# Can the velocity in a funnel be higher than in freestream?

• John Mcrain
John Mcrain
If I put funnel out of car when driving 100km/h, can speed in narrow section in funnel be higher than 100km/h(freestream) and does bernuli equation works for this case?

Gold Member
Have you tried to work on this at all on your own?

John Mcrain
Have you tried to work on this at all on your own?
yes I know how to solve it using bernulli,total pressure must be same,but I don't know can I use it for this case..

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John Mcrain

Homework Helper
Gold Member
The speed of airflow within the narrow section should be higher than the speed of the freestream.
There should be a pressure differential between inlet and outlet cross-sections.

I believe that there is enough turbulence and drag around the funnel for the Bernoulli principle not to be fully applicable in this case.

Copied from
https://en.m.wikipedia.org/wiki/Bernoulli's_principle

"Bernoulli's equation is valid for ideal fluids: those that are incompressible, irrotational, inviscid, and subjected to conservative forces. It is sometimes valid for the flow of gases: provided that there is no transfer of kinetic or potential energy from the gas flow to the compression or expansion of the gas."

Gold Member
There will almost always be some inviscid core flow through such a funnel in which Bernoulli is perfectly applicable.

I was more interested in what thought process @John Mcrain had already gone through one way or the other here.

hutchphd
John Mcrain
The speed of airflow within the narrow section should be higher than the speed of the freestream.

Mentor
Suppose the funnel throat were totally closed (i.e., zero diameter exit opening). What do you think the streamlines would look like?

Homework Helper
Gold Member
You are welcome.
Consider that more mass of air will be able to flow through the narrow section as the slope of the funnel is smaller (more gradual transition between wide and narrow sections).

Also, watch the attached video to see how much disturbance of air is created by the the car next to the funnel.
That disturbance greatly affects the the stability of the direction of the flow entering the funnel, as well as the static pressures upstream and downstream, all of which move the situation away from the conservation of energy involved in Bernoulli's equation.

Homework Helper
Indy racing league race cars use underbody tunneling to speed up the free stream flow (relative to the car), to lower pressure for more downforce. Formula 1 race cars are required to use skid-plates for their underbody, but still benefit from air being sped up under the race car body. Both use rear end "diffusers" that provide a transition region behind the car for the lower pressure, faster moving air to increase pressure and slow down, which increases the underbody effects.

Gold Member
You are welcome.
Consider that more mass of air will be able to flow through the narrow section as the slope of the funnel is smaller (more gradual transition between wide and narrow sections).

That's not at all a generally true statement.

Also, watch the attached video to see how much disturbance of air is created by the the car next to the funnel.
That disturbance greatly affects the the stability of the direction of the flow entering the funnel, as well as the static pressures upstream and downstream, all of which move the situation away from the conservation of energy involved in Bernoulli's equation.

Where is there any kind of funnel in that video?

Arjan82
To increase the velocity through the small end of the funnel the kinetic energy must be increased. To increase the kinetic energy the static pressure must be lowered as per the Bernoulli equation. The flow coming out of the funnel needs to have the same static pressure as the surroundings, flow upstream of the funnel exit can only have a higher static pressure.

This means there is a buildup of static pressure in front of the funnel lowering the kinetic energy of the flow before it enters the funnel. Only then it can increase its velocity again through the small part of the funnel. So when air approaches the funnel its kinetic energy will first be converted to static pressure and then to kinetic energy again. For a perfect conversion the kinetic energy will thus be at most what it began with, thus the velocity through the small end of the funnel can thus at most be equal to the surrounding velocity.

However, at the moment the pressure just before (or in the cone of) the funnel is increased, flow will seep (escape) alongside the funnel, meaning that not all of the kinetic energy that 'hits' the upstream end of the funnel can be used to increase the static pressure. Therefore you 'loose' pressure and the flow through the small end of the funnel is lower than the surrounding flow, always.

On top of this there are also losses due to turbulence and friction.

256bits and Lnewqban
Homework Helper
Gold Member
That's not at all a generally true statement.
How would you improve the statement, if at all possible?

Greg Bernhardt
Gold Member
How would you improve the statement, if at all possible?

Well for one, I've been avoiding throwing out answers in this thread since @John Mcrain has not shown us any evidence of trying to figure this out on his own, but for starters, your statement pretends there is only one factor affecting mass flow through the funnel. In fact, there are many. The slope is only one possible factor.

The slope of the funnel, for example, can either increase or decrease the amount of mass that might reasonably flow through the funnel. A funnel with a better contour (which likely includes some length) will reduce the risk of boundary-layer separation, which would tend to reduce mass flow through the funnel. On the other hand, the longer you make it, the thicker the boundary layers get, so that will reduce the mass flow through the funnel.

Lnewqban
John Mcrain
If "funnel" looks like this,than constriction cause increase static pressure and lower speed then freestream?

Arjan82
I don't see how any of my arguments would be different for this case. Why do you think this makes a difference?

