# Chapter 6 : Momentum and Forces in Fluid Flow¶

## Example 6.1 Page No : 153¶

In [10]:
import math

#Initialization of variables
g = 9.81 	#kN/m**3
V2 = 12. 	#velocity - m/s
V3 = 12. 	#m/s
A2 = 10.**2
A1 = 15.**2
A3 = 7.5**2
t1 = 15.
t2 = 30.

#calculations
V1 = (A2*V2 + A3*V3)/A1
Q1 = round(math.pi /4 *A1*10**-4 *V1,3)
Q2 = round(math.pi /4 *A2*10**-4 *V2,3)
Q3 = round(math.pi /4 *A3*10**-4 *V3,3)
P1g = round(V3**2 /(2*g) - V1**2 /(2*g),2)
P1 = round(P1g*g,1)
rho = 10**3
V1x = V1
Fx =  -P1*A1*10**-4 + (rho*Q2*V2x + rho*Q3*V3x - rho*Q1*V1x)
Fx = Fx*10**-3
V1y = 0
Fy = rho*Q2*V2y +rho*Q3*V3y -rho*Q1*V1y
Fy = Fy*10**-3
Fnlx = 0.659 - Fx

#Results
print "Force in x directio  =  %.3f kN"%(Fx)
print " Force in y direction  =  %.3f kN"%(Fy)
print "(Fl/n)x = %.3f kN"%Fnlx
print "(Fl/n)y = %.3f kN"%-Fy

# rounding off error

Force in x directio  =  0.415 kN
Force in y direction  =  -0.026 kN
(Fl/n)x = 0.244 kN
(Fl/n)y = 0.026 kN


## Example 6.2 Page No : 155¶

In [11]:

#Initialization of variables
V1x = 100.       	#ft/sec
V2x = 0.866*95
V1y = 0.
V2y = .5*95
A1 = 0.0218 	#ft**2

#calculations
Q = A1*V1x
rho = 1.94
Fx = rho*Q*(V2x-V1x)
Fxr = -Fx
Fy = rho*Q*(V2y-V1y)

#Results
print "Horizontal force on the blade  =  %.1f lb"%(Fxr)
print " Vertical force on the blade  =  %.f lb"%(Fy)

Horizontal force on the blade  =  75.0 lb
Vertical force on the blade  =  201 lb


## Example 6.3 Page No : 159¶

In [12]:
import math

#Initialization of variables
v2 = 36.         	#fps
beta = 150.      	#degrees
u = 60.          	#velocity - fps
rho = 1.94
Qd = 0.0218
V1 = 100.        	#fps
gam = 62.4
g = 32.2

#calculations
V2 = 34.     	#fps
alpha = 32 	    #degrees
Fx = rho*Qd*(v2c-V1)*(V1-u)
Fy = -rho*Qd*(V1-u)*v2s
Fx2 = rho*Qd*V1*(v2c-V1)
HPin = gam*Qd*V1*(V1**2 /(2*g))/550
HPout = gam*Qd*V1*(V2**2 /(2*g))/550
HPtransfer = -Fx2*u/550
HPfl = HPin-HPout-HPtransfer

#Results
print "Force exerted by water on the vane  =  %d lb"%(Fx2)
print " Friction loss  =  %.1f hp "%(HPfl)

# rounding off error

Force exerted by water on the vane  =  -301 lb
Friction loss  =  1.1 hp


## Example 6.4 Page No : 162¶

In [1]:
import math

#Initialization of variables
z1 = 35. 	#ft
z3 = 20. 	#ft
P1 = 30. 	#psi
g = 32.2
z2 = 10. 	#ft
d2 = 4. 	#in
rho = 1.94
be = 20. 	#degrees
W = 150. 	#lb

#calculations
V3 =  math.sqrt(2*g*(P1*144/55 + z1-z3))
Q = 3.81 	#cfs
V2 = 43.6 	#fps
P2 = round(55*(z3+ V3**2/(2*g) - z2 - V2**2/(2*g))/144,1)
Fx = round(P2*math.pi/4 *d2**2 - rho*55/62.4 *Q*(V3*math.cos(math.radians(be)) - V2) )
Fy = rho*55/62.4 *Q*(V3*math.sin(math.radians(be)) ) + W
Fres = math.sqrt(Fx**2 + Fy**2)

#calculations
print " resultant force  =  %.f lb"%(Fy)
print " horizontal component of force  =  %d lb"%(Fsx)

 resultant force  =  323 lb
horizontal component of force  =  475 lb


## Example 6.5 Page No : 168¶

In [18]:
import math

#Initialization of variables
omega = 300. 	#rpm
r1 = 1.6 	    #ft
Q = 120. 	    #cfs
z = 0.8     	#ft
beta1 = 80. 	#degrees
r2 = 1.      	#ft
rho = 1.94
g = 32.2
gam = 62.4

#calculations
print ("part a")
u1 = round((2*math.pi/60)*omega*r1,1)
Vr1 = round(Q/(2*math.pi*r1*z),2)
V1c = round(u1+v2c,1)
u2 = round((2*math.pi/60)*omega*r2,1)
Vr2 = round(Vr1*(r1/r2),1)
beta2 = Vr2/u2
beta = 37.2
print "required Blade angle  =  %.1f degrees"%(180-beta)
print ("part b")
T = round(rho*Q*(r1*V1c),-2)
power = round(T*u2,-3)
print "Torque exerted  =  %d ft lb/s"%(power)
print ("part c")
h2 = round(u1*V1c/g,1)
Power = round(gam*Q*h2,-3)
print "Torque exerted  =  %d ft lb/s"%(Power)

part a
required Blade angle  =  142.8 degrees
part b
Torque exerted  =  619000 ft lb/s
part c
Torque exerted  =  619000 ft lb/s


## Example 6.6 Page No : 174¶

In [24]:
import math

#Initialization of variables
V1 = 150.*44/30
Q = 20000./2
d = 6.5 	    #diameter - ft
rho = 0.072

#calculations
A = math.pi/4 *(d)**2
V = int(Q/A)
dV = 2*(V-V1)
Ft = round(rho/32.2 *Q*2*dV,-1)
eta = round(1/(1+ dV/(2*V1)),2)
dP = Ft/2 /(math.pi/4) /d**2
hpp = Q*dP/550

#Results
print "pressure rise  =  %d psf"%(dP)
print " horsepower input  =  %d hp "%(round(hpp,-1))

pressure rise  =  109 psf
horsepower input  =  1980 hp


## Example 6.7 Page No : 175¶

In [9]:

#Initialization of variables
V1 = 8.02 	#fps
V2 = 16.04 	#fps
Q = 481. 	#cfs
rho = 1.94
A = 10*6
d = 3.

#calculations
Fx = 62.4*d*A - 62.4*d/2 *A/2 - rho*Q*(V2-V1)
V1m = 2.56 	#m/s
V2m = 5.12 	#m/s
Qm = 15.4 	#m**2/s
dm = 1
Am = 2*3
rhom = 1
Fxm = 9.81*dm*Am - 9.81*dm/2 *Am/2 - rhom*Qm*(V2m-V1m)

#Results
print "Force in x- direction  =  %d lb"%(Fx)
print "Force in x- direction  =  %.1f kN"%(Fxm)

Force in x- direction  =  940 lb
Force in x- direction  =  4.7 kN