Chapter 8 : Impact of Jets

Example 8.1 Page No : 164

In [1]:
# Variables
V = 25.        #m/s velocity
F = 300.       # N
g = 9.81       
p = 1000.

# Calculations 
w = g*p
A = (F*g)/(w*V*V)
V1 = 35
F1 = (w*A*V1*V1)/(g)

# Results 
print "force in N on the plate if the velocity of the jet is increased to 35 m/sec",F1

force in N on the plate if the velocity of the jet is increased to 35 m/sec 588.0

Example 8.2 Page No : 164

In [3]:
import math

# Variables
d = 0.05       # mm water 
V = 15.        #m/s velocity
g = 9.81            
p1 = 1000.

# Calculations 
w = g*p1
a = math.pi*d*d/4
F = (w*a*V*V)/g
u = 5
F1 = (w*a*((V-u)**2))/g

# Results 
print "force in N on plate if plate is stationary",round(F,3),"N"
print "force in N on plate if plate is moving in the direction of the jet",round(F1,2),"N"

force in N on plate if plate is stationary 441.786 N
force in N on plate if plate is moving in the direction of the jet 196.35 N

Example 8.3 page no : 165

In [3]:
import math 

# Variables
d = 0.03             #m diameter
Fx = 900             # N 
x = 30.              #degree angle  
g = 9.81             
w = g*1000
a = 3.142*d*d/4

# Calculations 
V = ((Fx*g)/(w*a*math.sin(math.radians(x))*math.sin(math.radians(x))))**0.5
Q = a*V

# Results 
print "rate of flow in m3/sec",round((Q*1000),2)

rate of flow in m3/sec 50.45

Example 8.4 Page No : 166

In [6]:
import math 

# Variables
d = 0.02     #m diameter
V = 20.      #m/s, velocity 
x = 15.      #degree angle
g = 9.81      
p1 = 1000.

# Calculations 
w = g*p1
a = math.pi*d*d/4
W = (w*a*V*V)/(g*math.sin(math.radians(x)))
F1 = (w*a*V*V)/(2*g)

# Results 
print "weight of the plate in N",round(W,3),"N"
print "force in N required at the lower edge of the plate : %.4f"%F1,"N"

weight of the plate in N 485.527 N
force in N required at the lower edge of the plate : 62.8319 N

Example 8.5 Page No : 167

In [8]:
import math 

# Variables
d = 0.05       #m diameter
V = 20.        #m/s velocity 
y = 120.       #degree angle
x = 180.-y      
g = 9.81
p1 = 1000.

# Calculations 
w = g*p1
a = math.pi*d*d/4
F = (w*a*V*V*(1+math.cos(math.radians(x))))/(g)

# Results 
print "force in N exerted by the water jet %.4f"%F,"N"

force in N exerted by the water jet 1178.0972 N

Example 8.6 Page No : 167

In [9]:
import math

# Variables
d = 0.05                  #m diameter
V = 20.                   #m velocity
u = 7.                    #m/s 
a = math.pi*d*d/4           
g = 9.81
p1 = 1000.

# Calculations 
w = g*p1
F = (w*a*V*V)/g
F1 = (w*a*((V-u)**2))/g
work = F1*u

# Results 
print "force in N if plate is fixed ",F
print "force in N if plate is moving with a velocity of 7 m/sec",round(F1,2)
print "work done per sec by the jet",round(work,3)

# note : rounding off error.

force in N if plate is fixed  785.398163397
force in N if plate is moving with a velocity of 7 m/sec 331.83
work done per sec by the jet 2322.815

Example 8.7 Page No : 168

In [10]:
import math 

# Variables
W = 58.86             #N weighing
d = 0.02              #m diameter  
V = 5.                #m/s velocity
z = 0.15              #m axis 
g = 9.81            
p1 = 1000.    
w = g*p1

# Calculations 
a = math.pi*d*d/4
F = (w*a*V*V)/g
cog = 0.1
x = 30
P = (F*z)/cog
F1 = ((P*cog*(math.cos(math.radians(x))))+(W*cog*(math.sin(math.radians(x)))))
V1 = ((F1*g)/(w*a))**0.5

