from __future__ import division
import math
#variable initialization
Ht=H=30 #Height
Sp=2.0 #speed ratio
Db=0.35 #Diameter of the boss
F=0.65 #Flow ratio
ga=9.81 #density
eta0=0.90 #overall efficiency
P=15000E3
#Calculation
U1=round(Sp*math.sqrt(2*ga*H),2)
Vf1=round(F*math.sqrt(2*ga*H),2)
#using power equation,P=ga*Q*H*eta0
Q=P/(ga*998*H*eta0) #Discharge
D=math.sqrt(Q/((math.pi/4)*(1-Db**2)*Vf1))
print "(i)D=",round(D,3),"m" #Diameter of the runner
Db=D*Db
N=(U1*60)/(math.pi*D) #If Speed=N rpm
print "(ii)N=",round(N,1),"rpm" #Rotational speed
Ns=(N*math.sqrt(P/1000))/(H**(5/4))#Specific speed
print "(iii)Ns=",round(Ns,1)
from __future__ import division
import math
#variable initialization
H=N=300 #Height
Cv=0.98 #Coefficient of velocity of jet
D=2.5 #Diameter
d=0.20 #Diameter of the jet
F=0.65 #Flow ratio
k=0.95 #Blade friction coefficient
Beta=165 #Blade angle
ga=9.81 #density
g=9.79 #gravity
etam=0.95 #Mechanical efficiency
#Calculation
BetaD=180-Beta
V1=round(((Cv*math.sqrt(2*ga*H))),3) #Jet velocity
Q=round((math.pi/4)*((d**2)*V1),3) #Discharge
u=(math.pi*D*H)/(60)
BetaD=BetaD*0.0175 #converting into radians
He=round((1/ga)*(u*(V1-u))*(1+k*(math.cos(BetaD))),1)#Head extracted
etaH=He/H #Hydraulic efficiency
print "(i)etaH=",round(etaH,3)
P=g*Q*H*etaH*etam #Power developed
print "(ii)P=",int(round(P,0)),"kW"
Ns=(N*math.sqrt(P))/(H**(5/4)) #Specific speed
print "(iii)Ns=",round(Ns,1)
import math
#variable initialization
u=14.0 #man bucket diameter in m^3/s
beta=165 #angle deflected in degree
k=1.0 #assumed value
Q=0.8 #discharge
H=45 #height
etam=0.95 #overall efficiency
Cv=0.985 #Given value
g=9.81 #gravity
rho=998 #relative density
#Calculation
BetaD=180-beta #in degrees
V1=((Cv*math.sqrt(2*g*H)))
BetaD=BetaD*0.0175 #converting into radians
P=((rho*Q*u*((V1-u)*(1+math.cos(BetaD))))/1000) #Power produced
Ps=round(P*etam,2)
print "Ps=",round(Ps,1),"kW"
eta0=Ps/(((g*rho)/1000)*Q*H) #Overall efficiency
#Answer given in the book varies slightly and correct answer is,
print "eta0=",round(eta0,3)
import math
#variable initialization
f=0.05 #friction loss
h=400 #height
N=420 #speed in rpm
ga=9.79 #density
eta0=0.85 #overall efficiency
Cv=0.98 #Given value
Ns=14 #Specific Speed
P=500 #Power per jet
phy=0.46 #speed ratio
g=9.81 #gravity
#Calculation
H=h*(1-f) #Net available Head
N=int((Ns*(H**(5/4)))/(math.sqrt(P))) #Rotational speed
print "N=",N,"rpm"
V1=round((Cv*math.sqrt(2*g*H)),2)
U=phy*(math.sqrt(2*g*H))
D=round((U*60)/(math.pi*N),3)
print "D=",D,"m" #mean diameter of bucket circle
Q=P*1000/(ga*998*H*eta0) #Discharge
d=math.sqrt(Q/((math.pi/4)*V1))
print "d=",round((d*100),2),"cm"
import math
#variable initialization
H=270 #Height
D=1.5 #Diameter
N=400 #speed in rpm
ga=9.81 #density
eta0=0.90 #overall efficiency
I=3000 #Impulse
Cv=0.95 #Given value
#Calculation
P=I/2
#using power equation,P=ga*Q*H*eta0
Q=P*1000/(ga*998*H*eta0) #Discharge
V1=round(Cv*math.sqrt(2*ga*H),2)
d=math.sqrt(Q/((math.pi/4)*V1))
print "(i)d=",round(d*100,2),"cm" #Diameter of the nozzle
U=round(((math.pi*D*N)/60),2) #Peripheral velocity of the bucket
phy=U/(math.sqrt(2*ga*H))
print "(ii)phy=",round(phy,3) #Speed ratio
Ns=(N*math.sqrt(P))/(H**(5/4)) #Specific speed
print "(iii)Ns=",round(Ns,2)
import math
#variable initialization
H=500 #Head in m
Cv=0.98 #specific heat
g=9.81 #gravity
fi=0.45 #assume
eta_o=0.85 #assume
d=18 #diameter in cm
