Chapter 8 : Impact of Jets

Example 8.1 Page No : 276

In [1]:
import math 
		
#initialisation of variables
d = 1. 		#in
v = 36. 		#ft/sec
b = 30. 		#degrees
w = 62.4 		#lbs/ft**3
g = 32.2
		
#CALCULATIONS
a = math.pi/4 * (d/12)**2
thrust = w*a*v**2/g
P = w* math.sin(math.radians(b))*v**2*(math.pi*(d/12)**2/4)/g
		
#RESULTS
print "The trust when the plate is normal to the jet = %.1f lbs. wt."%thrust
print  'Total thrust on the plate when inclined = %.2f lb wt'%(P)

The trust when the plate is normal to the jet = 13.7 lbs. wt.
Total thrust on the plate when inclined = 6.85 lb wt

Example 8.2 Page No : 277

In [2]:
import math 
		
#initialisation of variables
a = 180. 		#degrees
g = 32.2 		#ft/sec**2
w = 62.4 		#lbs/ft**3
d = 1.  		#in
H = 100. 		#ft
u = 0.95
		
#CALCULATIONS
v = u*math.sqrt(2*g*H)
Px = w*(1- math.cos(math.radians(a)))*(math.pi*(d/12)**2/4)*v**2/g
		
#RESULTS
print  'force it exerts = %.1f lb wt'%(Px)

force it exerts = 122.9 lb wt

Example 8.3 Page No : 278

In [2]:
import math 
		
#initialisation of variables
d = 30. 		#in
a = 90. 		#degrees
Q = 62.5 		#ft**3/sec
w = 62.4 		#lbs/ft**3
n =4.
g =32.2
		
#CALCULATIONS
v = Q*4/(math.pi*(d/12)**2)
P = w*math.pi*(d/12)**2*v**2/(4*g)
Px = P/n

#RESULTS
print  'pull on each bolt = %.1f lbs'%(Px)

# rounding off error. please check.

pull on each bolt = 385.5 lbs

Example 8.4 Page No : 278

In [4]:
import math 
		
#initialisation of variables
d = 4. 		#in
v = 30. 		#ft/sec
a = 22.5 		#degrees
w = 62.4 		#lbs/ft**3
g = 32.2 		#ft/sec**2
		
#CALCULATIONS 
P = w*(math.pi*(d/12)**2/4)*v**2*math.sqrt(2*(1-math.cos(math.radians(a))))/g
		
#RESULTS
print  'Resultant force tending to move the pipe = %.f lbs'%(P)


		#ANSWER GIVEN IN THE TEXTBOOK IS WRONG

Resultant force tending to move the pipe = 59 lbs

Example 8.5 Page No : 284

In [5]:
import math 
		
#initialisation of variables
d = 3. 		#in
v1 = 80. 		#ft/sec
v2 = 40. 		#ft/sec
w = 62.4 		#lbs/ft**3
g = 32.2 		#ft/sec**2
		
#CALCULATIONS
vr = v1-v2
P = w*vr*v2*math.pi*(d/12)**2/(g*4)
		
#RESULTS
print  'normal pressure on the plate when jet strikes = %.1f lbs'%(P)

normal pressure on the plate when jet strikes = 152.2 lbs

Example 8.6 Page No : 285

In [6]:
import math 
		
#initialisation of variables
d = 2.  		#in
v1 = 50. 		#ft/sec
v2 = 20. 		#ft/sec
W = 62.4 		#lbs/ft**3
g = 32.2 		#ft/sec**2
		
#CALCULATIONS
vr = v1-v2
P = W*vr*v1*math.pi*(d/2)**2/(g*4)
W = P*v2
KE = 2*vr*v2*100/v1**2
		
#RESULTS
print  'Efficiency = %.f per cent'%(KE)

Efficiency = 48 per cent

Example 8.7 Page No : 286

In [3]:
import math 

#initialisation of variables
d = 1. 		#in
v = 10. 		#f/sec
v1 = 30. 		#ft/sec
w = 62.4 		#lbs/ft**3
a = 180. 		#degrees
g = 32.2 		#ft/sec**2
		
#CALCULATIONS
A = math.pi*(d/12)**2/4
vr = 80-v1
M = w*vr*A
Px = M*vr*(1- math.cos(math.radians(a)))/g
W = Px*v1
M1 = w*80*A
Px1 = M1*vr*(1-math.cos(math.radians(a)))/g
W1 = Px1*v1
		
#RESULTS
print  'total force when there is a math.single cup = %.1f ft lbs'%(W)
print  ' total force when there is a series of cups = %.1f ft lbs'%(W1)

# rounding off error.

total force when there is a math.single cup = 1585.4 ft lbs
 total force when there is a series of cups = 2536.7 ft lbs

Example 8.8 Page No : 287

In [19]:
import math 
		
#initialisation of variables
v = 100. 		#ft/sec
u = 40. 		#ft/sec
a = 25. 		#degrees
g = 32.2 		#ft/sec**2
vr = 66. 		#ft/sec
a1 = 20. 		#/degrees
a2 = 8. 		#degrees
r = 0.14
		
#CALCULATIONS
Uw = v * math.cos(math.radians(a))
Uv = v * math.sin(math.radians(a))
tanA = Uv/(Uw - u)
A = math.degrees(math.atan(tanA))
v1 = vr*.14/0.342
W = (v**2-v1**2)/(2*g)
e = (v**2-v1**2)*100/v**2

#RESULTS
print  'inlet blade angle  = %.2f degrees'%(A)
print  ' Work done  = %.f ft lbs'%(W)
print  ' efficiency  = %.2f ft per cent'%(e)

inlet blade angle  = 39.85 degrees
 Work done  = 144 ft lbs
 efficiency  = 92.70 ft per cent

Example 8.9 Page No : 291

In [10]:
		
#initialisation of variables
Q = 60. 		#ft**3/sec
v = 12. 		#m.p.h
A = 3.  		#ft**2
D = 64. 		#lbs/ft**3
g = 32.2 		#ft/sec**2
M = 64. 		#lbs
		
#CALCULATIONS
vr = Q/A
u = v*44/30
v1 = vr-u
P = M*Q*v1/g
		
#RESULTS
print  'propelling force = %.1f lbs'%(P)

propelling force = 286.2 lbs

Example 8.10 Page No : 291

In [11]:
		
#initialisation of variables
vr = 20. 		#f/sec
u = 9.  		#knots
D = 64. 		#lbs per cubic foot
g = 32.2 		#ft/sec**2
p = 40. 		#per cent
		
#CALCULATIONS
u1 = u*6080/3600
v = vr-u1
P = D*2*vr*4.8/g
HP = P*u1/550
HP1 = 100*HP/p
		
#RESULTS
print  'cylinder H.P = %.2f H.P'%(HP1)

cylinder H.P = 26.37 H.P

Example 8.11 Page No : 293

In [12]:
import math 
		
#initialisation of variables
W = 62.4 		#lbs/ft**3
A = 4. 	    	#ft**2
P = 1000. 		#lbs
g = 32.2 		#ft/sec**2
v = 10.  		#ft/sec
		
#CALCULATIONS
vr = math.sqrt(25+(P*g/(W*A)))+5
Q = vr*W*A/10
e = 2*v*100/(vr+v)
		
#RESULTS
print  'quantity of water pumped = %.1f lbs'%(Q)
print  ' efficiency = %.1f per cent'%(e)

quantity of water pumped = 434.6 lbs
 efficiency = 73.0 per cent

Example 8.12 Page No : 294

In [13]:
import math 
		
#initialisation of variables
g = 32.2 		#ft/sec**2
		
#CALCULATIONS
v = math.sqrt(32*g)
		
#RESULTS
print  'speed that delivery commence = %.1f ft/sec'%(v)

speed that delivery commence = 32.1 ft/sec