# Chapter7-Centrifugal Pumps,Fans and Compressors¶

## Ex1-pg216¶

In [2]:
import math
#calculate the

##function to calculate blade cavitation coefficient

##given data
Q = 25;##flow rate in dm^3/s
omega = 1450;##rotational speed in rev/min
omega_ss = 3;##max. suction specific speed in rad/sec
r = 0.3;##inlet eye radius ratio
g = 9.81;##in m/s^2

##Calculations
k = 1.-(r**2);
sigmab = 0.3;##initial guess
d = (sigmab**2)*(1. + sigmab)- (((3.42*k)**2)/(omega_ss**4));
i = 0;
if sigmab>0:
sigmab = sigmab - 0.0001;
elif sigmab<0:
sigmab = sigmab + 0.0001;

phi = (sigmab/(2.*(1.+sigmab)))**0.5;
rs1 = ((Q*10**-3.)/(math.pi*k*(omega*math.pi/30.)*phi))**(1./3.);
ds1 = 2.*rs1;
cx1 = phi*(omega*math.pi/30.)*rs1;
Hs = (0.75*sigmab*cx1**2)/(g*phi**2);

##Results
print'%s %.2f %s'%('(i)The blade cavitation coefficient = ',sigmab,'');
print'%s %.2f %s %.2f %s '%('\n (ii)The shroud radius at the eye = ',rs1,' m' and '\n The required diameter of the eye = ',ds1*10**3,'mm');
print'%s %.2f %s'%('\n (iii)The eye axial velocity = ',cx1,' m/s');
print'%s %.2f %s'%('\n (iv)The NPSH = ',Hs,' m');

#asnwer is wrong due to round off error

(i)The blade cavitation coefficient =  0.30

(ii)The shroud radius at the eye =  0.06
The required diameter of the eye =  110.70 mm

(iii)The eye axial velocity =  2.85  m/s

(iv)The NPSH =  1.62  m


## Ex2-pg220¶

In [3]:
import math
#calculate the

##given data
alpha1 = 30.;##prewhirl in deg
hs = 0.4;##inlet hub-shrub radius ratio
Mmax = 0.9;##max Mach number
Q = 1;##air mass flow in kg/s
p01 = 101.3;##stagnation pressure in kPa
T01 = 288.;##stagnation temperature in K
gamma = 1.4;
Rg = 287.;##in J/(kgK)

##Calculationsasza
beta1 = 49.4;##in deg
f = 0.4307;
a01 = math.sqrt(gamma*Rg*T01);
rho01 = p01*1000./(Rg*T01);
k = 1-(hs**2);
omega = (math.pi*f*k*rho01*a01**3)**0.5;
N = (omega*60./(2.*math.pi));
rho1 = rho01/(1. + 0.2*(Mmax*math.cos(beta1*math.pi/180.))**2)**2.5;
cx = ((omega**2.)/(math.pi*k*rho1*(math.tan(beta1*math.pi/180.) + math.tan(alpha1*math.pi/180.))**2.))**(1/3.);
rs1 = (1./(math.pi*rho1*cx*k))**0.5;

ds1 = 2.*rs1;
U = omega*rs1;

##Results
print'%s %.2f %s %.2f %s '%('(i)The rotational speed of the impeller = ',omega,' rad/s'and 'N = ',N,' rev/min.');
print'%s %.2f %s %.2f %s '%('\n (ii)The inlet static density downstream of the guide vanes at the shroud = ',rho1,' kg/m^3.'and'\n The axial velocity = ',cx,' m/s.');
print'%s %.2f %s %.2f %s '%('\n (iii)The inducer tip diameter = ',ds1*100,' cm'and '\n U = ',U,' m/s.');

##there are small errors in the answers given in textbook

(i)The rotational speed of the impeller =  7404.94 N =  70711.94  rev/min.

(ii)The inlet static density downstream of the guide vanes at the shroud =  1.04
The axial velocity =  187.38  m/s.

(iii)The inducer tip diameter =  8.83
U =  326.81  m/s.


## Ex3-pg228¶

In [4]:
import math
#calculate the

##given data
Q = 0.1;##in m^3/s
N = 1200.;##rotational speed in rev/min
beta2_ = 50.;##in deg
D = 0.4;##impeller external diameter in m
d = 0.2;##impeller internal diameter in m
b2 = 31.7;##axial width in mm
eff = 0.515;##diffuser efficiency
De = 0.15;##diffuser exit diameter
A = 0.77;
B = 1.;
g = 9.81;

##Calculations
U2 = math.pi*N*D/60.;
cr2 = Q/(math.pi*D*b2/1000.);
sigmaB = (A - H*math.tan(beta2_*math.pi/180.))/(B - H*math.tan(beta2_*math.pi/180.));
ctheta2 = sigmaB*U2*(1.-H*math.tan(beta2_*math.pi/180.));
Hi = U2*ctheta2/g;
c2 = math.sqrt(cr2**2 + ctheta2**2);
c3 = 4.*Q/(math.pi*De**2);
HL = 0.1*Hi + 0.485*((c2**2)-(c3**2))/(2.*g) + (c3**2.)/(2.*g);
H = Hi - HL;
eff_hyd = H/Hi;

##Results
print'%s %.2f %s'%('The slip factor = ',sigmaB,'');
print'%s %.2f %s'%('\n The manometric head = ',H,' m.');
print'%s %.2f %s'%('\n The hydraulic efficiency = ',eff_hyd*100,' percentage.');

##there is a very small error in the answer given in textbook

The slip factor =  0.74

The manometric head =  30.11  m.

The hydraulic efficiency =  71.84  percentage.


## Ex4-pg235¶

In [5]:
import math
#calculate the

##given data
T01 = 22.;##stagnation temperature in degC
Z = 17.;##number of vanes
N = 15000.;##rotational speed in rev/min
r = 4.2;##stagnation pressure ratio between diffuser and impeller
eff_ov = 0.83;##overall efficiency
mdot = 2;##mass flow rate in kg/s
eff_m = 0.97;##mechanical efficiency
rho2 = 2.;##air density at impeller outle in kg/m^3
gamma = 1.4;
R = 0.287;##in kJ/(kg.K)
b2 = 11.;##axial width at the entrance to the diffuser in mm

##Calculations
Cp = gamma*R*1000./(gamma-1.);
sigmaS = 1 - 2./Z;
U2 = math.sqrt(Cp*(T01+273.)*((r)**((gamma-1.)/gamma) -1.)/(sigmaS*eff_ov));
omega = N*math.pi/30.;
rt = U2/omega;
Wdot_act = mdot*sigmaS*(U2**2)/(eff_m);
cr2 = mdot/(rho2*2.*math.pi*rt*b2/1000.);
ctheta2 = sigmaS*U2;
c2 = math.sqrt(ctheta2**2 +cr2**2);
delW = sigmaS*U2**2;
T2 = T01+273.+(delW - 0.5*c2**2)/Cp;
M2 =  c2/math.sqrt(gamma*R*1000.*T2);

##Results
print'%s %.2f %s'%('Absolute mach number, M2 = ',M2,'');

Absolute mach number, M2 =  1.01