# Chapter 7 : The momentum balance¶

### Example 7.2 page no : 248¶

In :
#Calulate the final velocity of duck after being hit by a bullet

# Variables
m_duck=3.                 #lbm
v_duck=-15.               #ft/s due west
m_bullet=0.05             #lbm
v_bullet=1000.            #ft/s due east

# Calculation
#total initial momentum = final momentum
v_sys=((m_duck*v_duck)+(m_bullet*v_bullet))/(m_duck+m_bullet)#ft/s

# Result
print "The final velocity of the duck is %f ft/s"%v_sys

The final velocity of the duck is 1.639344 ft/s


### Example 7.3 page no : 250¶

In :
#calculate the force required to hold of water from a hoze

# Variables
rho=998.2                #Kg/m^3
q=0.01                   #m^3/s
v_initial=30.            #m/s
v_final=0.               #m/s

# Calculation
F=q*rho*(v_final-v_initial)       #N

# Result
print "The force required to hold of water from a hoze %f N"%F

The force required to hold of water from a hoze -299.460000 N


### Example 7.4 page no : 251¶

In :
#calculate the force required to hold of water from a hoze

# Variables
rho=998.2                    #Kg/m^3
q=0.01                       #m^3/s
v_initial=30.                #m/s
v_final=-15.                 #m/s

# Calculation
F=q*rho*(v_final-v_initial)  #N

# Result
print "The force required to hold of water from a hoze %f N"%F

The force required to hold of water from a hoze -449.190000 N


### Example 7.5 page no : 252¶

In :
#Calculate the force exerted on the flange when the valve of the nozzle is closed

# Variables
#Let the gauge pressure be denoted by Pg
Pg=100.                       #lbf/in^2
A=10.                         #in^2

# Calculation
#F_bolts = -F_liq-F_atm
#F_bolts = -(Pg + P_atm)A - (-P_atm.A)
#F_bolts = -Pg.A
F_bolts=-Pg*A

# Result
print "The force exerted on the flange when the valve of the nozzle is closed is %d lbf"%F_bolts

The force exerted on the flange when the valve of the nozzle is closed is -1000 lbf


### Example 7.6 page no : 254¶

In :
#Calculate the force exerted on the flange

# Variables
dP=100.                           #lbf/in^2
A_out=1.                          #in^2
rho=62.3                          #lbm/ft^3
ratio_A=0.1                       #dimentionless

# Calculation
#1 ft = 12 in
#1 lbf.s^2 = 32.2 lbm.ft
v_out=(2*dP/rho/(1-ratio_A**2)*32.2*144)**0.5            #ft/s
v_in=12.3                        #ft/s

m=rho*A_out*v_out/144.           #lbm/s
F=m*(v_out-v_in)/32.2            #lbf

# Result
print "The force exerted on the flange is %f lbf"%F

The force exerted on the flange is 181.755634 lbf


### Example 7.7 page no : 255¶

In :
#Calculate the support forces in x and y direction in a 90 degree bend tube

# Variables
p1=200.                     #KPa
A=0.1                       #m^2
m=500.                      #Kg/s
rho=998.2                   #Kg/m^3
q=m/rho                     #m^3/s
v=q/A                       #m/s
Vx_initial=v                #m/s
Vx_final=0.                 #m/s
Vy_initial=0.               #m/s
Vy_final=-v                 #m/s

# Calculation and   Result
neg_Fx=m*(Vx_final-Vx_initial)-p1*1000*A           #N
Fx = neg_Fx
print "The support force in the x direction is %f N"%Fx
neg_Fy=m*(Vy_final-Vy_initial)-p1*1000*A#N
Fy = neg_Fy
print "The support force in the y direction is %f N"%Fy

The support force in the x direction is -22504.508115 N
The support force in the y direction is -22504.508115 N


### Example 7.8 page no : 258¶

In :
#Calculate the thrust on a rocket

# Variables
m=1000.                       #Kg/s
v_out=-3000.                  #m/s its in the negative y direction
v_in=0.                       #m/s
A=7.                          #m^2
P=35000.                      #Pa

