On Jan 21, 10:29*am, Tman wrote:
Thanks, finally somebody on my nerdy wavelength, and a really thoughtful
reply, but...

Todd W. Deckard wrote:

The carb throat is a double venturi and a manometer between the opening and
the neck would show a theoretical pressure drop of:

p(opening) - p(neck) = .5 * density of air * { velocity(neck)^2 -
velocity(opening)^2 }
* * * * * * *(Lets ignore carb ice for a second and say that the air is
incompressible).

agreed.

{ Pressure / density } + .5 * { velocity ^ 2 } + gravity * change_in_height
= a constant

I think you are speaking of the velocity of the gas in the orfice system
and the density of the gas, relative to the pressure differential that
is driving the fuel flow. *If so, I agree (caveat below). *Note that
this is equivalent to saying that the fuel flow is proportional to the
square root of the pressure differential, same assumption I made.



so Air over Fuel cancels your density term.

Check your math carefully, are you sure that you are not confusing the
density of the fuel (constant) and density of the air (decreasing)
terms. *I gave this the quick and dirty back of the napkin verification,
and it seems I still had both density terms in the final equation
relating mass airflow to mass fuelflow. *If you think you're right...
I'll do a little more rigorous playing with the terms.

My current hunch on this: *The mass fuel flow is not proportional to the
* square root of the pressure differential, but more or less directly
proportional to the differential. *This is because of the viscous
friction effects of the avgas in going through the metering orfices. *If
those effects predominate, (not surprising given the very small orfice
sizes), I'd say Bernoulli has little to say about the mass flow rate of
the avgas, and it is more linearly related to the pressure differential.



Q.E.D. *Good question. * If I ever become a physics teacher I am going to
put this one on the final!

I think I'm going to forward this to one of my old fluid dynamics profs

I think your problem is the assumption that there's a linear
relationship between air density and pressure differential. The same
pressure differential is the force that lifts our airplanes off the
ground, and as they gain altitude the density decreases. The stall
speed will rise, but not linearly with the decrease in density; it's
the square root of the decrease in density that we're looking for. In
the carb, one-half the density should then cut the pressure
differential and therefore fuel flow by one quarter, which will give
us a mixture twice a rich as when we took off. We find half the
density at 18,000 feet, incidentally.

Dan