# Chapter 9: Similarity¶

## Example 9.1, Page 291¶

In :
from __future__ import division
import math

#Initializing  the  variables
Vp  =  10;
LpByLm  =  20;
rhoPbyRhoM  =  1;
muPbymuM  =  1;
#Calculations
Vm  =  Vp*LpByLm*rhoPbyRhoM*muPbymuM;

print "Mean water tunnel flow velocity (m/s) :",Vm

Mean water tunnel flow velocity (m/s) : 200


## Example 9.2, Page 292¶

In :
from __future__ import division
import math

#Initializing  the  variables
Vp  =  3;
LpByLm  =  30;
rhoPbyRhoM  =  1;
muPbymuM  =  1;

#Calculations
Vm  =  Vp*LpByLm*rhoPbyRhoM*muPbymuM;

print "Mean water tunnel flow velocity (m/s):",Vm

Mean water tunnel flow velocity (m/s): 90


## Example 9.3, Page 293¶

In :
from __future__ import division
import math

#Initializing  the  variables
Vp  =  100;
cP  =  340;
cM  =  295;
rhoM  =  7.7;
rhoP  =  1.2;
muM  =  1.8*10**-5;
muP  =  1.2*10**-5;

#Calculations
Vm  =  Vp*(cM/cP);
LmByLp  =  1/((Vm/Vp)*(muM/muP)*(rhoM/rhoP));
FmByFp  =  (rhoM/rhoP)*(Vm/Vp)**2*(LmByLp)**2;

print 'Mean wind tunnel flow velocity(m/s) :',round(Vm,2)
print "Percentage ratio of forces (%)      :",round(FmByFp*100,2)

Mean wind tunnel flow velocity(m/s) : 86.76
Percentage ratio of forces (%)      : 6.93


## Example 9.4, Page 295¶

In :
from __future__ import division
import math

#Initializing  the  variables
def pLossRatio(RatRho,RatMu,RatL):
Z  =  RatRho*RatMu**2*RatL**2;
return Z

#Calculations
#Case  (a)  :  water  is  used
RatRho  =  1;
RatMu  =  1;
RatL  =  10;
print "(a)Ratio of pressure losses between the model and the prototype if water is used :",pLossRatio(RatRho,RatMu,RatL)

# Case (b) : air is used
RatRho  =  1000/1.23;
RatMu  =  1.8*10**-5/10**-3;

print "(b)Ratio of pressure losses between the model and the prototype if air is used   :",round(pLossRatio(RatRho,RatMu,RatL),2)

(a)Ratio of pressure losses between the model and the prototype if water is used : 100
(b)Ratio of pressure losses between the model and the prototype if air is used   : 26.34


## Example 9.5, Page 296¶

In :
from __future__ import division
import math

#Initializing  the  variables
scale  =  1/50;
ratArea  =  scale**2;
Qp  =  1200;

#Calculations
LmByLp  =  (ratArea)**0.5;
VmByVp  =  (LmByLp)**0.5;
Qm  =  Qp*ratArea*VmByVp;

print "Water flow rate (m3/s ):",round(Qm,3)

Water flow rate (m3/s ): 0.068


## Example 9.6, Page 298¶

In :
from __future__ import division
import math

#Initializing  the  variables
Qa  =  2;
Na  =  1400;
rhoA  =  0.92;
rhoS  =  1.3;
DaByDs  =  1;
dPa  =  200;

#Calculations
Ns  =  Na*(rhoA/rhoS)*(DaByDs);
Qs  =  Qa*(Ns/Na);
dPs  =  dPa  *(rhoS/rhoA)*(Ns/Na)**2*(1/DaByDs)**2;

print "Fan test speed (rev/s):",round(Ns,1)
print "Flow rate (m3/s)      :",round(Qs,3)
print "Pressure rise (N/m2 ) :",round(dPs,1)

Fan test speed (rev/s): 990.8
Flow rate (m3/s)      : 1.415
Pressure rise (N/m2 ) : 141.5


## Example 9.8, Page 304¶

In :
from __future__ import division
import math

#Initializing  the  variables
V  =  300                                                                  #  Volume  rate
w  =  3;
d  =  65;
l  =  30;
scaleH  =  30/1000/18;
scaleV  =  1/60;
ZmByZr  =  1/60;
LmByLr  =  1/600;
rho  =  1000;
mu  =  1.14*10**-3;

#Calculations
Vr  =  V/(w*d);
Vm  =Vr*(ZmByZr)**0.5;
m  =  (w*d*scaleH*scaleV)/(d*scaleH  +  2*w*scaleV);
Rem  =  rho*Vm*m/mu;
TmByTr  =  LmByLr*(1/ZmByZr)**0.5;
Tm  =  12.4*60*TmByTr;

print "Tidal Period (minutes):",round(Tm,1)

Tidal Period (minutes): 9.6