Chapter 6 : Steady, One-Dimensional, Reversible Flow¶

Example 6.1 Page No : 157¶

In [3]:
import math

#initialisation of variables
g= 32.2 	#ft/sec**2 gravitational acceleration
h= 4.    	#ft diameter
d2= 0.16 	#ft
d1= 0.3 	#ft
dp= 13.6 	#lbf/in**2 mercury

#CALCULATIONS
Q= (math.pi/4)*math.sqrt(2*g*dp*h/((1/d2**4)-(1/d1**4)))

#RESULTS
print  'Volumetric flow rate = %.2f ft**3/sec'%(Q)

# note: book answer is not accurate.

Volumetric flow rate = 1.24 ft**3/sec


Example 6.2 Page No : 158¶

In [4]:

#initialisation of variables
w= 0.0765 	#lbm/ft**3 density
v1= 120. 	#ft/sec velocity
go = 62.4   	#lmb/ft**3

#CALCULATIONS
dp= (w*v1**2)/(2*go)

#RESULTS
print  'Difference in pressure= %.2f lbf/ft**2'%(dp)

Difference in pressure= 8.83 lbf/ft**2


Example 6.3 Page No : 161¶

In [5]:
import math

#initialisation of variables
r=1.4
g= 32.2 	#ft/sec**2 gas
R= 53.3 	#lbf ft/lbm
T1= 760. 	#R  Temperature
p2= 2.   	#lbf/in**2
p1= 3. 	    #lbf/in**2

#CALCULATIONS
V2= math.sqrt(2*r*R*g*T1*(1-(p2/p1)**((r-1)/r))/(r-1))

#RESULTS
print  'Velocity in working section = %.f ft/sec'%(V2)

Velocity in working section = 999 ft/sec


Example 6.4 Page No : 166¶

In [6]:
import math

#initialisation of variables
y = 1.4
g = 32.2 	#ft/sec**2
R = 53.3 	#lbf ft/lbm
T = 32.   	#C air
T1 = 2000. 	#R air
y1 = 1.32
p = 1440.     	#lbf/in**2
v1 = 1.2306 	    #ft**3/lbm
v2 = 1.2546 	    #ft**3/lbm
bm = 3.13*10**5 	#lbf/in**2
w = 62.4 	    #lbf/ft**3

#CALCULATIONS
a1= math.sqrt(y*R*(460+T)*g)
a2= math.sqrt(y1*R*T1*g)
r2= p/(v1-v2)
a3= math.sqrt(-g*(v1+v2)**2*0.5**2*r2)
a4= math.sqrt(bm*144*g/w)

#RESULTS
print  ' Acoustic veloctiy in air at 32 F = %.f ft/sec'%(a1)
print  ' Acoustic veloctiy in air at 2000 R = %.f ft/sec'%(a2)
print  ' Acoustic veloctiy in steam at 480 F = %.f ft/sec'%(a3)
print  ' Acoustic veloctiy in water at 60 F = %.f ft/sec'%(a4)

 Acoustic veloctiy in air at 32 F = 1087 ft/sec
Acoustic veloctiy in air at 2000 R = 2129 ft/sec
Acoustic veloctiy in steam at 480 F = 1727 ft/sec
Acoustic veloctiy in water at 60 F = 4823 ft/sec


Example 6.5 Page No : 172¶

In [7]:

#initialisation of variables
r= 1.4
ma2= 2.5 	#ft/sec
g= 32.17 	#ft/sec**2
p2= 1.   	#lbf/in**2
ps= 17.08 	#lbf/in**2
ps2= 75. 	#lbf/in**2
Ts= 720. 	#R
R= 53.3 	#lbf ft/lbm gas
A= 4.    	#ft**2 flow area
ps3= 0.4 	#lbf/in**2
A2= 0.685 	#ft**2
P= 5.    	#per cent throat area

#CALCULATIONS
R1= (1+0.5*(r-1)*ma2**2)**(r/(r-1))
R2= (2*(r/(r-1))*(p2/ps)**(2/(r))*(1-(p2/ps)**((r-1)/r)))**0.5
m2= R2*ps2*144*(g/(R*Ts))**0.5*0.1
m= m2*A
At= A*R2/A2
m1= m*(1-(P/100))
mrp= (1-(P/100))*R2

#RESULTS
print  ' Mass flow rate= %.1f lbm/sec'%(m)
print  ' Area of throat= %.3f ft**2'%(At)
print  ' Mass flow rate= %.1f lbm/sec'%(m1)
print  ' Mass flow rate parameter = %.4f'%(mrp)

 Mass flow rate= 32.5 lbm/sec
Area of throat= 1.517 ft**2
Mass flow rate= 30.9 lbm/sec
Mass flow rate parameter = 0.2468


Example 6.7 Page No : 181¶

In [8]:

#initialisation of variables
r1= 10.  	#ft point - 1
r2= 0.2 	#miles point - 2
w= 0.0765 	#lbm/ft**2 density
g= 32.2 	#ft/sec**2
V1= 1.   	#ft/sec velocity

#CALCULATIONS
k= r2*5280*V1
dp= w*k**2*10*((1/r1)**2-(1/(5280*r2))**2)/(2*g)

#RESULTS
print  'k = %.f ft**2/sec'%(k)
print  ' pressure difference = %.1f lbf/ft**2'%(dp)

k = 1056 ft**2/sec
pressure difference = 132.5 lbf/ft**2


Example 6.9 Page No : 186¶

In [9]:

#initialisation of variables
w= 12.   	#ft wide
q= 300.  	#ft**3/sec rate
h= 10.   	#ft depth upstream of the gate
g= 32.2 	#ft/sec**2
R= 2.6

#CALCULATIONS
hc= ((q/12)**2/g)**(1./3)
r= h/hc
h1= hc*(((h/hc)+0.5*(hc/h)**2)-0.5*R**2)

#RESULTS
print  ' hc = %.2f ft'%(hc)
print  ' stream depth = %.3f ft'%(h1)
#rounding-off error

 hc = 2.69 ft
stream depth = 1.013 ft


Example 6.10 Page No : 190¶

In [10]:

#initialisation of variables
Q= 400. 	#ft**3/sec flow rate
b1= 25. 	#ft channel width
b2= 20. 	#ft channel width
h1= 6.   	#ft stream depth
z1= 2.5 	#ft elevation of channel bottom
z2= 3.3 	#ft elevation of channel bottom
g= 32.2 	#ft/sec**2

#CALCULATIONS
hc1= (Q**2/(g*b1**2))**(1./3)
hc2= (Q**2/(g*b2**2))**(1./3)
r= (hc1/hc2)*((h1/hc1)+0.5*(hc1/h1)**2)+((z1-z2)/hc2)

#RESULTS
print  ' hc1 = %.3f ft'%(hc1)
print  ' hc2 = %.3f ft'%(hc2)
print  ' Ratio = %.3f '%(r)

 hc1 = 1.996 ft
hc2 = 2.316 ft
Ratio = 2.293