# Calculation
F_thrust=(-m*(v_out-v_in)+P*A)/1000000.0          #MN

# Result
print "The thrust on the rocket is %f MN"%F_thrust

The thrust on the rocket is 3.245000 MN


### Example 7.9 page no : 258¶

In :
#Calculate the specific impulse for a rocket

# Variables
Vy_exh=-3000.                       #m/s in negative y direction

# Calculation
Isp=-Vy_exh/1000.0                  #KN.s/Kg

# Result
print "The specific impulse on the rocket is %d KN.s/Kg"%Isp

The specific impulse on the rocket is 3 KN.s/Kg


### Example 7.10 page no : 259¶

In :
#Calculate the Mass air flow rate required by a jet engine

# Variables
F_thrust=20000.                      #lbf
Vx_out=1350.0                        #ft/s
Vx_in=0.                             #ft/s

# Calculation
#1 lbf.s^2 = 32.2 lbm.ft
m=F_thrust/(Vx_out-Vx_in)*32.2       #lbm/s

# Result
print "The mass air flow rate required by a jet engine is %d lbm/s"%m

The mass air flow rate required by a jet engine is 477 lbm/s


### Example 7.12 page no : 267¶

In :
#Calculate the final velocity of a rocket after launch
import math

# Variables
Isp=430.                    #lbf.s/lbm specific impulse
#1 lbf.s^2 = 32.2 lbm.ft
Vrel_out=-Isp*32.2          #ft/s
ratio_m=0.1                 #dimentionless (ratio of final mass to initial mass)

# Calculation
v_final=Vrel_out*math.log(ratio_m)           #ft/s

# Result
print "The velocity of the rocket after launch is %d ft/s"%v_final

The velocity of the rocket after launch is 31881 ft/s


### Example 7.15 page no : 278¶

In :
#Calculate the velocity and height of flow in an open channel

# Variables
v1=4.                          #ft/s
g=32.2                         #ft/s^2
z1=0.0005                      #ft
Fr=v1**2/(g*z1)                #dimentionless (Fraude number)
ratio_z=-0.5+(0.25+2*Fr)**0.5  #dimentionless

# Calculation
#ratio_z = z2/z1
z2=ratio_z*z1                  #ft
#print "The height of flow in open channel is %f ft"%z2
v2=v1/(ratio_z)                #ft/s

# Result
print "The velocity of flow in open channel is %f ft/s"%v2

The velocity of flow in open channel is 0.090734 ft/s


### Example 7.16 page no : 280¶

In :
#calculate the verticle downward velocity of air hitting an aircraft wing

# Variables
l=15.                         #m length of wing
b=3.                          #m thickness of wing
A=l*b                         #m^2 area of the colliding surface of the wing
rho_air=1.21                  #Kg/m^3
Vx=50.                        #m/s
m=rho_air*A*Vx                #Kg/s
Fy=9810.                      #N Weight of the aircraft

# Calculation
Vy=Fy/m                       #m/s

# Result
print "The verticle downward velocity of air hitting the aircraft wing is %f m/s"%Vy

The verticle downward velocity of air hitting the aircraft wing is 3.603306 m/s


### Example 7.17 page no : 281¶

In :
#Calculate the ratio of the total weight of the aircraft to the weight of engine

# Variables
#Let ratio of weight to thrust be denoted by r1
#Let ratio of thrust to the engine weight be denoted by r2
r1=10.                     #dimentionless
r2=2.                      #dimentionless

# Calculation
#weight/engine wt = (weight/thrust)*(thrust/engine wt)
#let ratio of total wt to engine wt be denoted by r3
r3=r1*r2                   #dimentionless

# Result
print "The ratio of the total weight of the aircraft to the weight of engine is %d"%r3

The ratio of the total weight of the aircraft to the weight of engine is 20


### Example 7.18 page no : 284¶

In :
#Calculate the torque exerted on the rotor in a centrifugal pump
import math

# Variables
q=100.                        #gal/min
rho=8.33                      #lbm/gal
m=rho*q                       #lbm/min
f=1800.                       #rev/min frequency of impeller
omega=2*(math.pi)*f           #rad/min
r_in=1/12.0                   #ft
r_out=6/12.0                  #ft

# Calculation
#1 min = 60 sec
#1 lbf.s^2 = 32.2 lbm.ft
tou=m*omega*(r_out**2-r_in**2)/32.2/3600.              #lbf.ft

# Result
print "The torque exerted on the rotor is %f lbf.ft"%tou

The torque exerted on the rotor is 19.753523 lbf.ft