# Chapter 27 : Testing of Internal Combustion Engines According to Indian and International Standards¶

## Example 27.1 Page No : 483¶

In :
#Given:
Pr  =  500.      #Smath.radians(numpy.arcmath.tan(ard reference brake power in kW
eta_m  =  85.      #Mechanical efficiency in percent
br  =  220.      #Smath.radians(numpy.arcmath.tan(ard specific fuel consumption in g/kWh
px  =  87.      #Site ambient air pressure in kPa
Tx  =  45.+273      #Site ambient temperature in K
phix  =  80./100      #Relative humidity at site

#Solution:
#Refer table 27.1, 27.2 and 27.3
a  =  1.      #Factor
m  =  1.;n  =  0.75;q  =  0      #Exponents
psx  =  9.6      #Saturation vapour pressure at site in kPa
psr  =  3.2      #Smath.radians(numpy.arcmath.tan(ard saturation vapour pressure in kPa
pr  =  100.      #Smath.radians(numpy.arcmath.tan(ard total barometric pressure in kPa
Tr  =  298.      #Smath.radians(numpy.arcmath.tan(ard air temperature in K
phir  =  0.3      #Smath.radians(numpy.arcmath.tan(ard relative humidity
k  =  ((px-a*phix*psx)/(pr-a*phir*psr))**m*(Tr/Tx)**n      #The ratio of indicated power
alpha  =  k-0.7*(1-k)*(100/eta_m-1)      #Power adjustment factor
Beta  =  k/alpha      #Fuel consumption adjustment factor
Px  =  alpha*Pr      #Brake power at site in kW
bx  =  Beta*br      #Specific fuel consumption at site in g/kWh

#Results:
print " The site continuous net brake power, Px   =   %.1f kW"%(Px)
print " The site continuous specific fuel consumption, bx   =   %.1f g/kWh"%(bx)

 The site continuous net brake power, Px   =   366.8 kW
The site continuous specific fuel consumption, bx   =   228.8 g/kWh


## Example 27.2 Page No : 488¶

In :
#Given:
Pr  =  1000.      #Smath.radians(numpy.arcmath.tan(ard reference brake power in kW
eta_m  =  90.      #Mechanical efficiency in percent
Pir  =  2.      #Boost pressure ratio
Tra  =  313.      #Substitute reference air temperature in K
Pimax  =  2.36      #Maximum boost pressure ratio
h  =  4000.      #Altitude in m
px  =  61.5      #Site ambient air pressure in kPa
Tx  =  323.      #Site ambient temperature in K
Tcx  =  310.      #Charge air coolent temperature at site in K

#Solution:
#Refer table 27.1, 27.2 and 27.3
m  =  0.7
n  =  1.2
q  =  1.      #Exponents
pr  =  100.      #Smath.radians(numpy.arcmath.tan(ard total barometric pressure in kPa
Tcr  =  298.      #Smath.radians(numpy.arcmath.tan(ard charge air coolent temperature in K
Tr  =  298.      #Smath.radians(numpy.arcmath.tan(ard air temperature in K
pra  =  pr*Pir/Pimax      #Smath.radians(numpy.arcmath.tan(ard reference pressure in kPa
pra  =  round(10*pra)/10
k  =  (px/pra)**m*(Tra/Tx)**n*(Tcr/Tcx)**q      #The ratio of indicated power
alpha  =  k-0.7*(1-k)*(100/eta_m-1)      #Power adjustment factor
Px1  =  round(alpha*Pr)      #Brake power at site in kW
#If reference conditions are not changed
k  =  (px/pr)**m*(Tr/Tx)**n*(Tcr/Tcx)**q      #The ratio of indicated power
alpha  =  k-0.7*(1-k)*(100/eta_m-1)      #Power adjustment factor
Px2  =  round(alpha*Pr)      #Brake power at site in kW

#Results:
print " Power available at an altitude of 4000m, Px   =   %d kW"%(Px1)
print " Power available at an altitude of 4000m if reference conditions are not changed, Px   =   %d kW"%(Px2)

 Power available at an altitude of 4000m, Px   =   720 kW
Power available at an altitude of 4000m if reference conditions are not changed, Px   =   592 kW


