R or F I was in error...
Its been raining all day here in West Palm Beach so no flying which gave me a chance to dust off my trusty old Zucker - Fundametals Of Fluid Dynamics.
Don't try to impress the girls at the bar talking like this though it won't work
1st Law - Conservation of Energy: Q=W+change in Energy
a whole bunch of calculus to get the control volume equations:
station 1 is upper plenum, 2 is lower
h1 + (V1^2/2gc) + (g/gc)Z1 + q = h2 + (V2^2/2gc) + (g/gc)Z2 + Ws
Where: h = enthalpy = Cp(T) (well really Dh= Cp(dt) for a perfect gas) but since we will consider the flow in the cowl 1 dimensional and steady we can drop the diferential form.) Steady only means the flow at a point isn't changing with respect to time - it can change from point to point and still be considered steady.
V^2/2gc= Kinetic Energy (KE)
(g/gc)Z = Potential Energy
q = heat transfer to or from the control volume
Ws = Work done on or by the system
For our case: Ws=0
and across the cyl change in height will be very small ~ 0 (or we can calculate it if we want from inlet to exit which is more significant)
so:
h1 + KE1 + q = h2 + KE2
I believe we can look up heat transfered from engine tables or charts (Dan??)
h1=Cp(T1)
h2= Cp (T2) (Cp is for perfect gas at constant pressure which we know isn't exactly correct here but helps understand the process)
h2-h1 = Cp(T2-T1) so YES, you are correct either R or F is insignificant for this calculation assuming we can look up heat transfered. Sorry my bad
KE2-KE1 = (V2^2 - V1^2)/2gc
Therefore:
q = Cp(T2-T1) + (V2^2 - V1^2)/2gc
which may provide some uselful insight but we'll need to introduce the pressure-energy equation which includes concepts of entropy and the stagnation process to really understand what is going on under the cowl.
Area changes, friction and heat transfer are the 3 most important factors which affect flow properties. Its been a long time for me so I'm digging back in the books to understand Fanno Flow propeties, which include losses, and understand how this might or might not apply to under cowl flow characterization.
Ultimately we are limited by properties we can either measure during flight or look up in tables - I'm always trying to ensure my flight tests are done efficiently with the minimum of configuration/instrumentation changes. Understanding the theory helps ensure we set-up each test to this end.