# In carburetors, why can't we apply the continuity equation (A1 V1=A2 V2) for throttle valve?

## Main Question or Discussion Point

In carburetors, at the throat or ventury, the area decreases and so velocity of air increases (by continuity equation.).This is reason for suction of fuel from the float chamber.But in case of throttle valve, when the valve closes(area of flow reduced), the quantity of air fuel mixture passing reduces instead of velocity increase(with same flow rate) why?.Why cant we apply continuity equation(A1 V1=A2 V2) at the throttle valve?

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FactChecker
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A compressible fluid will not follow that equation since more can be squeezed into a smaller area.

Ranger Mike
Gold Member
old style carbs had two circuits. low speed idle and high speed to take advantage of the venturi effect.

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Chestermiller
Mentor
For the compressible gas, the continuity equation is $\rho vA =const$ (not $vA=const$), where $\rho$ is the gas density (which depends on pressure).

• FactChecker
Ok.For compressible fluids, A1V1=A2V2 will not hold.But in carburetors, till the throat they apply the continuity equation for incompressible fluids(air is the fluid). The throttle valve will be below the throat. At the throttle valve(air fuel mixture), in most of the books they would not apply A1V1=A2V2.Does air becomes compressible because of fuel addition?

A compressible fluid will not follow that equation since more can be squeezed into a smaller area.
Ok.For compressible fluids, A1V1=A2V2 will not hold.But in carburetors, till the throat they apply the continuity equation for incompressible fluids(air is the fluid). The throttle valve will be below the throat. At the throttle valve(air fuel mixtureis the fluid), in most of the books they would not apply A1V1=A2V2.Does air becomes compressible because of fuel addition?

FactChecker
Gold Member
in carburetors, till the throat they apply the continuity equation for incompressible fluids(air is the fluid). The throttle valve will be below the throat.
Air is always compressible. In some circumstances, the equations for incompressible fluids may give a good enough approximation.
At the throttle valve(air fuel mixtureis the fluid), in most of the books they would not apply A1V1=A2V2.Does air becomes compressible because of fuel addition?
The addition of fuel, with evaporation and cooling, may have an effect. I am not familiar enough with this subject to say more.

• Mohankpvk
Someone should probably mention friction losses. A Venturi attempts to minimize those. Throttle valves, not so much.

• Mohankpvk and 256bits
cjl
Continuity will still be followed, but keep in mind that continuity does not say that A1V1 at time 1 is the same as A1V1 or A2V2 at some other time 2 with different flow conditions. At all times, ρAV = constant throughout the flow (ignoring the fact that there's mass addition in the carb), but if you change the flow condition, ρAV (everywhere in the flow) will also change.

• Mohankpvk
Continuity will still be followed, but keep in mind that continuity does not say that A1V1 at time 1 is the same as A1V1 or A2V2 at some other time 2 with different flow conditions. At all times, ρAV = constant throughout the flow (ignoring the fact that there's mass addition in the carb), but if you change the flow condition, ρAV (everywhere in the flow) will also change.
So, the continuity equation doesnt hold for a throttle valve (i.e. when applied for two points one before and the other after the valve along the flow) because it alters the nature of flow by sudden reduction in cross sectional area.Is this conclusion right?

FactChecker
Gold Member
So, the continuity equation doesnt hold for a throttle valve because it alters the nature of flow by sudden reduction in cross sectional area.Is this conclusion right?
I don't think that is what he is saying, but you bring up a good point that may be very significant. All the Bernouli-related results are talking about smooth, steady-state flow. A throttle that introduces turbulent flow is completely different.

• Mohankpvk
I don't think that is what he is saying, but you bring up a good point that may be very significant. All the Bernouli-related results are talking about smooth, steady-state flow. A throttle that introduces turbulent flow is completely different.
Ok. So the continuity equation cannot be applied for two points one before and the other after the valve along the flow, because it alters the nature of flow(makes the flow turbulent) by sudden reduction in cross sectional area.Is this conclusion right?

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FactChecker
Gold Member
Ok. So the continuity equation cannot be applied for two points one before and the other after the valve along the flow, because it alters the nature of flow(makes the flow turbulent) by sudden reduction in cross sectional area.Is this conclusion right?
I would say that it is not just the reduction in the cross sectional area -- it's the non-aerodynamic way it is done. But otherwise, I think that is right. That being said, I would defer to those who know more about this subject.

Chestermiller
Mentor
Ok. So the continuity equation cannot be applied for two points one before and the other after the valve along the flow, because it alters the nature of flow(makes the flow turbulent) by sudden reduction in cross sectional area.Is this conclusion right?
No, it is because the density has to be present in the relationship. If the density is present, the continuity equation will apply even if the flow is turbulent. The continuity equation (in the for I specified) will be correct at steady state provided there is no additional gas added to the flow

• cjl
FactChecker
Gold Member
No, it is because the density has to be present in the relationship. If the density is present, the continuity equation will apply even if the flow is turbulent. The continuity equation (in the for I specified) will be correct at steady state provided there is no additional gas added to the flow
My thinking is that turbulent flow through a restricted area would have flow forward, backward, and crosswise, so that it would be equivalent to a net non-turbulent flow at a lower velocity. (or through a smaller area) -- No, I don't think either of those can be correct.

