I looked at the mathematics of carburetors and discovered some interesting features.
A simple carburetor has essentially these components, starting from air filter side (1) and ending to engine valve side (4):
- Choke valve. This is used to create a negative pressure in the main jet when the engine is cold, because fuel doesn't vaporize well when cold and thus more fuel is needed.
- A thin throat, where the main fuel jet is located. The main fuel jet is simply a small tube for fuel that ends in a nozzle spraying the fuel into the airflow.
- Throttle valve. This is the mechanism for limiting airflow into the engine.
- Idle jet. This is after the throttle valve so it works using the large negative pressure created by throttling the engine and the purpose is to offer enough fuel when the engine is throttled (I'll explain later why this is necessary).
The basic equation explaining carburetor operation is Bernoulli's principle. Using the interesting parts of it, the negative pressure of airflow is proportional to air_density * air_velocity2. This explains why the carburetor has a thin throat. By making the throat thin, to get enough air the velocity of the air rises to a large value. This increases the negative pressure of the airflow a lot.
However, note that negative pressure is proportional to air velocity squared. This has two problems:
- If the engine is operating at low RPM but at full throttle, the airflow is lower too than it would be at high RPM, and a second power relationship means the engine gets far less fuel than it would need. So you can expect a carbureted engine to run lean at low RPM, and to run rich at high RPM, when wide open throttle.
- If the engine is throttled, the airflow reduces markedly. This reduces the negative pressure so much that the engine gets practically no fuel -- in fact, there can be so little fuel the engine would not run without idle jet. To mitigate this issue, the idle jet is necessary. It operates not by negative pressure of airflow, but by negative pressure caused by throttling the engine.
These two jets, main jet and idle jet, give a rather poor approximation for the correct air/fuel ratio. You can't expect a carbureted engine to have as precise air fuel ratio than a fuel injected engine has. No wonder modern cars use fuel injection!
Ok, now we know that negative pressure is proportional to airflow squared, and that to mitigate the problems this causes when throttling the engine, a secondary idle jet is used. But how does the fuel flow relate to the negative pressure?
We can use the Darcy-Weisbach equation. According to it,
pressure/length = friction_factor * fuel_density/2 * fuel_velocity^2 / hydraulic_diameter
At first, it looks like fuel flow squared would be proportional to pressure (which is proportional to airflow squared), so the two squares would cancel out each other. However, not so! We know fuel density, length of the jet, pressure (from Bernoulli's principle) and hydraulic diameter of the nozzle. But we don't know the friction factor. Let's take a look at it first.
In laminar regime (probably the regime in most carburetors), the friction factor is:
friction_factor = 64/reynolds_number
And the Reynolds number is:
reynolds_number = fuel_velocity*characteristic_linear_dimension / kinematic_viscosity
= fuel_velocity*characteristic_linear_dimension*fuel_density / dynamic_viscosity
In this case, the characteristic linear dimension describes the size of the nozzle (and is the same as hydraulic diameter if it's circular nozzle). So Reynolds number is proportional to fuel velocity, which means Darcy friction factor is inversely proportional to fuel velocity, and this changes the fuel velocity in the final formula to be a linear relationship and not a square relationship.
So pressure (proportional to airflow squared) is proportonal to fuel flow (not squared here). Twice as much air, 4x as much fuel, unless the increased airflow is caused by reducing throttling (in which case the idle jet fuel flow reduces).
Another interesting observation about this is that fuel flow is affected by fuel viscosity. Different fuels have different viscosities.
If we put the dynamic viscosity form of Reynolds number in the formula, we get the result that fuel density cancels out, and fuel velocity is dependent on nozzle characteristics and dynamic viscosity. So dynamic viscosity dictates volume flow.
If we put the kinematic viscosity form of Reynolds number in the formula, we get the result that fuel density doesn't cancel out, and fuel mass flow rate (density times velocity) is dependent on nozzle characteristics and kinematic viscosity.