John Mcrain
I don't see how any of my arguments would be different for this case. Why do you think this makes a difference?
I just double check .So every constriction reduce speed compare to freestream..

John Mcrain
The flow coming out of the funnel needs to have the same static pressure as the surroundings
My first funnel...
Isnt flow higher speed then freestream when leave funnel outlet,becuase air has mass, so it has inertia,so it keep going for short time?
Or flow decelerate inside funnel narrow section to match freestrem speed when leave outlet?

Arjan82
Isnt flow higher speed then freestream when leave funnel outlet,becuase air has mass, so it has inertia,so it keep going for short time?

Air indeed has inertia, but to say that the speed at the outlet of the funnel is higher than free stream means that this inertia (or momentum actually, inertia times velocity) is increased, how would that work? What would be the energy source that does that? It is just not going to happen. Look at it this way:

Say you are standing on the side of the road and a car passes by from left to right. It is a day without any wind. The car drags air along with it and therefore, when the car has just passed, a part of the air will also go from left to right because it was dragged along with the car.

Now someone holds a funnel out of the window of the car the way you drew it. What you claim by saying that the outlet speed of this funnel is higher than the free stream velocity means that after the car has passed, some of the air will go from right to left! This is intuitively very strange isn't it? you move something through air from left to right, and afterwards the air is supposed to move from right to left... This is not possible.

Or flow decelerate inside funnel narrow section to match freestrem speed when leave outlet?

It will not match the freestream velocity, it will always be slower. First because there is always some friction. Second because of a more theoretical argument that I made in my first post which doesn't need any friction or turbulence to work.

Arjan82
So every constriction reduce speed compare to freestream..

Correct. The only way to increase the speed is when you add energy to the flow, like with some kind of pump.

John Mcrain
Therefore you 'loose' pressure and the flow through the small end of the funnel is lower than the surrounding flow, always.
So basicly you answer is opposite from other members

Arjan82
So basicly you answer is opposite from other members

Apparently, should I have conceded? ;)

John Mcrain
Apparently, should I have conceded? ;)
So bernulli will take me to wrong answer...

Arjan82
So bernulli will take me to wrong answer...

First: I don't see @boneh3ad making any statement about the exit velocity of the funnel being higher or lower than free stream in any of his posts here.

Second: Even if he did, so what?!? Are we going to vote now as to whether the outlet velocity is higher or lower than the surroundings? Do you think the air would care? What are you trying to say here? My arguments don't count because someone else who you apparently think high of doesn't agree? Shall we please keep it to actual arguments on physical processes please? This is a physics forum, not an opinion forum!

Third: Even if he was correct and I was wrong. What are you trying to say here? You are still to point out why he is correct! He is not correct because he's called boneh3ad!

Fourth: I also used Bernoulli (that's how you write it) in my argument...

Fifth: I have a lot of respect for @boneh3ad, he seems to know a lot about the topic and I agree with his remarks in this thread.

John Mcrain
First: I don't see @boneh3ad making any statement about the exit velocity of the funnel being higher or lower than free stream in any of his posts here.

Second: Even if he did, so what?!? Are we going to vote now as to whether the outlet velocity is higher or lower than the surroundings? Do you think the air would care? What are you trying to say here? My arguments don't count because someone else who you apparently think high of doesn't agree? Shall we please keep it to actual arguments on physical processes please? This is a physics forum, not an opinion forum!

Third: Even if he was correct and I was wrong. What are you trying to say here? You are still to point out why he is correct! He is not correct because he's called boneh3ad!

Fourth: I also used Bernoulli (that's how you write it) in my argument...
Leave now exit of outlet velocity,this was disccused between only you and me..

You said that velocity in narrow section in funnel will be allways slower then freestream.
bonh3ad wrote " There will almost always be some inviscid core flow through such a funnel in which Bernoulli is perfectly applicable" as respons to Lnewquban post. So he implies that using Bernulli I will get answer...

Lnewquban wrote that speed will be higher then freestream(opposite from yours),bonh3ad didnt complain nothing about it,he just add it that I can use bernulli for core flow..

I am suprised becuase I think he is proffesor of fluid dynamics

Arjan82
You said that velocity in narrow section in funnel will be allways slower then freestream.

I did and I stand by that.

bonh3ad wrote " There will almost always be some inviscid core flow through such a funnel in which Bernoulli is perfectly applicable" as respons to Lnewquban post. So he implies that using Bernulli I will get answer...

I agree with what boneh3ad said here, in fact, as I mentioned, in my first argument I also used Bernoulli. But it has no implication to whether the exiting flow speed will be higher or not than the surroundings.

Lnewquban wrote that speed will be higher then freestream(opposite from yours),

True, but he also liked my post on why I think that is not true.

bonh3ad didnt complain nothing about it,he just add it that I can use bernulli for core flow..

He also didn't complain about my post. Not posting anything tells you exactly nothing about what his viewpoint is on the topic.

