(g*1000) #meter(Head at the base of nozzle)
v = Cv*math.sqrt(2*g*Hb); #m/s(velocty of jet)
print "Velocity in the jet(m/s) : %.2f"%v
A = math.pi/4*Dn**2; #m**2(Cross sction of jet)
Q = Cc*A*v; #m**3/sec(Discharge)
Q = Q*1000; #litres/sec
print "Rate of discharge(litres/second) : %.2f"%Q
E = g*1000*Q/1000*Hb/1000; #kW(Energy transmitted)
print "Energy per second n the jet(kW) : %.2f"%E
#Answer in the book is not accurate.
import math
# Variables :
g = 9.81; #gravity consmath.tant
D = 100./1000; #meter(Pipe diameter)
L = 700.; #meter(Total length)
Lin = 300.; #meter(inlet length)
hf = 10.; #meter(Available head)
h = 1.4; #meter(height)
f = 0.02; #coefficient of friction
# Calculations and Results
v = math.sqrt(hf*2*g*D/4/f/L); #m/s
Q = math.pi*D**2/4*v*1000; #litres/sec
print "Discharge in pipe(litres/second) : %.2f"%Q
#Applying Brnaullis theorem
p1 = 0
v1 = 0
Z1 = 0; #(Neglecting minor losses)
v2 = v; #m/s
Z2 = h; #meter
hf = 4*f*Lin*v**2/(2*g*D); #meter
p2BYw = -v2**2/2/g-Z2-hf; #meter of water
hatm = 10.3; #meter(Atmospheric pressure head)
habs = p2BYw+hatm; #meter(Absolute pressure head)
print "Pressure at the summit of siphon(meter) : %.3f"%habs
import math
# Variables :
g = 9.81; #gravity consmath.tant
D = 150./1000; #meter(Pipe diameter)
Q = 40.; #litres/sec(rate of discharge)
l = 500.; #meter(valve dismath.tance)
T = 0.5; #second
# Calculations
v = Q/1000/(math.pi/4*D**2); #m/s(velocity of flow)
pi = 1000/g*(l*v/T); #kg/m**2
# Results
print "Increase in pressure intensity(kg/m**2) : %.3e"%pi
import math
# Variables :
g = 9.81; #gravity consmath.tant
l = 10000.; #meter(length of pipe line)
D = 0.2; #meter(Diameter of pipe)
p = 60.*10**5; #N/m**2
f = 0.007; #coefficient of friction
w = g*1000.; #N/m**3
# Calculations
H = p/w; #meter
hf = H/3; #meter(friction head loss is 1/3rd)
v = math.sqrt(hf*2*g*D/4/f/l); #m/s
P = w*math.pi*D**2/4*v*(H-hf)/1000; #kW
# Results
print "Maximum power(kW) : %.3f"%P