gamma=9.79 #specific weight
N=420
#solution
V1=Cv*(math.sqrt(2*g*H)) #Velocity
d=d/100 #diameter in m
Q=(math.pi/4)*(d**2)*V1 #Discharge
P=eta_o*gamma*Q*H #Power developed
Ns=(N*math.sqrt(P))/(math.pow(H,5/4)) #Specific speed
print "Ns=",int(Ns)
import math
#variable initialisation
N1=100 #speed of turbine in rpm
H1=30 #head on turbine in m
H2=18 #head reduced in m
P1=8000 #p in kW
#solution
#For geometrically similar turbines,the unit speed,Nu=N/math.sqrt(H)
N2=round(N1*(math.sqrt(H2/H1)),2) #speed
print "N2=",N2,"rpm"
P2=P1*(math.pow((H2/H1),3/2)) #power developed
print "P2=",int(P2),"kW"
import math
#variable initialisation
P1=6750 #p in kW
N1=300 #speed in rpm
H1=45 #net head in m
H2=60 #net head under homologus conditions in m
ete_o=85 #efficiency in percentage
ga=9.81*998 #density in kg/m^3
#solution
#using unit relationships,
eta_o=85/100
Q=round(P1/((eta_o)*(ga/1000)*H1),2)
N2=round(N1*(math.sqrt(H2/H1)),1) #revolutions per minute
print "N2=",N2,"rpm"
Q1=18.03 #Q value
Q2=Q1*(math.sqrt(H2/H1)) #Discharge
print "Q2=",round(Q2,2),"m^3/s"
P2=P1*(math.pow((H2/H1),3/2)) #brake power
print "P2=",int(round(P2,5)),"kW"
import math
#variable initialization
r=0.15 #radius in m
N=60 #speed at rpm
rho=9800 #density
Ht=15 #Height
Qa=310 #actual discharge in l/min
#calculation
A=math.pi/4*(r**2) #Calculating area
L=2*r
Qt=round(((A*L*N)/60),4)
Qt1=Qt*60*1000 #converting into l/min
slip=(Qt1-Qa)*100/Qt1
print "slip=",round(slip,2),"%"
Cd=round(Qa/Qt1,3) #Coefficient of discharge
print "Coefficient of discharge=",Cd
Pt=rho*(Qt)*Ht #Power
print "Answer in the book for power is wrong.It should be as,"
print "Power,Pt=",round(Pt/1000,3),"kW"
import math
#variable initialization
r=0.40 #radius in cm
Ld=45.0 #length in m
g=9.81 #gravity
A=20 #size of cylinder in cm
Ad=10 #suction pipe in cm
Hv=2.5 #in m water (abs)
Hatmo=10 #atmospheric pressure of water in m
Hd=40 #height of water
#Calculation
Had=int(-(Hv-Hd-Hatmo))#At incipient caviation in the delivery pipe
N=Had/((Ld/g)*((A/Ad)**2)*(((2*math.pi)/60)**2)*r)
print "N=",round(N**(1/2),2),"rpm"
import math
#variable initialization
N=30 #speed in rpm
D=0.30 #radius of cylinder
Ls=5.0 #length in m
g=9.81 #gravity
A=15 #size of cylinder in cm
As=5 #suction pipe in cm
Hv=2.0 #in m water (abs)
Hatmo=10 #atmospheric pressure of water in m
Hs=2.5 #Suction head
#Calculation
omega=(2*math.pi*N)/60
r=D/2
Hasm=(-Hv-Hs+Hatmo)
N=Hasm/((Ls/g)*((A/As)**2)*(((2*math.pi)/60)**2)*r)#At limiting condition for a suction pipe,
print "N=",round(N**(1/2),0),"rpm"
import math
#variable initialization
N=30 #speed in rpm
S=40 #stroke in cm
Ls=5.0 #length in m
g=9.81 #gravity
A=20 #size of cylinder in cm
As=10 #suction pipe in cm
Hv=2.5 #in m water (abs)
Hatmo=10 #atmospheric pressure of water in m
#Calculation
omega=(2*math.pi*N)/60
r=(S/100)/2
Hasm=(Ls/g)*((A/As)**2)*(omega**2)*r
Hs=Hatmo-Hv-Hasm
print "Hs=",round(Hs,3),"m"
import math
#variable initialization
N=50 #speed in rpm
Ls=5.0 #length in m
g=9.81 #gravity
r=0.20 #size of cylinder in cm
Hv=2.5 #in m water (abs)
Hatmo=10.0 #atmospheric pressure of water in m
Hs=3.0 #in m
d=25 #diameter in cm
#Calculation
N=N/2 #since there are 2 strokes per revolution
omega=round((2*math.pi*N)/60,3)
Hasm=round((Ls/g)*(omega**2)*r,2)#Maximum acceleration head in suction pipe
Ds=(Hatmo-Hs-Hv)/(Hasm) #At limiting condition for a suction pipe
print "ds=",round(d/Ds**(1/2),2),"cm"