Chapter 12 : Turbomachines: Further Analysis

Example 12.1 Page No : 461

In [1]:
%matplotlib inline
from matplotlib.pyplot import *
import math 
	
#initialisation of variables
d= 0.0764 	        #lbm/ft**3
u= 3.74*10**-7 	    #lbf sec/ft**2
D= 15.           	#in
g= 32.2 	        #ft/sec**2
p= 14.7 	        #lb/in**2
r1= [0.02, 0.04, 0.06, 0.08, 0.1, 1.15]
r2= [0.0338, 0.0267, 0.0199, 0.0159, 0.0132, 0.0100]
r3= [0.46, 0.92, 1.38, 1.84, 2.3, 2.64]
r4= [2.97, 2.35, 1.75, 1.4, 1.16, 0.88]
r5= [0.0206, 0.0163, 0.0121, 0.0097, 0.0081, 0.0061]
	
#CALCULATIONS
re= (d/u)*(p*100*2*math.pi/60)*(D/12)**2/g
	
#RESULTS
print  'Reynolds Number = %.2e '%(re)
print "m/qwD**3     g0deltaPe/QW**2D**2     m(lbm/sec)      deltap(lbf/ft**2)      deltap(lbf/in**2)"
for i in range(len(r1)):
    print "%7.2f     %8.4f              %7.2f         %7.2f              %8.4f"%(r1[i],r2[i],r3[i],r4[i],r5[i])

plot(r3,r5)
xlabel("m lbm/sec")
ylabel( "dPs lbf/ft**2") 
suptitle("Actual perfomance curve")

Populating the interactive namespace from numpy and matplotlib
Reynolds Number = 1.53e+06 
m/qwD**3     g0deltaPe/QW**2D**2     m(lbm/sec)      deltap(lbf/ft**2)      deltap(lbf/in**2)
   0.02       0.0338                 0.46            2.97                0.0206
   0.04       0.0267                 0.92            2.35                0.0163
   0.06       0.0199                 1.38            1.75                0.0121
   0.08       0.0159                 1.84            1.40                0.0097
   0.10       0.0132                 2.30            1.16                0.0081
   1.15       0.0100                 2.64            0.88                0.0061
Out[1]:
<matplotlib.text.Text at 0x1c015d0>

Example 12.2 Page No : 464

In [2]:
import math 
	
#initialisation of variables
psif= 10.2       	#lbf/in**2 pressure
usit= 3.8*10**-7 	#lbf sec/ft**2 viscosity
usif= 3.52*10**-7 	#lbf sec/ft**2 viscosity
Tsit= 530.       	#R temperature
Tsif= 480.          #R temperature
wf= 15000.       	#rev/min speed
	
#CALCULATIONS
Psit= psif*usit*math.sqrt(Tsit/Tsif)/usif
wt= wf*math.sqrt(Tsit/Tsif)
	
#RESULTS
print  'Pressure in the test cell = %.1f lbf/in**2'%(Psit) 
print  ' Compressor speed = %.f rev.min'%(wt) 

# book answer is wrong.

Pressure in the test cell = 11.6 lbf/in**2
 Compressor speed = 15762 rev.min

Example 12.3 Page No : 474

In [3]:
import math 
	
#initialisation of variables
w= 62.3 	#lbf/ft**3 weight
d= 0.375 	#in diameter
ro= 0.75 	#ft radius
l= 1.25 	#ft length
b= 120. 	#degrees angle
do= 0.25 	#in diameter
p= 750. 	#lbf/in**2
g= 32.1 	#ft/sec**2
f= 0.03     # friction factor
f1= 0.9
f2= 0.3
w1= 60. 	#rad/sec
	
#CALCULATIONS
Q= math.sqrt(((p/w)+((60*ro)**2/(2*g))+do)*math.pi**2*g*(d/12)**4/((d/do)**4-1+(l*f/(d/12))+f1+f2))*0.353
Vwo= w1*ro+(4*Q/(math.pi*(do/12)**2))*math.cos(math.radians(b))
C= w*Q*Vwo*ro/g
	
#RESULTS
print  ' Flow Rate = %.4f ft**3/sec'%(Q) 
print  ' Vwo = %.2f ft/sec'%(Vwo) 
print  ' Driving Torque = %.3f lbf ft'%(C) 

 Flow Rate = 0.0160 ft**3/sec
 Vwo = 21.56 ft/sec
 Driving Torque = 0.502 lbf ft

Example 12.4 Page No : 491

In [4]:
	
#initialisation of variables
W= 38.   	#rev/sec speed
w= 62.4 	#lbf/ft**3 density
m= 2000. 	#lbm/sec flow rate
g= 32.2 	#ft/sec**2
ps= 5000. 	#lbf/ft**2 pressure rise
S3= 4.6
e= 0.91
	
#CALCULATIONS
S1= W*(w*m**2/(g*ps)**3)**0.25
D= S3*(m**2/(w*g*ps))**0.25
	
#RESULTS
print  ' S1 = %.3f'%(S1)  
print  ' Diameter = %.2f ft'%(D)  
print  ' efficiency = %.2f '%(e)

 S1 = 0.594
 Diameter = 3.65 ft
 efficiency = 0.91

Example 12.5 Page No : 495

In [5]:
import math 
	
#initialisation of variables
d= 6.    	#in diameter
f= 0.25
l= 1200. 	#ft long
p= 55.   	#lbm/ft**3
w= 740.  	#rev/min
g= 32.2 	#ft/sec**2
n= 0.87     # efficiency
d1= 1.78 	#ft
	
#CALCULATIONS
D= (0.13*math.pi**2*(d/12)**5/(8*f*l*0.012**2))**0.25*d1
m= 0.012*p*(w*2*math.pi/60)*D**3
dps= 0.13*p*(w*2*math.pi*D/60)**2/g
P= m*10*dps/(p*n)
	
#RESULTS
print  ' Diameter = %.2f ft'%(D) 
print  ' Mass flow rate = %.1f lbm/sec'%(m) 
print  ' pressure rise = %.1f lbf/ft**2'%(round(dps,-1))
print  ' shaft power = %.2e ft lbf/sec'%(P)

# rounding off error

 Diameter = 1.04 ft
 Mass flow rate = 57.3 lbm/sec
 pressure rise = 1440.0 lbf/ft**2
 shaft power = 1.72e+04 ft lbf/sec