I am suprised becuase I think he is proffesor of fluid dynamics

Maybe he is, maybe he knows more about fluid dynamics than I do, but what does that mean? Status doesn't count, only arguments do. (status does make me take his arguments more serious though :) )

Alright, enough of this nonsense... This was my last post in this thread. There is already more than enough nonsense going on in the world this day... 😢

John Mcrain
Maybe he is, maybe he knows more about fluid dynamics than I do, but what does that mean? Status doesn't count, only arguments do. (status does make me take his arguments more serious though :) )

Look I am here to learn,not to teach.
How do you expect me to know which answer is correct,if members have opposite answers?

If you know that you are 100% correct,then you first sentences must be: "Why you write man wrong answers?" or "shame on you,you are giving man wrong answers..etc

wing has higher speed on upper surface then freestream, without pump.

wing has higher speed on upper surface then freestream, without pump.
Similarly, the flow outside your funnel might be faster than freestream. But that doesn't imply, that the flow somewhere in the funnel will be faster than freestream.

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Gold Member
First, if fluid is incompressible and the flow is steady and moving into the funnel at a rate of ##\dot{m}##, it is therefore also leaving the funnel at a rate of ##\dot{m}##. Obviously the exit velocity has to be faster than the inlet velocity. It would break conservation of mass otherwise.

Second, one of the issues that people seem to have here is that the flow through the funnel does not occur independently of the flow outside the funnel. The funnel presents some resistance to flow that doesn't exist in the free stream. This makes it very difficult to generalize anything. If the opening is small, consider that it will behave in some ways like a Pitot probe where the flow in the front slows down (though doesn't entirely stagnate). If the opening is very large, this effect would only be large near the edges.

Also consider that the flow outside the funnel would be important. The outer shape of the funnel is important in determining what the wake of the funnel looks like into which the flow through the center would be discharged. The external flow will accelerate around the funnel and the pressure will drop, so the pressure into which the funnel discharges is not the same as that of the free stream.

But all of this is heavily dependent on both the internal and external shapes of the funnel. Incompressible fluids are governed by elliptical equations. What happens in one location affects every other location simultaneously (obviously an approximation to what we observe in real life, where nothing is actually perfectly incompressible).

hutchphd and Lnewqban
First, if fluid is incompressible and the flow is steady and moving into the funnel at a rate of ##\dot{m}##, it is therefore also leaving the funnel at a rate of ##\dot{m}##. Obviously the exit velocity has to be faster than the inlet velocity. It would break conservation of mass otherwise.

Second, one of the issues that people seem to have here is that the flow through the funnel does not occur independently of the flow outside the funnel. The funnel presents some resistance to flow that doesn't exist in the free stream. This makes it very difficult to generalize anything. If the opening is small, consider that it will behave in some ways like a Pitot probe where the flow in the front slows down (though doesn't entirely stagnate). If the opening is very large, this effect would only be large near the edges.

Also consider that the flow outside the funnel would be important. The outer shape of the funnel is important in determining what the wake of the funnel looks like into which the flow through the center would be discharged. The external flow will accelerate around the funnel and the pressure will drop, so the pressure into which the funnel discharges is not the same as that of the free stream.

But all of this is heavily dependent on both the internal and external shapes of the funnel. Incompressible fluids are governed by elliptical equations. What happens in one location affects every other location simultaneously (obviously an approximation to what we observe in real life, where nothing is actually perfectly incompressible).
Maybe the more general question would be:

Is it at all possible to increase the flow speed through some kind of "funnel" beyond the free-stream speed?

Shrouded turbine designs have the funnel placed the other way around, compared to what the OP suggests, with the rear getting wider.

Gold Member
Is it at all possible to increase the flow speed through some kind of "funnel" beyond the free-stream speed?
With the initial configuration, I would say no.

With another configuration, yes .

A.T.
Arjan82
Increasing the flow speed to beyond the free stream velocity with an object of any shape without it adding energy to the flow, disregarding local flow accelerations (i.e. behind the object), is a perpetuum mobile...

John Mcrain
Also consider that the flow outside the funnel would be important. The outer shape of the funnel is important in determining what the wake of the funnel looks like into which the flow through the center would be discharged. The external flow will accelerate around the funnel and the pressure will drop, so the pressure into which the funnel discharges is not the same as that of the free stream.

So it seems that speed in narrow section in funnel will be faster then freestream,because of pressure drop in wake?

John Mcrain
Increasing the flow speed to beyond the free stream velocity with an object of any shape without it adding energy to the flow, disregarding local flow accelerations (i.e. behind the object), is a perpetuum mobile...
I think perpetuum mobile is if we increase total pressure of flow,without adding energy.
But playing with speed(kinetic energy) and static pressure is possible if their sum not exceed total pressure of freestream.

Isnt it?

Arjan82
Downstream of this object, the pressure is necessarily equal to the surrounding pressure. If the velocity is then higher than the free stream velocity, the total pressure has indeed increased.

256bits