# Results 
print "velocity in m/sec of the jet if the plate is deflected through 30 degree",round(V1,2)

velocity in m/sec of the jet if the plate is deflected through 30 degree 3.55

Example 8.8 Page No : 169

In [8]:
import math 

# Variables
V = 25.                #m velocity
u = 10.                #m velocity 
q = 0.001              #m**3/s
g = 9.81
p1 = 1000.
w = g*p1
x = 180.             #degree 
u1 = 8.              #m velocity

# Calculations 
F1 = (w*q/g)*V*(1-math.cos(math.radians(x)))
F2 = (w*q*((V-u)**2)*(1-math.cos(math.radians(x))))/(g*V)
F3 = (w*q*(V-u1)*(1-math.cos(math.radians(x))))/g

# Results 
print "force of jet in N when,the cup is stationary,the cup is moving with velocity of 10m/sec,series of cup with velocity of 8m/sec" ,\
F1,F2,F3

force of jet in N when,the cup is stationary,the cup is moving with velocity of 10m/sec,series of cup with velocity of 8m/sec 50.0 18.0 34.0

Example 8.9 Page No : 170

In [19]:
import math 

# Variables
x1 = 30.          #m/s velocity
V1 = 30.          #degree  
Q = 0.001         
g = 9.81
w = g*1000.
Vf1 = V1*math.sin(math.radians(x1))
Vw1 = V1*math.cos(math.radians(x1))
u = 15.
x2 = 120.
y1 = math.degrees(math.atan(Vf1/(Vw1-u)))
Vr1 = ((Vf1*Vf1)+((Vw1-u)**2))**0.5
z = u*math.sin(math.radians(x2))/Vr1
y2 = 60-math.degrees(math.asin(z))
V2 = Vr1*math.sin(math.radians(y2))/math.sin(math.radians(x2))
Vw2 = V2*math.cos(math.radians(x2/2))
W = (w*Q*(Vw1+Vw2)*u)/g
n = W*2/(V1*V1)
print "angle of vane : %.3f degrees \
\nwork done of water entering the vane : %.3f Nm/s \
\nefficiency : %.2f %%"%(y2,W,n*100)

angle of vane : 15.670 degrees 
work done of water entering the vane : 433.194 Nm/s 
efficiency : 96.27 %

Example 8.10 Page No : 172

In [21]:
import math 

# Variables
Q = 0.283         #m**3/s, flow of water 
d = 0.05          #m diameter
x = 170.          #angle 
u = 48.           #m/s velocity 
g = 9.81          
p1 = 1000.

# Calculations 
w = g*p1
a = math.pi*d*d/4
V1 = Q/a
Vw1 = V1
Vr1 = V1-u
x1 = 0
Vr2 = Vr1
Vw2 = (Vr2*math.cos(math.radians(180-x)))-u
Fx = (w*a*(V1-u)*(Vw1+Vw2))/g
P = Fx*u/1000
n = (P*1000*g*2)/(w*Q*V1*V1)

# Results 
print "force exerted by the jet : %.3f N \
\npower developed by the vane : %.4f kW \
\nefficiency : %.1f %%"%(Fx,P,(n*100))

force exerted by the jet : 36014.111 N 
power developed by the vane : 1728.6773 kW 
efficiency : 58.8 %

Example 8.11 Page No : 174

In [30]:
import math 

# Variables
y1 = 30.                 #angle
y2 = 15.                 #angle  
a = 13.*(10**-4)         #cm**2 
x1 = 15.                 #incline
V1 = 60.                 #m/s area moving 

# Calculations 
Vf1 = V1*math.sin(math.radians(y2))
Vw1 = V1*math.cos(math.radians(y2))
u = Vw1-(Vf1/math.tan(math.radians(y1)))
Vw2 = u-(Vf1*math.cos(math.radians(y2))/math.sin(math.radians(y1)))
Vf2 = (u-Vw2)*math.tan(math.radians(y2))
V2 = (Vf2*Vf2+Vw2*Vw2)**0.5
x2 = math.degrees(math.atan(Vf2/Vw2))
g = 9.81
p1 = 1000
w = g*p1
Fx = (w*a*V1*(Vw1-Vw2))/g
Fy = (w*a*V1*(V1*math.sin(math.radians(y2))-V2*math.sin(math.radians(x2))))/g
Fr = (Fx*Fx+Fy*Fy)**0.5
o = math.degrees(math.atan(Fy/Fx))