## Example 27.3 Page No : 493¶

In :
from math import floor

#Given:
Px  =  640.      #Brake power at site in kW
px  =  70.      #Site ambient air pressure in kPa
Tx  =  330.      #Site ambient temperature in K
Tcx  =  300.      #Charge air coolent temperature at site in K
eta_m  =  85.      #Mechanical efficiency in percent
py  =  100.      #Test ambient pressure in kPa
Tcy  =  280.      #Charge air coolent temperature at test in K
Ty  =  300.      #Test ambient temperature in K
#Solution:
#Refer table 27.1, 27.2 and 27.3
m  =  0.7
n  =  1.2
q  =  1.      #Exponents
pr  =  100.      #Smath.radians(numpy.arcmath.tan(ard total barometric pressure in kPa
Tcr  =  298.      #Smath.radians(numpy.arcmath.tan(ard charge air coolent temperature in K
Tr  =  298.      #Smath.radians(numpy.arcmath.tan(ard air temperature in K
kr  =  (px/pr)**m*(Tr/Tx)**n*(Tcr/Tcx)**q      #The ratio of indicated power
kr  =  floor(1000*kr)/1000
alphar  =  kr-0.7*(1-kr)*(100/eta_m-1)      #Power adjustment factor
Pr  =  Px/alphar      #Smath.radians(numpy.arcmath.tan(ard reference brake power in kW
ky  =  (py/pr)**m*(Tr/Ty)**n*(Tcr/Tcy)**q      #The ratio of indicated power at test
alphay  =  ky-0.7*(1-ky)*(100/eta_m-1)      #Power adjustment factor at test
Py  =  Pr*alphay      #Brake power at test in kW (Round off error)

#Results:
print " Power developed under test ambient conditions, Py   =   %.0f kW"%(Py)
#Round off error in the value of 'Py'

 Power developed under test ambient conditions, Py   =   1054 kW


## Example 27.4 Page No : 498¶

In :
#Given:
#Datas are taken from Ex. 27.3
Px  =  640.      #Brake power at site in kW
eta_m  =  85.      #Mechanical efficiency in percent
px  =  70.      #Site ambient air pressure in kPa
py  =  100.      #Smath.radians(numpy.arcmath.tan(ard total barometric pressure in kPa
Tx  =  330.      #Site ambient temperature in K
Ty  =  300.      #Test ambient temperature in K
p2_py  =  2.5      #Pressure ratio
by  =  238.      #Specific fuel consumption at test in g/kWh

#Solution:
#Refer table 27.1, 27.2 and 27.3
m  =  0.7
n  =  1.2
q  =  1.      #Exponents
ky  =  (py/px)**m      #The ratio of indicated power at test
alphay  =  ky-0.7*(1-ky)*(100/eta_m-1)      #Power adjustment factor at test
Py  =  round(Px*alphay)      #Brake power at test in kW
#From fig 27.1
Tx_Ty  =  Tx/Ty      #Temperature ratio
p1_py  =  0.925      #Ratio
p1  =  p1_py*py      #Air pressure after throttle in kPa (printing error)
Betay  =  ky/alphay      #Fuel consumption adjustment factor at test
bx  =  by/Betay      #Specific fuel consumption at site in g/kWh

#Results:
print " Power developed on the test bed, Py   =   %d kW"%(Py)
print " The pressure behind the throttle plate, p1   =   %.1f kPa"%(p1)
print " The fuel consumption adjusted to site ambient conditions, bx   =   %d g/kWh"%(bx)

#Answer in the book is printed wrong

 Power developed on the test bed, Py   =   844 kW
The pressure behind the throttle plate, p1   =   92.5 kPa
The fuel consumption adjusted to site ambient conditions, bx   =   244 g/kWh


## Example 27.5 Page No : 503¶

In :
#Given:
Py = 640.      #Brake power at test in kW
py = 98.      #Test ambient pressure in kPa
Ty = 303.      #Test ambient temperature in K
phiy = 0.8      #Relative humidity at test

#Solution:
#Refer table 27.1, 27.3
psy = 4.2      #Saturation vapour pressure at test in kPa
psr = 3.2      #Smath.radians(numpy.arcmath.tan(ard saturation vapour pressure in kPa
pr = 100.      #Smath.radians(numpy.arcmath.tan(ard total barometric pressure in kPa
Tr = 298.      #Smath.radians(numpy.arcmath.tan(ard air temperature in K
phir = 0.3      #Smath.radians(numpy.arcmath.tan(ard relative humidity
alpha_a = ((pr-phir*psr)/(py-phiy*psy))**1.2*(Ty/Tr)**0.6      #Correction factor for CI engine
Pr = round(alpha_a*Py)      #Smath.radians(numpy.arcmath.tan(ard reference brake power in kW

