# Chapter 6 : Dimensional Analysis and Similitude¶

## Example 6.11 Page No : 222¶

In [1]:
import math

#Initialization of variables
dw = 1000. 			#density of water - kg/m**3
muw = 0.001 		#viscosity of water - N s /m**2
da = 1.225 			#density of air - kg/m**3
mua = 18.*10**-6 	#viscosity of air - N s /m**2
lr = 1./10

#calculations
dr = da/dw
mur = mua/muw
vr = mur/dr
velocity =  vr/lr
discharge  = lr*vr
pressure  =  mur**2 /(dr*lr**2)
force  =  mur**2 /dr

#results
print "Scale ratio for velocity  =  %.f "%(velocity)
print "Scale ratio for discharge  =  %.2f "%(discharge)
print "Scale ratio for pressure  =  %.1f "%(pressure)
print "Scale ratio for force  =  %.3f "%(force)

Scale ratio for velocity  =  147
Scale ratio for discharge  =  1.47
Scale ratio for pressure  =  26.4
Scale ratio for force  =  0.264


## Example 6.12 Page No : 223¶

In [2]:
import math

#Initialization of variables
dr = 1000.
mur = 100.           #times
lr = 1./10          #prototype size
dpm = 60.           #kN/m**2

#calculations
Vr = mur/dr/lr
dpr = dr*Vr**2
dpp = dpm/dpr

#results
print "Pressure drop in prototype  =  %d N/m**2"%(dpp*10**3)

Pressure drop in prototype  =  60 N/m**2


## Example 6.14 Page No : 225¶

In [4]:
import math

#Initialization of variables
lr = 1./25
Tp = 6. 			#sec
dr = 1./1.025
Fm = 70. 			#N

#calculations
Tr = lr**(0.5)
Tm = Tr*Tp
Fr = dr*lr**3
Fp = Fm/Fr

#results
print "Wave period  =  %.1f sec"%(Tm)
print "Force  =  %.3f kN"%(Fp/1000)

Wave period  =  1.2 sec
Force  =  1121.094 kN


## Example 6.16 Page No : 227¶

In [5]:
import math

#Initialization of variables
lr = 1./10          #scale ratio
Vp = 10. 			#speed - knots
Fm = 12. 			#tension - N

#calculations
Vm = Vp*math.sqrt(lr)
Fp = Fm/lr**3

#results
print "force  =  %.1f kN"%(Fp/1000)

force  =  12.0 kN


## Example 6.17 Page No : 229¶

In [7]:
import math

#Initialization of variables
lr = 1./7200

#calculations
Tr = 60./(12*3600)
yr = (lr/Tr)**2

#results
print "vertical scale to be adopted is 1 in %d"%(1/yr)

vertical scale to be adopted is 1 in 100