# Results 
print "velocity of the vane : %.4f m/s \
\ndirection of velocity at exit : %.4f m/s \
\nresultant force : %.4f N \
\nangle between forces : %.1f degrees"%(u,V2,Fr,o)

velocity of the vane : 31.0583 m/s 
direction of velocity at exit : 8.1078 m/s 
resultant force : 4476.2818 N 
angle between forces : 7.5 degrees

Example 8.12 Page No : 177

In [36]:
import math 

# Variables
V1 = 13.             # m/s
y1 = 30.                  
y2 = y1
u = 4.5              # m/s
g = 9.81
p1 = 1000.

# Calculations 
w = g*p1
Q = 0.001
x1 = math.degrees(math.acos(0.9394))
Vw1 = V1*math.cos(math.radians(x1))
Vr1 = (Vw1-u)/math.cos(math.radians(y1))
Vw2 = Vr1*math.cos(math.radians(y1))-u
Vf2 = Vr1*math.sin(math.radians(y1))
V2 = (Vf2*Vf2+Vw2*Vw2)**0.5
x2 = math.degrees(math.atan(Vf2/Vw2))
W = (w*Q*(Vw1+Vw2)*u)/g

# Results 
print "direction of velocity : %.3f \
\nvelocity of water at exit : %.3f m/s \
\ndirection of work : %.3f \
\nmagnitude of work done per kg of water : %.3f"%(x1,V2,x2,W)

# note : rounding off errors.

direction of velocity : 20.049 
velocity of water at exit : 5.490 m/s 
direction of work : 54.193 
magnitude of work done per kg of water : 69.410

Example 8.13 Page No : 179

In [41]:
import math 

# Variables
V1 = 40.         #m/s velocity
u = 12.          #m/s  
x1 = 20.         #angle
x2 = 90.         #velocity   

# Calculations 
Vw1 = V1*math.cos(math.radians(x1))
Vf1 = V1*math.sin(math.radians(x1))
y1 = math.degrees(math.atan(Vf1/(Vw1-u)))
Vr1 = Vf1/math.sin(math.radians(y1))
Vr2 = 0.9*Vr1
y2 = math.degrees(math.acos(u/Vr2))
W = 1*Vw1*u
n = W/(V1*V1*0.5*1)

# Results 
print "vane angle at the exit : %.4f and %.4f \
\nwork done on the vane per kg of water : %.4f N m/s\
\nefficiency : %.2f %%"%(y1,y2,W,(n*100))

vane angle at the exit : 28.1318 and 62.6435 
work done on the vane per kg of water : 451.0525 N m/s
efficiency : 56.38 %

Example 8.14 Page No : 180

In [44]:
import math 

# Variables
d = 0.05           #m diameter
V1 = 25.           #m/s velocity 
x1 = 30.           #angle
x = 50.            #angle
x2 = x1+x
g = 10.           #m/s**2
p1 = 1000.

# Calculations 
a = 3.142*d*d/4
w = g*p1
Fx = (w*a*V1*V1*(math.cos(math.radians(x1))-math.cos(math.radians(x2))))/g
Fy = (w*a*V1*V1*(math.sin(math.radians(x1))-math.sin(math.radians(x2))))/g
F = (Fx*Fx+Fy*Fy)**0.5
z = math.degrees(math.atan(-Fy/Fx))

# Results 
print "resultant force %.3f and %.3f \
\nangle made by the resultant force with the horizontal  : %.4f"%(round(Fy,3),round(Fx,3),round(z,4))

# note : It seems book answers are wrong. Kindly check.

resultant force -595.026 and 849.785 
angle made by the resultant force with the horizontal  : 35.0000

Example 8.15 Page No : 182

In [46]:
import math 

# Variables
x1 = 0.          
x2 = 60.         # angle
V1 = 30.         #m/s velocity
V2 = 25.         #m/s velocity 
m = 0.8          #Kg/s nozzle 

# Calculations 
Fx = m*((V1*math.cos(math.radians(x1)))-(V2*math.cos(math.radians(x2))))
Fy = m*((V1*math.sin(math.radians(x1)))-(V2*math.sin(math.radians(x2))))
R = (Fx*Fx+Fy*Fy)**0.5
z = math.degrees(math.atan(-Fy/Fx))

# Results 
print "magnitude and direction of resultant force  :",round(R,3),round(z,4)

magnitude and direction of resultant force  : 22.271 51.0517
In [ ]: