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In a recent question, it was stated that

particles in high pressure air always flow to lower pressure.

In a pipe with a constriction, fluid flows from from low to high pressure after the constriction. (From here.)

How are these concepts related?

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Particle do NOT always move from high pressure to low pressure. They can move from a low pressure region to high pressure region and experience a decrease in speed.

The question is analogous to asking if objects always move in the direction of the net force on them. They don't, but they do always accelerate in the direction of the net force on them. If an object has a velocity in a direction opposite the net force on it, the object will slow down.

Consider a small parcel of fluid at a particular location. The pressure gradient at that location (plus the weight of the parcel) is the net force on a parcel of fluid there. This determines the direction the parcel accelerates, which could be different that its velocity.

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  • $\begingroup$ Discussing the acceleration of the fluid in terms of the pressure gradient and weight per unit volume is equivalent to discussing the Bernoulli equation. I don't understand what it is that you are claiming is untrue about my answer. $\endgroup$ – Noah Jan 7 '15 at 3:15
  • $\begingroup$ I'm sorry. I read your last paragraph incorrectly. I'll delete the earlier comment. You were correct to say that particles would be decelerating (on average) as they moved out of the venturi. $\endgroup$ – DWin Jan 7 '15 at 3:18
  • $\begingroup$ At the orifices at the outlet end of a venturi there are exchanges of energy between kinetic and potential forms where the pressure gradient will not explain the flow. Its essentially like a pendulum on the upswing where kinetic energy is being continuously converted into potential energy. $\endgroup$ – DWin Jan 7 '15 at 3:19
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Particles do not always flow from high pressure to low pressure, but there is a good reason why they claim so.

First order of business, particles move in a quasi-random manner. Sometimes they go one direction, sometimes they go another. On average they flow in a direction. However, I don't believe that is exactly what you are asking about.

The claim that particles always flow from high pressure to low pressure is only true as long as the particle velocities are low. If you have high velocity (such as in the middle of a venturi), that momentum can drive particles from lower pressure to higher pressure. This is seen in the graph.

The claim is useful because there are many situations where velocity can be ignored. For example, if you have a tank of compressed air and let it decompress into the air through a nozzle, there may be many pressure variations inside the tube, but the general airflow will be from high pressure standing still (inside the tank) to low pressure standing still(outside air).

The other way that claim is useful is if you use what is known as "static pressure" rather than the usual dynamic pressure. If, instead of taking the pressure from the sides of the walls, your example had a pitot tube like device which sampled from the middle of the tube, pointing towards the tank, you'd see a different distribution of pressures. In the middle of the Venturi, you would have a lot of particles "piling up" to get into the pitot tube, slowing down as they do. This piling up would drive the apparent pressure (when measured) higher... to its "static pressure."

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Flow of a fluid is from high pressure to low pressure.

This is explained in the first link of your question.

In the second link, the author is describing the fact that fluid pressure in a pipe is reduced at a point where the pipe diameter is reduced ('constricted', sometimes called a 'venturi'). This is explained using the Bernoulli principle. In the static case, there is no flow, since the pressure on either side of the venturi is the same. In the case of a fluid flowing through a venturi, the fluid pressure drops in the venturi. Flow is still from high to low pressure. As the fluid flows out of the venturi, its velocity decreases and pressure increases (Bernoulli principle). This time however, there is a pressure differential across the venturi. That is, the pressure on the 'inlet' side is higher than the pressure on the 'outlet' side, so flow is still from high pressure to low pressure side.

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  • $\begingroup$ Not so. The flow is from low pressure to high pressure. Pressure is just a measure of one local form of energy gradient. $\endgroup$ – DWin Jan 7 '15 at 3:07
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The determinants of the net velocity of particles is a combination of the kinetic energy and the potential energy. In a venturi the kinetic energy is higher than on either the inlet side or the outlet side. At the outlet side the kinetic energy will be decreasing as the particles exit the pipe into the high pressure "reservoir." They are essentially giving up their kinetic energy to increase the pressure (and potential energy) on the other side.

