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I made a few very conservative educated guesses about the conditions inside the exhaust pipe. These can be easily verified by measurement's which is the next step.

Gas velocity in the 3 inch diameter exhaust pipe is assumed to be 1000 FPS or 681 MPH. A variable nozzle would increase that at the expense of some back
pressure.

Air density in the pipe is assumed to be half sea level or .0013 for the MPH constant. That affects the dynamic pressure directly. Not to be confused with static pressure.

Paul Lamar

Hi Paul,

Exhaust velocity seems to be very much higher than 1000 FPS. Check this:

NACA Report No. 822:
Calculatons of economy of 18-cylinder radial aircraft engine with
exhaust-gas turbine geared to crankshaft

http://naca.central.cranfield.ac.uk/report.php?NID=2196

Page 8:

"For example, a system designed for geared operation with maximum
economy at the following conditions is considered;

Engine speed - 2000 rpm
Inlet manifold pressure - 40 InHg Abs.
Altitude - 30,000 ft.

At these conditions. a turbine with a closed waste gate and and an
effective nozzle area of 10 sq.in will produce an engine exhaust
pressure of 42 InHg Abs. and, according to fig. 7, will give a net BSFC
very close to a minimum (ie. 0.33 BSFC). For expansion from 42 InHg Abs.
to atmospheric pressure at 33,000 ft., the theoretical turbine-nozzle
discharge velocity is 3115 fps. For a turbine wheel pitch-line velocity
of 1200 fps, the corresponding blade-to-jet speed ratio is 0.385, which
gives an efficiency close to peak value for a single-stage impulse
turbine. The turbine should be equipped with a gear train to provide the
correct pitch-line velocity at an engine speed of 2000 rpm."
Cont. on Page 9:
"The range of satisfactory compound operation could be greatly increased
by the use of a variable gear ratio between the engine and the
turbo superchrger, variable turbine-nozzle area, and variable diffuser
vanes to prevent supercharger surge."

Cheers,

Petri

Yes I have that NACA paper. Here it is. do you have a better copy? I'll put it
on the web site for download.

I was trying to be conservative with my calculations.

Trouble is it is high altitude orientated which is good for aircraft
but not so hot for sea level. Pardon the pun :) It is early work test stand
and Curtiss Wright added to the practical knowledge base later on. Curtiss Wright moved away from the pressure turbine to the blow down turbine
and average back pressure on the engine was reduced to 2.8 psi above
atmospheric. That would be about 36 inches of Hg if my arithmetic is
correct.

Curtiss Wright claimed exhaust gas velocity was 2200 FPS 1.9 Mach, 1500 MPH,
214 Km/hour  on the R3350 TC. I was amazed. What happens to a turbine
blade when it is struck by a 2200 FPS blast of supersonic 1500 F,
815 C gases ? :)

Fully half the kinetic energy in the R3350 TC was absorbed by the exhaust
valves. No telling what the exhaust gas speed is out of a "piston" ported
Wankel rotary.

BTW As of May 1st 1956 Curtiss Wright had produced 9000 turbo compound engines.
Later engines were producing 3700 HP with ADI. Total flight hours were
7.5 million. 25,000 hours on the test stand.

Paul Lamar