I'm trying to find an equivalence to the situation of an airplane wing where the airflow has separated from the upper wing surface. There is turbulanceon the top surface and the usual Bernouli calculations do not apply.

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Chestermiller
Mentor
My thinking is that turbulent flow through a restricted area would have flow forward, backward, and crosswise, so that it would be equivalent to a net non-turbulent flow at a lower velocity. (or through a smaller area) -- No, I don't think either of those can be correct.
I have no idea what this means. At each and every cross section, if the flow is steady, irrespective of whether it is turbulent, the mass flow must be $\dot{m}=\rho v A$, where $\dot{m}$ is the (constant) mass flow rate, and v is the normal velocity averaged over the cross section.

• FactChecker
FactChecker
Gold Member
I have no idea what this means. At each and every cross section, if the flow is steady, irrespective of whether it is turbulent, the mass flow must be $\dot{m}=\rho v A$, where $\dot{m}$ is the (constant) mass flow rate, and v is the normal velocity averaged over the cross section.
How can steady flow include turbulance? They are not compatible.

cjl
To a certain extent, they are. You can look at bulk averages in a turbulent flow in some cases, and still get reasonable results - it depends on the length scale of the turbulence and the overall details of the problem.

• FactChecker
FactChecker
Gold Member
To a certain extent, they are. You can look at bulk averages in a turbulent flow in some cases, and still get reasonable results - it depends on the length scale of the turbulence and the overall details of the problem.
Ok. I'll buy that. I have gotten well out of my area of knowledge and will bow out.

Chestermiller
Mentor
To a certain extent, they are. You can look at bulk averages in a turbulent flow in some cases, and still get reasonable results - it depends on the length scale of the turbulence and the overall details of the problem.
More important is the time scale for the turbulence. We chemical engineers learned our fluid mechanics from the classical text Transport Phenomena by Bird, Stewart, and Lightfoot, and they were very clear in emphasizing that, if the flow is averaged over the very short time scale typically encountered with turbulence, it is manifestly valid to consider the flow steady.

• FactChecker
cjl
Yes, I forgot to mention that, but you are correct that turbulence frequently has very short time scales (which to a certain degree, goes hand in hand with small length scales, since time scales and length scales are related by velocity). It still cannot be neglected for some phenomena, but if you just look at mass flow through an orifice, you can largely just use averages and ignore the turbulence.

• Mohankpvk
I have no idea what this means. At each and every cross section, if the flow is steady, irrespective of whether it is turbulent, the mass flow must be $\dot{m}=\rho v A$, where $\dot{m}$ is the (constant) mass flow rate, and v is the normal velocity averaged over the cross section.
Ok.But if mass flow rate is constant, how will the valve reduce the rate of air fuel mixture flowing through it?
Even in case of flow control valves in hydraulic circuits(in case of piston cylinder arrangement), the speed of the piston movement can be controlled by controlling the flow rate.Here incompressible hydraulic oils are used.In this case if we apply continuity equation( i.e. if we assume the flow rate to be constant),how can the speed of the piston movement be changed?

FactChecker
Gold Member
Looking at the mass flow rate only, it looks as though the velocity can just go to infinity as the valve area decreases. But kinetic energy is proportional to velocity squared, so the limited energy limits the mass flow for smaller valve areas. Consider a bucket of water with a small hole in the bottom. The energy available to push water through the hole is coming from the potential energy of the water level in the bucket. There is a balance point of the velocity through the hole where that potential energy reduction equals the kinetic energy of the water going through the hole. That is what limits the flow out of a smaller hole. Smaller the hole => the greater the velocity => the greater the velocity squared and the kinetic energy of the fluid going through the hole per unit of mass flow => so the mass flow must be reduced to keep the kinetic energy matching the potential energy reduction (which is only proportional to velocity, not velocity squared).

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Chestermiller
Mentor
Ok.But if mass flow rate is constant, how will the valve reduce the rate of air fuel mixture flowing through it?
Even in case of flow control valves in hydraulic circuits(in case of piston cylinder arrangement), the speed of the piston movement can be controlled by controlling the flow rate.Here incompressible hydraulic oils are used.In this case if we apply continuity equation( i.e. if we assume the flow rate to be constant),how can the speed of the piston movement be changed?
When I said that the mass flow rate is constant, it was implicit that I was talking about "constant with respect to spatial position within the control volume." When you use a valve to control the mass flow rate, you are changing the mass flow rate by increasing the resistance to flow (but this only affects the mass flow rate with respect to time, not spatial position at a given mass flow rate). The speed of the piston movement can change by applying more or less "oomph" to the piston (higher force).

• Mohankpvk
cjl