# Are eductors working on the Bernoulli principle?

This is a picture of an eductor. The wikipedia article claims that it works on the Bernoulli principle.

The Bernoulli principle is famous due to the misconception about how aeroplanes fly and because it is convenient for highschools. Children are introduced to the Bernoulli principle because doesn't need calculus to "understand" it.

Pressure difference is the obvious reason behind acceleration and that's all. Acceleration cannot diminish the pressure around a flow

My question is; What is the reason behind suction?

## Edit:

From the book "Fluid mechanics" of Frank.M.White

When a fluid flow leaves a confined internal duct and exits into an ambient “atmosphere,” its free surface is exposed to that atmosphere. Therefore the jet itself will essentially be at atmospheric pressure also.

Only two effects could maintain a pressure difference between the atmosphere and a free exit jet. The first is surface tension which is usually negligible.

The second effect is a supersonic jet, which can separate itself from an atmosphere with expansion or compression waves . For the majority of applications, therefore, we shall set the pressure in an exit jet as atmospheric.

• Comments are not for extended discussion; this conversation has been moved to chat. Apr 17, 2016 at 12:07
• "Therefore the jet itself will essentially be at atmospheric pressure also." Nothing is at atmospheric pressure. Pressure is something exerted and not a property. Pressure exerted is different in different directions. Towards flow of liquid, its high. Along wall its, slight low. Opposite to flow its lowest. Inlet push fluid with huge pressure and pull creating a low pressure towards source. So, you need to clarify this part. Apr 20, 2016 at 1:24

# What is the reason behind suction?

The main reason behind suction in an eductor is due to a special case of Bernoulli principle called the Venturi Effect.

When fluid flows through a pipe, it has a specific rate of flow which can be identified by the equation of continuity

$$P_1v_1A_1 = P_2v_2A_2$$

Where $$\boldsymbol {v_1}$$ and $$\boldsymbol{v_2}$$ are the velocities at position $$(1)$$ and $$(2)$$ respectively. Similarly $$P$$ and $$A$$ are the pressure and area.

At position $$(1)$$, the area is $$A_1$$ and velocity is $$\boldsymbol {v_1}$$. As the fluid reaches position $$(2)$$, The area of cross-section decreases to $$A_2$$, which means the velocity increases to $$\boldsymbol{v_2}$$

In fluid dynamics, a fluid's velocity must increase as it passes through a constriction in accord with the principle of mass continuity, while its static pressure must decrease in accord with the principle of conservation of mechanical energy. - wikipedia

Now by the equation of continuity, At position $$(2)$$, the pressure should decrease i.e $$P_2 < P_1$$. Now pressure outside the suction chamber is equal to atmospheric pressure ($$P_{atm}$$) which is greater than $$P_2$$. This low pressure area inside the suction chamber forces fluid in the container to enter the chamber. This is how suction in an eductor works.

Search for Venturi Eductor to know more.

P.S: It seems that your main question is "How increase in rate of flow(higher velocity) results in decrease in pressure of that region?"

This can be explained in a number of ways. One way is to use the conservation of mechanical energy.

$$P+hρg+\frac{1}{2}ρv^2$$

This is constant through out the motion of the fluid. Hence increase in velocity results in reduce of pressure.

I suggest you to read this question from Quora : Why does pressure in a nozzle decrease as the fluid velocity increases?

Watch these videos which clearly answers how increase in velocity results in decrease in pressure:

• @AnubhavGoel. All answers are on about the same axis and all are acceptable. What do you think on this subject? Apr 17, 2016 at 12:48
• @HariPrasad Sorry, but after getting so much comments showing lack of understanding, I just want to correct this too; The educator on your picture wouldn't work at all. The shape from suction chamber to the Output is so bad, that probably some of the input will flow out through the suction pipe. I found it amusing how writing just the continuity equation provides so high amount of votes in this site, but if the answer would be tested in the lab, you couldn't use it at all, cause it doesn't work! Your are even calculating the wrong continuity here. The only relevant thing would be "V2".... Apr 19, 2016 at 17:47
• @JokelaTurbine Thanks for your information. But I just made a rough diagram to show the points where there is pressure differences and the working.
– hxri
Apr 19, 2016 at 17:57
• @HariPrasad Yes. It's nice. But as said, the position (1) has no relevance here. The pressure difference between (1) and (2) doesn't provide anything usable. See ie. the answer of Marty Green. Apr 19, 2016 at 18:01
• @JokelaTurbine Also the pressure difference is actually what causes the suction.
– hxri
Apr 19, 2016 at 18:14

Yes, the Bernoulli priciple is an integral concept in understanding the operation of this device.

