homework- steadimath example

["Lawson, Dave" <dlawson@ball.com>]

> *  S.O.c claims and audi facts:
> *  26psi in 2nd thru 5th
> *  2.5 bar PT
> *  16+psi in 1st gear
> *  .5 PD accross modded IC
> *  Audi --> RS2 gets 310hp @ 460CFM
> *  1325 EGT
> *  Audi --> MC motor = 134ci
>
> The homework would be
> A) How does a 134ci motor flow 513CFM in 10v trim?  Can it?
> B)  Why such a large PR?  I thought Density Ratio was more the goal?
>  

engine displacement
D=135.8 in^3

engine speed
w=5500 rpm

ideal air flow of n/a engine, VE = .85
Fi = 216.1* .85 = 183.7 cfm

ambient temp
Ta = 70 degF

boost pressure
Pb = 26 psi

ambient air pressure
Pi = 14.7

Pressure ratio
Pr = 2.77

ideal temp gain
Tgi = 177 degF

turbo eff = .72

actual temp gain
Tg = Tgi/.72 = 246 degF

turbo outlet temp
To = Ta+Tg = 316 degF

air density ratio
Rd = (530/776)*2.77 = 1.89

modded I/C eff = .834

i/c temp reduction
Tir = 246*.834 = 205 degF

intake manifold air temp
Tm = 316-205 = 111 degF

net air temp rise
Tr = 111-70 = 41 degF

intake track efficiency
Eintake = 530/571 = .93

net air density ratio in intake manifold
Rm = 2.77*.93 = 2.57

effective air flow
Fe = Fa*Rm = 183.7*2.57 = 473.2 cfm


Dr. science's hand calc showed 184*2.79 = 513cfm.
Mine is a bit lower given the revised air density number when taking
the temperature increases and decreases into account. It is
< 10% delta effect using the short form, and pretty close given the
back-o-the-envelope calculations.

Lots of RDEs for initial conditions, that I/C efficiency is one that I 
didn't check, just used a previous assumption.

Now why is any of this important? The goal here is to get the greatest
volume of the coldest(densest) air we can, and cram it into our
cylinders.
When you go for greater volume, the temperature goes up and density 
goes down, and you will eventually reach the point where the volume 
increase is negated by the hotter, less dense air. 

-
Dave