Is Bernoulli's Principle Related to Potential Energy and Lifting Water?

[striphe]

The Bernoulli's principle ?

I'm having difficulty understanding the principle. Particularly the concept of lowering potential energy.

What i am also interested in is the effects of this principle. Would a segment of hose with water running through it be easier to lift than the same segment if it was full of stationary water?

 

[330s]

the way i think of bernoullis therorem is by an aircraft wing- the design of the wing is such that the air flow on top will have to go further than the air below the wing. there is higher pressure under the wing than on top because the particles are all trying to get through the one space but on top the air slips over the wing quick meaning it will have a lower pressure. this is demonstrated by a venturi tube- the fluid pressure is high before it reaches the smaller funnel in the middle- the reason its high is because all the particles are trying to get into a small space and all the other particles behind them are squishing them to get into the small hole. As the particles go through the small hole their speed increases due to all the high pressure built up and so their pressure will be lowered depending how small the gap is. There is that much pressure once the particles have entered the narrower gap. I hope this sort of helps, I don't think my explanation was worded too well but do find a venturi tube or a site that explains one.

 

[mechprog]

Bernoulli's equation in fluid dynamics is a peculiar thing. Although it is one of the most popular equations in science, it is a source of controversy and confusion (in fact I was going to start a thread for discussion on its limitations and validity).
It is extensively applied for real world situations (sometimes blindly) and in most of the cases it is helpful (this is quite amazing-in reality there are no inviscid flows as implied by the equation).
Bernoulli,s principle is the qualitative statement of this equation. You can avoid it and just have the math do the work for you- simply use the equation. In fact, there is not much insight involved-just correctly interpret the various terms and you will see a famous law sitting behind it(guess what,s it?).
If you are interested you can find a rigorous discussion of it in some introductory fluid mechanics text (say shames or white). There you will see that it can be derived either by integrating the Euler's equation or by placing certain restrictions on Ist law of thermodynamics. And this is not surprising as Euler's equation is a statement of Newton's 2nd law (from which law of conservation of mechanical energy comes which is a special case of Ist law of thermodynamics) for ideal fluid.
For applications to actual situations you can see book by Fay.

 

[russ_watters]

What i am also interested in is the effects of this principle. Would a segment of hose with water running through it be easier to lift than the same segment if it was full of stationary water?

Could you explain why you would think that? -- pressure and weight are utterly unrelated.

 

[rcgldr]

The only potential component in Bernoulli's equation is density x gravity x height. The gravitational potential component in Bernoulli's equation just notes that pressure increases with depth in a fluid, regardless of the static pressure or velocity absent gravity effects. As already mentioned, a hose full of water weighs the same if the water is still or flowing.

Pressure is energy per unit volume, so you need to multiply Bernoulli's equation by volume to get an energy equation. This would then make the potential component an energy component = mass x gravity x height, which is the normal expression for gravitational potential energy assuming a constant gravity field, which is approximated at distances near the Earth's surface.

 

[striphe]

Could you explain why you would think that? -- pressure and weight are utterly unrelated.

Some bad info seemed to be suggesting something similar and it didn't sit well. Thought i would just make sure that it wasn't the case.

I've go another question regarding the effects of the principle. A fireman's hose rolls out flat when it has no water in it. Imagine that you have a length of fireman's hose, at one end is the nozzle and at the other it has been cut, but the cut end is stitched to itself so it is water tight. The hose is filled with water and laid on the ground, the nozzle is aimed in the air so that the water doesn't run out of it.

This water is then forced out of this hose, by running a rolling pin from the stitched end to the nozzle. As the water runs through the hose, does the decrease in pressure reduce the volume of the hose and assist in forcing water out of the hose?

 

[russ_watters]

You're misunderstanding what the "reduced pressure" is. Bernoulli's principle is saying that the pressure in different parts of a hose that have different diameters will be different. In no case will that pressure be negative - it'll just be a little less in a narrower part than in a wider part...but still very positive.

It can also be said that the pressure in your scenario is reduced from what the no-flow static pressure would be. So if you have a rolling pin trying to force water out of the fire hose, but you have a closed valve at the end of the hose, you'd have a very high pressure inside the hose. Open the valve and that static pressure decreases, but you still have positive static pressure in the hose holding it's shape.

 

[striphe]

If this pressure that holds the shape of the hose was the minimum required pressure and there is no restrictions to flow by the nozzle or friction, would some effect emerge.

 

[russ_watters]

If this pressure that holds the shape of the hose was the minimum required pressure and there is no restrictions to flow by the nozzle or friction, would some effect emerge.

Well, if you've ever seen a fire hose, when you shut off the water, they'll collapse as they drain, so in that sense you might see something like what you suggest, but that's the hose's weight and desire to be flat that counteracts the pressure inside it.

Remember, absolute pressure can only be positive, never negative. And the pressure inside the hose can never be less than atmospheric (negative gauge pressure), otherwise you wouldn't be able to get the water to flow out of the hose.

 

[striphe]

But isn't the pressure different in different directions. I remember years and years ago in a school experiment blowing air through a straw and having two balloons move towards each other.

See similar experiment:

I would have considered that a flow would have different pressure in different directions and so even though there is negative pressure on the sides the water can flow out.

 

[russ_watters]

But isn't the pressure different in different directions.

Ehh, I don't like that. One of the fundamental princples of pressure is that the pressure at a point is the same in all directions. However:

I remember years and years ago in a school experiment blowing air through a straw and having two balloons move towards each other.

That's a demonstration of the Venturi effect, but it happens in the atmosphere, not in a tube.

I would have considered that a flow would have different pressure in different directions and so even though there is negative pressure on the sides the water can flow out.

There are different types or pressure and they are measured in different directions, but the total pressure of an airstream is the same everywhere in the airstream and in all directions. Static pressure is the component of the pressure measured perpendicular to it and dynamic pressure is the component measured parallel to it. In a Venturi tube, static pressure gets traded for velocity pressure.

 

[striphe]

Thanks for the replies, i think i will have to do some more reading.

 

[rcgldr]

Water is then forced out of this hose, by running a rolling pin from the stitched end to the nozzle. As the water runs through the hose, does the decrease in pressure reduce the volume of the hose and assist in forcing water out of the hose?

In the initial state, the pressure of the water is slightly higher than ambient depending on how high the water level in the nozzle is compared to the water in the hose. This would correspond to the gravitational potential component (density x gravity x height) in Bernoulli's equation. The rolling pin increases the pressure a bit in front of it, just enough to overcome friction and viscosity required for the water to flow up and out of the nozzle. The pressure behind the pin would be ambient, since the only force on the hose would be ambient pressure from the air (unless internal forces in the hose caused it to retain some non-flat state which would result in slightly lower than ambient pressure).

I remember years and years ago in a school experiment blowing air through a straw and having two balloons move towards each other.

See similar experiment:

That could also be explained by coanda effect. Because of friction and viscosity. The flow going between and then around the far side of the balloons remains attached for a brief moment on the aft surfaces, and is diverted outwards, resulting in the balloons exerting an outwards force on the airstream, coexistant with that air stream exerting an inwards force on the balloons, causing them to converge.

Although mis-labled as Bernoulli effect, this video demonstrates Coanda effect, you can clearly see the water stream is diverted to the left, which means the ball (and string) exert a left force on the water, coexistant with the water exerting a right force onto the ball (and string).

But isn't the pressure different in different directions.

Static pressure is independent of direction. It's the pressure that would be sensed by an object inside of the stream moving at the same velocity as the stream (like a hovering balloon in a wind). Dynamic pressure occurs when the speed of the air is changed. In the case of a pitot tube, the relative air flow is accelerated (or decelerated) to the speed of the pitot tube, and the change in momentum causes the pressure inside the pitot tube to be higher if oriented into the direction of the wind. Similarly the pressure just aft of a moving bus will be lower than ambient.

It is possible to sense static pressure with a static port oriented perpendicular to a relative air flow, but that static port has to be flush mounted on a flat surface, and be hiding in a shear "boundary layer" where friction and viscosity create a thin zone (the shear boundary layer) where the air flows at zero relative speed at the surface and increases in speed with distance from the surface. By definition the outer part of the shear boundary layer occurs when the relative speed is 99% of the relative speed between the unaffected air stream and the flat surface.

If an open ended tube is oriented perpendicular to an air flow, the air flow is diverted away from the open end of the tube, creating a vortice and reducing the pressure at the opening of the tube. Carburetors will often use a 1 or 2 stage venturi section combined with a tube protuding into the inner venturi pipe so it's open end is perpendicular or aft of the air flow in the venturi pipe to take advantage of this effect. Some sprayers, such as the old hand pump Flit Gun (insecticide sprayer) use this principle also.

 

[highdream]

The article was very usefull

 

[highdream]

The article was very usefull

 

[highdream]

what is correct defintion of trust ?