Bernoulli's Eqn which is really a restatement of conservation of energy for incompressible fluids says that along streamlines:

 {v^2/2} + gz + {p/rho} = {constant}

where :

    v is velocity

    g is gravitational acceleration , z is height above reference level

    p is pressure and rho is density

So pressure is just one contribution to the relevant conservation principle, and thinking of both kinetic and potential energy is a more comprehensive viewpoint. In the more realistic situation there are dissipative forces where energy is being lost to heat and sound, but this equation will remain an excellent approximation.

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Flow always flows from high total pressure to low total pressure. And if its gets obstruction at any point then static pressure at that point gets high

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  • $\begingroup$ Hello, and welcome to Stack Exchange. This does not answer the original question; you may want to edit it so that it addresses the question. $\endgroup$ – Daniel Griscom Nov 26 '15 at 12:22
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The statement "fluid flows from region of high pressure to region of low pressure" in the original question may be corrected as "velocity of fluid increases from region of high pressure to region of pressure and decreases from region of low pressure to region of high pressure." Comments solicited.

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  • $\begingroup$ This doesn't really answer the question, it recommends a change to the verbiage used. $\endgroup$ – Kyle Kanos Mar 21 '17 at 10:04
  • $\begingroup$ I don't see how this improves on or clarifies any other answers here. It seems like a less detailed version of most of the other answers. $\endgroup$ – JMac Mar 21 '17 at 10:31
  • $\begingroup$ If the initial velocity of the particle is zero, it will flow from high pressure air region to lower pressure region. $\endgroup$ – Feynman Mar 21 '17 at 10:46
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The net movement of particles is from high to low pressure however individual particles may not move this way.

Let us assume that the particles have negligible inter-molecular forces - ideal gas assumption but probably appropriate in most fluids. This would imply that a particle wouldn't 'know' if it was in a high or a low pressure region, it would just whizz along as would either way.

However, in a high pressure region there are more, faster, particles. If you had 2 regions, one with high pressure and one with low pressure, connected by a pipe, particles would move both ways. However, just out of statistics, more particles would move from high pressure to low pressure.

There is no extra force on the high pressure area, just more particles flowing.

Granted, for highly viscous fluids the inter-molecular forces will play a larger role and cannot be neglected like this.

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It doesn't necessarily flow from higher pressure to lower, but from higher energy to lower energy, as per Bernoulli's theorem. That's the answer you want here when you are pertaining to the venturimeter.

Bernoulli's theorem states that total energy remains same between any two points. Total energy includes pressure energy plus kinetic energy and potential energy (datum head). So to maintain equilibrium if pressure reduces at any point, then kinetic energy has to increase, which means velocity increases.

$$\text{total energy}=\text{pressure energy}+\text{kinetic energy}+\text{datum energy}$$

Note that fluid flows from region of higher energy to lower energy. And not from higher pressure to lower pressure, which is a very common myth. Let's see the proof.

Let's look at venturimeter. Let section 1 be normal area section at starting point. Let section 2 be throat section. Let section 3 be the normal section after throat.

First half has converging section. Area reduces and therefore velocity increases to maintain equal discharge between two section to obey continuity ($\text{discharge}=\text{vel}\times\text{area}$). Now as the velocity increases its pressure has to decrease to maintain total energy equilibrium by Bernoulli equation.

$$\text{result: velocity 2 > velocity 1 and pressure 1 > pressure 2.}$$

So yes: fluid just flowed from higher pressure region to lower. The next half is more important than first half. Let's see what does it have.

In the second half the area increases which implies the velocity reduces in diverging section to satisfy continuity equation. Which means pressure energy has to increase to satisfy Bernoulli equation has to increase.

$$\text{result : velocity 2 > velocity 3 and therefore pressure 2 < pressure at 3.}$$

So fluid still flowed from lower to higher pressure region, which is against the myth of fluid only flows from higher pressure to lower pressure.

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