Chapter 9 : Impact of Jets

Example 9.1 Page No : 171

In [1]:
import math 

#initialisation of variables
d= 2. 	    #in
V= 210. 	#ft/sec
V1= 50. 	#ft/sec
g= 32.2 	#ft/sec**2
w= 62.4 	#lb/ft**3

#CALCULATIONS
M= math.pi*V*w/(4*36*g)
F= M*V
dV= V-V1
M1= math.pi*dV*w/(4*36*g)
F1= M1*dV
W= F1*V1
F2= M*dV
W1= F2*V1

#RESULTS
print  'Force on plate = %.f lb'%(F+1)
print  ' Force on plate = %.f lb'%(F1)
print  ' Work done/sec = %.f ft-lb/sec'%(W)
print  ' Force on plate = %.f lb'%(F2)
print  ' Work done/sec = %.f ft-lb/sec'%(round(W1,-3))

#The answer is a bit different due to rounding off error in textbook

Force on plate = 1865 lb
 Force on plate = 1082 lb
 Work done/sec = 54116 ft-lb/sec
 Force on plate = 1421 lb
 Work done/sec = 71000 ft-lb/sec

Example 9.2 Page No : 172

In [2]:
import math 

#initialisation of variables
v1= 15. 	#ft/sec
v2= 40. 	#ft/sec
a= 30.  	#degrees
b= 150. 	#degrees
v= 15.27 	#ft/sec
g= 32.2 	#ft/sec**2

#CALCULATIONS
a1= a-math.degrees(math.sin(v1*math.sin(math.radians(b))/v2))
w= math.cos(math.radians(a1))*v2
vr= v2*math.sin(math.radians(a1))/math.sin(math.radians(a))
v1= math.sqrt(v1**2+vr**2-2*v1*vr*math.cos(math.radians(a)))
r= 180-math.sin(math.radians(a))*vr/v
w1= v*math.cos(math.radians(r))
W= v1*(w-w1)/g

#RESULTS
print  'a = %.2f degrees'%(a1)
print  ' w = %.2f ft/sec'%(w)
print  ' vr = %.2f ft/sec'%(vr)
print  ' v1 = %.2f ft/sec'%(v1)
print  ' w = %.2f ft/sec'%(w)
print  ' Work done per pound = %.2f ft-lb/lb'%(W)

# Note : Answers are different because of rounding off error.

a = 19.32 degrees
 w = 37.75 ft/sec
 vr = 26.47 ft/sec
 v1 = 15.42 ft/sec
 w = 37.75 ft/sec
 Work done per pound = 25.39 ft-lb/lb

Example 9.3 Page No : 173

In [13]:
import math 

#initialisation of variables
d= 0.5    	#in
a= 165. 	#degrees
W= 7.35 	#lb
W1= 500. 	#lb
t= 148. 	#sec
g= 32.2 	#ft/sec**2
w= 62.3 	#lb/ft**3

#CALCULATIONS
Q= W1/(t*w)
v= Q*16*144/math.pi
dv= v*(1-math.cos(math.radians(a)))
F= dv*W1/(t*g)
r= W/F
k= (1-(W*t*g/(W1*v)))/math.cos(math.radians(a))

#RESULTS
print  'k = %.3f '%(k)

k = 0.788

Example 9.4 Page No : 174

In [18]:
import math 

#initialisation of variables
t= 0.25 	#in
a= 30.   	#degrees
w= 480. 	#lb/ft**3
h= 2.    	#in
d= 0.5  	#in
l= 6.    	#in
w1= 62.4 	#lb/ft**3
g= 32.2 	#ft/sec**2

#CALCULATIONS
W= t*l**2*w/1728
M= w1*math.pi*d**2*math.cos(math.radians(a))/(g*4*144)
v= math.sqrt(W*(l/2)*math.sin(math.radians(a))/(M*2*(1./math.cos(math.radians(a)))))

#RESULTS
print  'Velocity of jet = %.1f ft/sec'%(v)

Velocity of jet = 26.6 ft/sec

Example 9.5 Page No : 176

In [2]:
import math 

#initialisation of variables
V= 90. 	#ft/sec
a= 30. 	#degrees
u= 45. 	#ft/sec

#CALCULATIONS
w= V*math.cos(math.radians(a))
f= math.sqrt(V**2-w**2)
tanb= (math.atan(math.radians(f/(w-u))))
b = math.degrees(math.tan(tanb))
b = math.degrees(math.atan(b))
V1= math.sqrt(f**2+(u-f*1./math.tan(math.radians(b)))**2)

#RESULTS
print "B = %.2f degrees"%b
print  'absolute velocity of water at the exit = %.1f ft/sec'%(V1)

# rounding off error

B = 53.79 degrees
absolute velocity of water at the exit = 46.6 ft/sec

Example 9.6 Page No : 177

In [23]:
import math 

#initialisation of variables
u= 734. 	#ft/sec
v= 2000. 	#ft/sec
g= 32.2 	#ft/sec**2
da= 0.019 	#kg/m**3

#CALCULATIONS
W= g*v/(v-u)
A= W/(u*da)

#RESULTS
print  'Weight of the air = %.1f lb/sec'%(W)
print  ' Area of inlet = %.2f ft**2'%(A)

Weight of the air = 50.9 lb/sec
 Area of inlet = 3.65 ft**2