So, the answer to the main question I asked is:
- If there are two fuels with same dynamic viscosity, their volume flow is the same
- If there are two fuels with same kinematic viscosity, their mass flow is the same
- If there are two fuels with different viscosity, you can't say anything about their relative flow rates without knowing their viscosities.
Obviously, viscosity is dependent on temperature too, and air cooled engines usually don't have a stable temperature.
The alkylate fuel I used is almost pure isooctane produced by alkylation units in oil refineries (in fact, it has research octane rating of 98). If you know how octane rating is defined, isooctane is the "good stuff" (octane rating 100) and n-heptane is the "bad stuff" (octane rating 0). According to https://www.chemiway.co.jp/en/product/data/i_data01.html, the dynamic viscosity of isooctane is 0.503 cP at 20 degrees Celsius.
For regular gasoline, I found several sources (for 20 degrees Celsius):
So apparently we can conclude that the viscosity of gasoline can vary a lot.
Probably the way the small engine manufacturer decided to calibrate the fuel flow is that all gasoline variants (with viscosity 0.4 - 0.6 cP) have enough fuel flow to produce the maximum power the engine is capable of producing. If somebody buys 1900 W generator and finds out it's capable of producing only 1600 W power with a certain type of gasoline, the owner wouldn't be happy. So probably the manufacturer errs on the side of rich mixture if the viscosity happens to be less than 0.6 cP.
The viscosity of isooctane / alkylate gasoline is 0.503 cP, about the middle of the range of gasoline viscosities. So it's expected to have slightly rich mixture because normal gasoline can have a slightly higher viscosity in some cases.
Also, by observing that viscosity affects fuel flow, we can explain why carburetor engines are so sensitive to stale gasoline. Stale gasoline has higher viscosity, so it doesn't flow well enough into the engine, leading to all kinds of running problems. On the other hand, a fuel injected engine will just see from the oxygen sensor that fuel isn't flowing very well, and it automatically compensates by having the injectors open for a longer amount of time.
Edit: one of the answers suggested using Bernoulli's principle for the fuel flow too (
mass_flow = area * square root of (2 * density * pressure difference)). Let's investigate this.
Here's a GNU Octave / Matlab program determining whether Bernoulli's negative pressure or fuel viscosity loss is larger.
% Parameters begin here
rho = 735 % gasoline density in kg/m^3
mu_cP = 0.6 % gasoline viscosity in cP
fuel_line_diameter = 0.6e-3 % fuel jet diameter in meters
fuel_line_length = 20e-3 % fuel jet length in meters
fuel_liters_per_hour = 1.5 % how many liters per hour gas the engine uses
% Code begins here
kinvisc = mu_cP*1e-3/rho
v = fuel_liters_per_hour*1e-3/3600/(pi*(fuel_line_diameter/2)^2)
Re = v*fuel_line_diameter/kinvisc
if Re > 2300
error("Flow no longer perfectly laminar")
f_D = 64/Re
p_viscosity = fuel_line_length * f_D * rho/2 * v^2/fuel_line_diameter
p_flow = 0.5*rho*v^2
For 735 kg/m3 gasoline density, 0.6 cP gasoline viscosity, 1.5 liters/hour fuel consumption and 20 mm long fuel jet, regardless of the fuel jet diameter, viscosity pressure loss is about twice as significant as Bernoulli flow pressure loss is. Fuel jet diameter doesn't affect this relative relationship at all, it just affects the negative pressure that needs to be caused by the carburetor throat.
It would require 10 mm long fuel jet (shorter than my assumption of 20 mm), or 3.0 liters per hour fuel consumption (unrealistically high for this engine, about twice as much as this engine can consume) or 0.3 cP viscosity (very low for gasoline, although as the gasoline tank heats up this could be realistic) to have as significant Bernoulli flow pressure loss as the viscosity pressure loss is.
So it appears that the main equation determining fuel flow is the one for viscous flow in a tube, not the Bernoulli's principle applied for fuel flow too (you still apply Bernoulli's principle for airflow, however).