Chapter 10 : External Flows

Example 10.1 Page No : 367

In [3]:
import math 
from numpy import *
	
#initialisation of variables
g= 32.2 	#ft/sec**2
u= 3.6*10**-5 	#lbf sec/ft**2 viscosity
d= 64. 	#lbm/ft**2 density
l= 20. 	#ft long
a= 0.5
	
#CALCULATIONS
sw= u*g/(a*d)
sw1= u**2*g*l/(2*a*d)
Re=array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])*10**5
Vinf=Re*u*g/(d*a)
Cd= array([1.2, 1.15, 0.94, 0.68, 0.305, 0.31, 0.32, 0.33, 0.34, 0.35])
cdre=Cd*Re**2
D=sw1*cdre
	
#RESULTS
print  'velocity = %.3e ft/sec'%(sw)
print  ' Force = %.3e lbf'%(sw1)
print "V (ft/sec)        D(lbf)"
for i in range(len(D)):
    print "%6.1f         %6d"%(Vinf[i],D[i])


# note : answers are accurate. please check manually.

velocity = 3.623e-05 ft/sec
 Force = 1.304e-08 lbf
V (ft/sec)        D(lbf)
   3.6            156
   7.2            599
  10.9           1103
  14.5           1418
  18.1            994
  21.7           1455
  25.4           2044
  29.0           2754
  32.6           3591
  36.2           4564

Example 10.2 Page No : 368

In [1]:
%matplotlib inline
from numpy import *
from matplotlib.pyplot import *
	
#initialisation of variables
g= 32.2 	#ft/sec**2
u= 3.6*10**-5 	#lbf sec/ft**2
d= 64. 	#lbm/ft**2 density
l= 20. 	#ft long
a= 0.5
	
#CALCULATIONS
sw= u*g/(a*d)
sw1= u**2*g*l/(2*a*d)
Re = array([1 ,2, 3, 4, 5, 6, 7, 8, 9, 10])*10**5
Vinf=Re*u*g/(d*a)
Cd = array([1.2, 1.15, 0.94, 0.68, 0.305, 0.31, 0.32, 0.33, 0.34, 0.35])
cdre=Cd*Re**2
D=sw1*cdre
	
#RESULTS
plot(Vinf,D)
xlabel("Vinf, ft/sec")
ylabel("D, lbf") 
suptitle("Streamlinedbody curve")

	#data for curves b,c,d is not given

Populating the interactive namespace from numpy and matplotlib
Out[1]:
<matplotlib.text.Text at 0x2683050>

Example 10.3 Page No : 373

In [2]:
	
#initialisation of variables
v1= 10. 	#ft/sec
v2m= 9 	    #ft/sec wide
a= 1.02
hbyd= 5.95
	
#CALCULATIONS
ca= (v1/v2m)**2
Cd= hbyd*(ca-1+2-2*ca)+2*a*ca
	
#RESULTS
print  'Drag coeffcieicnt = %.2f'%(Cd)

Drag coeffcieicnt = 1.12

Example 10.4 Page No : 387

In [6]:
	
#initialisation of variables
A= 320.  	#ft/**2 area
w= 18000. 	#lbf weighs
v= 230.  	#ft/sec normal speed
ad= 0.0765 	#lbm/ft**3 density
p= 5.    	#per cent of the total lift force
c= 0.055
n= 1.75     # total drag
g= 32.2 	#ft/sec**2
	
#CALCULATIONS
CL= 2*w*(1-(p/100))*g/(ad*v**2*A)
D= w*(1-(p/100))*c*n/CL
	
#RESULTS
print  ' lift coefficient = %.2f'%(CL)
print  ' Drag force = %.f'%(D)

# note : answer is accurate

 lift coefficient = 0.85
 Drag force = 1935

Example 10.5 Page No : 396

In [7]:
import math 
	
#initialisation of variables
bi= 70. 	#degrees outlet angels
i= 8.    	#degrees incidence angle
bo= 130. 	#degrees outlet angels
s= 5.    	#degrees
vi= 1200. 	#ft/sec
g= 32.2 	#ft/sec**2
a= 0.48
s1= 1.4 	#in
b= 5.    	#in
Cx= 0.06    # co-efficient 
	
#CALCULATIONS
O= bo-s-bi+i
Vo= vi*math.sin(math.radians(bi-i))/math.sin(math.radians(bo-s))
Fy= -a*vi*math.sin(math.radians(bi-i))*(s1/12)*(b/12)*(Vo*math.cos(math.radians(bo-s))-vi*math.cos(math.radians(bi-i)))/g
dp= a*(Vo**2*(1+Cx)-vi**2)/(2*g)
	
#RESULTS
print  'Fluid deflection angle = %.f degrees'%(O)
print  ' Vo = %.f ft/sec'%(Vo)
print  ' Force on each blade = %.f lbf'%(Fy)
print  ' Pressure difference = %.f lbf/ft**2'%(dp)

# note : answer is accurate. please check.

Fluid deflection angle = 63 degrees
 Vo = 1293 ft/sec
 Force on each blade = 1002 lbf
 Pressure difference = 2485 lbf/ft**2

Example 10.6 Page No : 397

In [8]:
import math 
	
#initialisation of variables
ari= 62. 	#degrees
aro= 125. 	#degrees
vri= 1200. 	#ft/sec
vro= 1294. 	#ft/sec
vrr= 550. 	#ft/sec velocity
	
#CALCULATIONS
v1= vri*math.sin(math.radians(ari))
v2= vrr+vri*math.cos(math.radians(ari))
vi= math.sqrt(v1**2+v2**2)
ai= round(math.degrees(math.atan(v1/v2)),1)
vo= round(vro*math.sin(math.radians(aro)))
vo1= round(vro*math.cos(math.radians(aro))+vrr)
vo2= round(math.sqrt(vo**2+vo1**2))
ao= math.degrees(math.atan(vo/vo1))+180

#RESULTS
print  ' absolute velocity = %.f ft/sec'%(vi)
print  ' direction = %.1f degrees'%(ai)
print  ' absolute velocity = %.f ft/sec'%(vo2)
print  ' direction = %.1f degrees'%(ao)

 absolute velocity = 1537 ft/sec
 direction = 43.6 degrees
 absolute velocity = 1077 ft/sec
 direction = 100.3 degrees