Carb & Mixture question

sarangan

sarangan

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Andrew, CFI-I
This is something I always wondered about but never got a clear answer. We normally lean the mixture at higher altitude because carburetors are supposedly volumetric (i.e they deliver a constant air:fuel ratio by volume), so as air density decreases we need to decrease the volumetric ratio to maintain the same mass flow ratio. The stoichiometric mass flow ratio for complete combustion is 14.7:1. That seems to be the standard answer that is stated in every literature.

I am not an aeronautical expert, but as far as I know the pressure in a venturi is described by
dP= 0.5 * rho * v^2
where
dP = pressure difference (compared to ambient)
rho = density of air
v = flow speed in venturi

From this, dP should change linearly with the density of air. Since dP is the pressure that pushes the fuel into the air stream, fuel delivery rate should automatically decline as air density declines. In other words, one should not have to adjust the mixture with altitude. Additionally, dP changes as the square of the flow speed (which is controlled by RPM). That would suggest that fuel delivery rate will increase faster than the RPM, which means one would have to lean the mixture at high RPM. Obviously neither of these are true. I am trying to figure out what is really going on here.
 
Think in terms of mass flow. Mass flow is proportional to density and the velocity - not the velocity squared.
So, for a given delta pressure, the air mass flow at low air pressure / density is reduced. But, the density of the fuel does not change (much) so the fuel flow at a that delta pressure is not reduced. So, the mass ratio between the air and the fuel changes with air density.
 
The fuel flow is governed by the pressure differential created by the venturi, and that is caused by velocity, not density. As density decreases as you climb, the fuel flow is still the same because the velocity is the same, and the mix gets richer.

If density was the big factor, lift would disappear with increasing altitude and we wouldn't be flying very high at all.
 
Dan Thomas said:
The fuel flow is governed by the pressure differential created by the venturi, and that is caused by velocity, not density. As density decreases as you climb, the fuel flow is still the same because the velocity is the same, and the mix gets richer.

If density was the big factor, lift would disappear with increasing altitude and we wouldn't be flying very high at all.
Click to expand...

But the pressure differential caused by the venturi effect depends on density and velocity, as I wrote in that equation. If it were independent of density then you would be right. https://en.wikipedia.org/wiki/Venturi_effect
 
Liquid flow through an orifice is proportional to the square root of the differential pressure, not linearly. So if you halve the air density (and thus the differential pressure), the fuel flow is 71%, not half, and thus will be rich.
 
Dana said:
Liquid flow through an orifice is proportional to the square root of the differential pressure, not linearly. So if you halve the air density (and thus the differential pressure), the fuel flow is 71%, not half, and thus will be rich.
Click to expand...

Wow, thank you!!! That's exactly the link I was missing. The square-root dependence doesn't seem intuitive at first, but it explains why the mixture richens with altitude.
 
Don't forget that fuel simply weighs the same (mass) at the altitudes we fly, but air doesn't.
 
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