# Chapter 12 : Dimensional and Model Analysis¶

## Example 12.1 Page No : 260¶

In [1]:
import math

#initialisation of variables
d= 0.0625 	#in
sg= 0.91
vs= 1.62
ss= 7.85
g= 981. 	#cm/sec**2

#CALCULATIONS
v= 4*(d*2.54/2)**2*(ss-sg)*g/(3*6*30.45*vs)

#RESULTS
print  'steady speed attained = %.4f ft/sec '%(v)

steady speed attained = 0.1932 ft/sec


## Example 12.3 Page No : 263¶

In [2]:
import math

#initialisation of variables
vs= 16. 	#ft/sec
lm= 1. 	#ft
l= 16. 	#ft
R= 9.6 	#lb
ds= 64. 	#lb/ft**3
dm= 62.4 	#/lb/ft**3
A= 40. 	#ft**2

#CALCULATIONS
vm= vs*math.sqrt(lm/l)
rs= 0.0095*vm**1.9*A
rw= R-rs
Rw= rw*ds*(l/lm)**3/dm
Rs= 0.009*vs**1.85*A*l**2
R1= Rw+Rs

#RESULTS
print  'speed = %.f b ft/sec'%(vm)
print  ' Total resistance = %.f lb '%(round(R1,-2))

speed = 4 b ft/sec
Total resistance = 33700 lb


## Example 12.4 Page No : 264¶

In [3]:
import math

#initialisation of variables
H2= 0.75 	#ft
v1= 1. 	#ft/sec
v2= 6. 	#ft/sec
k= 1.433

#CALCULATIONS
H1= H2*(v1/v2)**(2./3)
Q1= k*H1**2.47
Q2= Q1*(H2/H1)**2.5

#RESULTS
print  'Flow = %.3f cuses '%(Q2 )

Flow = 0.730 cuses


## Example 12.5 Page No : 265¶

In [1]:
import math

#initialisation of variables
nm= 360.
d= 1.5 	#in
n= 100.
dp= 12. 	#in
vm= 4.8 	#ft/sec
Tm= 52. 	#sec
T= 16. 	#lb-ft
t= 133. 	#lb ft

#CALCULATIONS
vp= n*dp*vm/(nm*d)
Tp= round(Tm*dp**2*vp**2/(d**2*vm**2),-2)
N= Tm*vm*6080*100/(T*2*math.pi*nm*60)
W= Tp*65000
T1= W/(.7*2*math.pi*n*60)

#RESULTS
print  'Speed of advance = %.2f knots '%(vp)
print  ' Thrust = %.f lb '%(Tp)
print  ' Efficiency = %.f per cent '%(N)
print  ' Torque = %.f lb ft '%(round(T1,-2))

Speed of advance = 10.67 knots
Thrust = 16400 lb
Efficiency = 70 per cent
Torque = 40400 lb ft


## Example 12.6 Page No : 267¶

In [5]:
import math

#initialisation of variables
w= 62.4 	#lb/ft**3
d= 4 	#in
D= 0.0765 	#lb/ft**3
Da= 8 	#in
vw= 1./13
nw= 20
va= 13 	#ft/sec

#CALCULATIONS
na= nw*va*d**2/Da**2

#RESULTS
print  'power = %.f r.p.m '%(na)

power = 65 r.p.m


## Example 12.7 Page No : 269¶

In [13]:
import math

#initialisation of variables
dtp= 120. 	#in
dpd= 48. 	#in
vim= 1.25 	#ft/sec
vip= 5. 	#ft/sec
lp = 600. 	#ft
lm= 40.  	#ft

#CALCULATIONS
Rm= (dtp/dpd)**2/((lp/lm)*(vim/vip)**2)
d= math.sqrt(4*Rm)

#RESULTS
print  'Diameter = %.2f in '%(d)

Diameter = 5.16 in