As David White has observed, it is the momentum of the input stream which causes the output stream to flow out of the nozzle at a high velocity. However, if one were to neglect the Bernoulli principle, one might be puzzled as to why the input stream interacts with the suction stream at all, rather than just spraying straight out the nozzle and leaving the suction stream stagnant.

Let us consider the above hypothetical scenario of a stagnant suction stream. By application of the Bernoulli principle, the pressure in the output nozzle must be lower than in atmosphere outside of the eductor, since the two regions are connected via the nozzle, and the flow is much faster in the nozzle than out.

But now we see that the pressure at the end of the suction stream in the nozzle must be lower than at the start of the suction stream outside of the eductor, so the suction stream has suction and must start flowing!

This is precisely how and why the device functions.

Take another look at your picture and imagine that the suction port is actually in outer space...in a real vacuum. And imagine that the inlet port is hooked up to a 100psi air compressor. And the outlet port is connected to a balloon.

Is it clear that up to a certain point, you will be able to get quite a bit of air into the balloon? And if the suction port is quite big (and there's no reason it wouldn't be) there's going to be not much pressure difference between, the suction chamber and the external vacuum? So I don't think it's hard to convince yourself that the pressure at the outlet (B) can be quite a bit higher than the pressure in the suction chamber(C). If you replace the vaccuum with a supply pressure that is greater than (C) and less than (B), the device will then function as an eductor.

Of course, that condition can only persist as long as there is air still flowing straight through. Once you get to the steady state (the balloon is full), the net flow is from the air compressor to the vaccuum, and the pressure in the balloon (the outlet port) is the same as the pressure in the suction chamber. But at this stage, it's no longer functioning as an eductor.

• I upvoted your answer and your argument is really elegant but the notion that i don't understand and you will agree with me lots of people also can't explain is why a stream of water if it has high velocity lowers the pressure around it Apr 16, 2016 at 19:10
• Yes, you're right about that. I've had lots of discussions about this and I agree with you about the airplane wing. I have only one really good argument for the venturi effect. If you have water in a pipe, and there is a venturi, you agree that the water is flowing faster at the constriction. So it speeds up, and then it slows down. If it slows down, it is decellerating, and there is F=ma to make it slow down. The only force is (pressure)x(area). So the pressure must be higher downstream. Apr 16, 2016 at 20:33
• And you don't need a supercomputer to figure that out. Apr 16, 2016 at 20:36
• I edited the question and added the observation that the pressure of a jet can't fall below the atmosphere. Do you any thoughts about that? Apr 16, 2016 at 20:40
• for the outlet, true: but the pressure in the suction chamber can be quite low. Apr 16, 2016 at 23:07

The input stream is high pressure and high velocity. When the input stream mixes with the suction stream, it slows down, and entrains the suction stream. This means that the velocity of the output stream is higher than that of the suction stream, and lower than that of the input stream.

• The suction stream could come from 500 meters away. This photo shows a vacuum pump. The question is what is responsible for the suction? Mar 21, 2016 at 15:22
• I don't think that I would go so far as to claim that the Bernoulli principle is the main concept for this device. It is probably more correct to say that conservation of momentum leads to entrainment of the suction stream. And technically, the photo does not show a vacuum pump. The photo shows an eductor, which is a device which can pull a moderate vacuum on the suction stream. Mar 21, 2016 at 22:22
• @ David White. How the conservation of momentum leads to the entrainment of the suction stream? Mar 21, 2016 at 23:06
• The high velocity stream has mass and velocity, and it contacts the suction stream, which also has mass and a lower velocity. The "mixed" stream will have a velocity which is intermediate between the high velocity stream and the suction stream. Mar 21, 2016 at 23:42

Is the output stream a mixture of air and water? If so, that air must come from somewhere, that somewhere being the inflow of the suction. On a molecular level, you might imagine that some of the air molecules will bounce against the water flow from the nozzle and thus be accelerated towards the 'output' and quickly enough exit the eductor entirely. That creates a low pressure inside the eductor which will cause air molecules to flow into the eductor via the suction inlet.

• Yes, why air molecules accelerate when they bounce against the water flow? Apr 14, 2016 at 21:21
• Remember all molecules are in constant motion. In a gas, like air, the molecules move around all over the place. They bounce around like billiard balls on a pool table. Some of those moving molecules will strike the water stream just from pure luck. Those air molecules will be accelerated by their contact with the moving water. Just like a when a soccer ball bounces against another soccer ball. You might look at the following animation and imagine those air molecules being struck by water molecules which are moving in a straight(ish) line. Apr 14, 2016 at 21:26
• Look at the following animation and imagine those air molecules being struck by water molecules which are moving in a straight line. en.wikipedia.org/wiki/File:Translational_motion.gif Apr 14, 2016 at 21:32
• If i get it right, suction is due to viscosity ( viscosity as diffusion of momentum)? Apr 14, 2016 at 21:36
• I would say the suction is a direct result of the Bernoulli Principle. The stream of water causes a low pressure and that low pressure creates suction. I would say that the entrainment of the suction fluid is a result of viscosity. But the reason stuff flows into the suction inlet is a result of Bernoulli. But, that's my opinion - don't bet the farm on it. Apr 14, 2016 at 21:48

Why should an accelerated flow diminish pressure next to the flow? Yet, this device works.