#Results:
print " The power at standard reference conditions, Pr  =  %d kW"%(Pr)

 The power at standard reference conditions, Pr  =  683 kW


## Example 27.6 Page No : 508¶

In :
import math

#Given:
Py = 896.      #Brake power at test in kW
py = 96.      #Test ambient pressure in kPa
Ty = 302.      #Test ambient temperature in K
phiy = 0.2      #Relative humidity at test
px = 98.      #Site ambient air pressure in kPa
Tx = 315.      #Site ambient temperature in K
phix = 0.4      #Relative humidity at site
N = 1800.      #Engine speed in rpm
V_s = 51.8      #Swept volume in litres
m_f = 54.5      #Fuel delivery in gm/s
pi = 2.6      #Pressure ratio

#Solution:
#Refer table 27.1, 27.3
psy = 4.8      #Saturation vapour pressure at test in kPa
psx = 8.2      #Saturation vapour pressure at site in kPa
q = m_f*1000/(N/(2*60)*V_s)      #Fuel delivery in mg/litrecycle
qc = round(q/pi)      #Corrected fuel delivery inmg/litrecycle
#Applying condition given in fig 27.2 for value of engine factor (fm)
if (qc  <=  40):
fm = 0.3;
elif (qc >=  65):
fm = 1.2;
else:
fm = 0.036*qc-1.14;

fa = ((px-phix*psx)/(py-phiy*psy))**0.7*(Ty/Tx)**1.5      #Atmospheric factor
alpha_d = fa**fm      #Correction factor for CI engine
Px = alpha_d*Py      #Brake power at site in kW

#Results:
print " Power at site ambient conditions, Px  =  %d kW"%(Px)

 Power at site ambient conditions, Px  =  878 kW


## Example 27.7 Page No : 513¶

In :
import math

#Given:
Py = 700.      #Brake power at test in kW
py = 96.      #Test ambient pressure in kPa
Ty = 302.      #Test ambient temperature in K
phiy = 0.2      #Relative humidity at test
px = 69.      #Site ambient air pressure in kPa
Tx = 283.      #Site ambient temperature in K
phix = 0.4      #Relative humidity at site
N = 1200.      #Engine speed in rpm
V_s = 45.      #Swept volume in litres
m_f = 51.3      #Fuel delivery in gm/s
pi = 2.0      #Pressure ratio
eta_m = 85.      #Mechanical efficiency in percent

#Solution:
pr = 100.      #Smath.radians(numpy.arcmath.tan(ard total barometric pressure in kPa
Tr = 298.      #Smath.radians(numpy.arcmath.tan(ard air temperature in K
phir = 0.3      #Smath.radians(numpy.arcmath.tan(ard relative humidity
#Refer table 27.1, 27.3
psy = 4.1      #Saturation vapour pressure at test in kPa
psx = 1.2      #Saturation vapour pressure at site in kPa
psr = 3.2      #Smath.radians(numpy.arcmath.tan(ard saturation vapour pressure in kPa
q = m_f*1000/(N/(2*60)*V_s)      #Fuel delivery in mg/litrecycle
qc = round(q/pi)      #Corrected fuel delivery in mg/litrecycle
#Applying condition given in fig 27.2 for value of engine factor (fm)
if (qc <=  40):
fm = 0.3;
elif (qc >=  65):
fm = 1.2;
else:
fm = 0.036*qc-1.14;

fa = ((px-phix*psx)/(py-phiy*psy))**0.7*(Ty/Tx)**1.5      #Atmospheric factor
alpha_d = fa**fm      #Correction factor for CI engine
#Applying condition given in section 27.4.2
if (alpha_d > 0.9) and (alpha_d < 1.1):
Px = alpha_d*Py
else:
fa = ((pr-phir*psr)/(py-phiy*psy))**0.7*(Ty/Tr)**1.5      #Atmospheric factor
alpha_d = fa**fm      #Correction factor for CI engine
Pr = alpha_d*Py      #Smath.radians(numpy.arcmath.tan(ard reference brake power in kW
m = 0.7;n = 2      #Exponents
k = (px/pr)**m*(Tr/Tx)**n      #The ratio of indicated power
alpha = k-0.7*(1-k)*(100/eta_m-1)      #Power adjustment factor
Px = alpha*Pr      #Brake power at site in kW

#Results:
print " Power at site ambient conditions, Px  =  %d kW"%(Px)
#Answer in the book is wrong

 Power at site ambient conditions, Px  =  612 kW