First , I would throw some light on venturi effect with water.

As you can clearly see in image, I have represented arrows to show distance b/w water molecules.

Initially , water molecules are very close as they flow in wider pipe. When pipe becomes narrow, speed of water increases. As a result when water molecules pass towards narrow tube, they cover more distance than molecules behind them. This causes, distance b/w water molecules to increase as shown by black lines.

Further towards more narrow end of tube, distance between water molecules increases very much.

This reduces density of water. But, water does not want to change its density. To counter this change, a region of low pressure is induced. Water in pipe attracts water from vertical tube. This reduces level of water by ∆x in vertical tube.

Now, similarly for sprayers used by barbers, when air passes with huge velocity, more air is attracted from chamber by the stream. This reduces pressure in chamber. As a result water sucks in.

Edit: Sorry! I never read what an eductor is.

Wiki quote

"It consists of a large bore straight tube to which is attached a hose pipe through which clean water is pumped . The Bernoulli effect from the flow of pumped water causes suction at the mouth of the dredge. Water and sediment are sucked from the excavation site and released from the far end of the tube"

This time water/ air/ steam etc.(usually water) at more velocity attracts water, create suction, lift water and then debris along with it.

@Jokela Wiki quote:

The lifting injector uses the Venturi effect of a converging-diverging nozzle to convert the pressure energy of a motive fluid to velocity energy which creates a low pressure zone that draws in and entrains a suction fluid. After passing through the throat of the injector, the mixed fluid expands and the velocity is reduced which results in recompressing the mixed fluids by converting velocity energy back into pressure energy. The motive fluid may be a liquid, steam or any other gas. The entrained suction fluid may be a gas, a liquid, a slurry, or a dust-laden gas stream. The adjacent diagram depicts a typical modern injector. It consists of a motive fluid inlet nozzle and a converging-diverging outlet nozzle. Water , air , steam , or any other fluid at high pressure provides the motive force at the inlet.

• No, thank you for great question. I had the same doubt last year till now. I could never understand it. But , when you asked and I tried , I was enlightened. Apr 18, 2016 at 6:26
• This is a great answer, and it seems more sound than JokelaTurbine's. Indeed, why would accelerating the gas in one direction reduce pressure along the other directions? If $a_x>0$, $v_x$ increases but $v_y$ and $v_z$ do not change. Anubhav Goel, your answer is so simple, really enlightening! Apr 18, 2016 at 20:39
• @L.Levrel These were just my own thoughts, so I don't have any source. So, you can't trust it totally. You may like S Bateman Answer as well. I also think Jokela did not deserve bounty. Other answers were much better. Apr 18, 2016 at 22:26
• @L.Levrel Your comment question; Total Energy is constant. This answer is a good simplified explanation easy to absorb, but there is no suction; in nature. Never nowhere. When the water come's out of nozzle, the "low Pressure" has vanished. -Totally. Try this with garden hose, or with any water tap. According to your answer the output-pipe is not needed. But if you leave it out and use only an exit hole, it surely won't work. Just test it, and you'll see. The outside pressure brings the stuff to the chaber, and it's first accelerated at the output-pipe. It's always push and never pull. Apr 19, 2016 at 14:24

My question is; What is the reason behind suction?

This is a conceptual misunderstanding. There is no negative pressure, and thus there is no suction. Vacuum has a zero pressure. (Absolute zero temperature analogy)

After you get this concept right, you understand, that the "suction" is nothing else than the atmospheric-pressure pushing material to the low pressure chamber. The nozzle produces this low pressure. But it's always the higher pressure pushing.

This is why it works, though you can't get it working inside the nozzle by using just newton's second.

It's always "push" and newer "pull". You can test this by closing the intake. All material inside the "suction-channel" will immediately stop moving as you prevent the "push" though there is full "pull" present.

Edit; Pressure must be understood by the kinetic theory of gases. It's nothing else than particles with velocity colliding to the wall in continuous rates. So there is actually no "pressure" there is only velocity distribution to all directions. When all movement is rectified and directed to only one direction, the pressure on other directions must be zero as there are no particle colliding to these directions. This is what truly happens in Bernoulli principle. You can also say this other vice; there is pressure only in one direction in the flow of the nozzle. Now, as nothing is pushing here particles away from this jet, but the outside particles are pushing particles in the jet, there will be collisions and behavior according to the Newtons second in front of the nozzle, but only there.

Why should an accelerated flow diminish pressure next to the flow? Yet, this device works. My intuition is that it is an effect of vorticity. But i don't know any sources that support my intuition.

The vorticity is not the cause, it's what follows form the mixing of two velocities. The pressure just beside the jet out of the nozzle is actually very close the atmospheric pressure. (Blue arrows in your question), only the flow losses from the "suction" is reduced. The pressure is thus "very low" only inside the nozzle. (light grey in your picture) Google "Pelton Turbine Nozzle".

Edit 3;

The answer of A.Goel and it's comment forced me to make this clarifying picture;

At the left picture it's shown how the pure nozzle doesn't produce any suction. At the right picture it's shown how the educator would work even if the the first nozzle is just a pipe providing a high speed flow! The nozzle in the input side is NOT used to change the pressure; it's only used to decrease the flow velocity on the providing pipe-line and to reduce the flow losses there. Ofcourse this simultaniously means that the velocity is increased on the nozzle, and the pressure is thus degreased, but this doens't mean anything for the functionality of the educator.

• Of course, it is "push" and not "pull". But my query is how the nozzle produces this low pressure Apr 16, 2016 at 19:01
• If i get it right, the flow after the nozzle has much higher velocity so it is more orientated towards the exit and the surrounding air is for this reason entrained in the flow Apr 17, 2016 at 8:54
• @veronika Yes, The surrounded air is pushed in the flow, as nothing in the flow is pushing it away from the flow, as the kinetic movement is orientated in one direction. The hydrostatic pressure is nothing else than this kinetic movement distributed with equal amounts to all directions. That's why it's force is always perpendicular to the surface. Apr 17, 2016 at 10:24
• Maybe the assumptions of my question were wrong. Now that i think of it maybe such devices work with convergent-divergent nozzles and that means supersonic flows. Pressure cannot diminish under atmospheric when flow is sonic or subsonic. All these flows follow straight lines. Pressure differences make flows to curve.And only supersonic flows curve, expand, make waves Apr 19, 2016 at 21:02

From the book Applied Gas Dynamics of Ethirajan Rathakrishnan:

"As the jet fluid travels further away from its origin, it slows down due to mixing with the stagnant ambient fluid entrained and inducted into the jet field.

This is due to the boundary layer at the nozzle exit which develops roll up structures, or ring vortices that grow in size when they move downstream due to the entrainment of ambient fluid into the jet stream. Hence, to conserve momentum the centerline velocity decreases

...The law of conservation of mass is not valid for jet flow.The entrained mass is at a lower momentum compared to the momentum of fluid elements and they will try to come to an equilibrium"

I think that turbulence and conservation of momentum is the answer.

When two masses stick together, usually energy is not conserved( some escape to heat mostly), but momentum is always conserved.

A divergent- convergent nozzle always gives supersonic flows. In supersonic flows the fluid expands outwards all around and so the pressure is not constant across the flow. Only for supersonic flows we can assume the pressure at the exit is not equal to atmospheric pressure.

I don't understand the arguments of the given answers and so i will try to half-answer my own question.

The Bernoulli equation is derived from the conservation of energy strictly along a streamline. If a fluid accelerates, then the cause must be a pressure difference.

Pressure difference is the cause and acceleration the effect. It cannot be the other way. Pressure is not lowered just because a fluid flows.

Why should an accelerated flow diminish pressure next to the flow? Yet, this device works.

My intuition is that it is an effect of vorticity. But i don't know any sources that support my intuition.

• "Pressure difference is the cause and acceleration the effect. It cannot be the other way." Why come here and ask questions if you have such certainties? "Pressure is not lowered just because a fluid flows." Yes, it is. If you've ever hidden behind the corner of a house to protect you from wind, you may have noticed some suction "into" the wind flow. Also, give a good blow over a paper sheet, it will be sucked upwards; video here phymain.unisciel.fr/vive-le-vent Apr 14, 2016 at 20:24
• @L.Levrel Pressure difference is the cause because the force is the cause of acceleration and not acceleration the cause of the force. I agree with you that suction exists. I want to understand why. Apr 14, 2016 at 21:16
• @L.Levrel The equation of Bernoulli doesn't hold between two different streamlines and also in moving frames of reference. I have certainties but not too many that's why i come here. Apr 14, 2016 at 21:19
• About your 2nd comment. Outside the eductor output, all streamlines end with zero velocity and atmospheric pressure, that's why the constant in the Bernoulli equation for them is the same. See Duncan Harris's answer. Apr 15, 2016 at 7:32
• Not offended, just mildly amused. Apr 15, 2016 at 12:15