Fluid mechanic, Total pressure

[tsochiu]

When I blow some air though two pieces of paper, the experience told me that two pieces of paper will move toward each other.
However, there should be work done by me on the air I blowed that changes its total pressure.
As there is a work done, we cannot simply apply Bernoulli's equation.
So how can we tell will the two pieces of paper will move toward each other?
And in what other situations will change the total pressure?

 

[russ_watters]

Bernoulli's equation doesn't concern itself with how an airstream gets it's total pressure, only with the fact that it is constant along a streamline.

 

[tsochiu]

So it can not be used in this case, as total pressure is not the same with air in the room and the air I beathe out.
My concern is in what situation the total pressure will change and when will it keep the same so that I can use the Bernoulli's equation

 

[russ_watters]

No, you're not understanding. It is the same along a streamline - meaning from your mouth, through the paper, it stays the same. So you can use it.

 

[tsochiu]

I'm sorry. I still can't understand it, the air passing between the two pieces of paper is in the same steamline with that from my mouth.
But how about the air on the left side of the left paper and that on the right of the right one.
They are in different steamlines with the gas I blowed out and have different total pressure.
So how can I design how is the paper move? Or I have some wrong concept?

 

[russ_watters]

I'm sorry. I still can't understand it, the air passing between the two pieces of paper is in the same steamline with that from my mouth.
But how about the air on the left side of the left paper and that on the right of the right one.
They are in different steamlines with the gas I blowed out and have different total pressure.
So how can I design how is the paper move? Or I have some wrong concept?

The air on either side of the paper is not on any streamline. It is static.

Air blown from your mouth leaves your lips at essentially the same total pressure as the air around you, so to calculate the pressure difference between the papers, you need only to find the dynamic pressure of the moving stream of air and give it a negative value:

SP + VP = TP
TP=0, so
SP = -VP

 

[tsochiu]

I see, the total pressure is equal, but, in what situation, as a gas, the total pressure will change?

 

[Cyrus]

When there are viscous forces (shear stresses) to dissipate the energy (velocity) into thermal energy.

 

[cesiumfrog]

Some of these problems seem to depend on the continuation of the streamlines (eventually, the breath will have the same pressure and velocity as the surrounding air, so the pressure to velocity relationship must be the same on both sides of the paper). I'm not sure whether turbulence invalidates the [edit: Bernoulli] principle.

 

[Cyrus]

Which principle?

 

[tsochiu]

So the wind has the same total pressure with the steady gas if they appear in the same place, and only two isolated system will have different total pressure, isn't it?

 

[Cyrus]

Some of these problems seem to depend on the continuation of the streamlines (eventually, the breath will have the same pressure and velocity as the surrounding air, so the pressure to velocity relationship must be the same on both sides of the paper). I'm not sure whether turbulence invalidates the [edit: Bernoulli] principle.

The assumptions made for the Bernoulli equation is steady, inviscid flow, with no body forces, as $$\frac{ \partial u}{\partial t}$$ is equal to zero in the Navier-Stokes Equations.

So, yes. Turbulence is not when you want to use Bernoulli.

 

[Cyrus]

So the wind has the same total pressure with the steady gas if they appear in the same place, and only two isolated system will have different total pressure, isn't it?

I have no idea what you mean by this tsochiu?

 

[rcgldr]

As there is a work done, we cannot simply apply Bernoulli's equation

It can be used, but the small increase in total pressure needs to be taken into account. The key point here is that as long as the dynamic pressure increases more than the total pressure, there will be a decrease in static pressure.

The air on either side of the paper is not on any streamline. It is static.

My understanding is that viscousity would cause nearby air to follow the flow of the air stream. The shear boundary would not be infinitely thin, but in the case of human blown air, it would be very small, as opposed to the output of a high pressure nozzle, or output from a jet or rocket engine.

Air blown from your mouth leaves your lips at essentially the same total pressure as the air around you

My understanding here is that there is a slightly higher total pressure as it leaves, but as posted, the dynamic pressure is increased more than the total pressure, so there's a decrease in static pressure.

two pieces of paper

Note - pause between blowing air, unless you like getting hyperventilated. A better example would be air blown through a spool used for sewing thread, onto a 3 inch or so size of index card with tack through it or something else to prevent the index card piece from moving sideways. You can start blowing through the spool, and lift up the cardboard. Although the total pressure of the flowing air is a bit higher than the static air nearby, the reduction in static pressure of the fast moving air stream is enough to lift the piece of cardboard. A blow dryer on cold setting and paper plate with tooth pick (I wouldn't recommend sticking something metal into a blow dryer) can be used also (don't overheat the motor). Similarly, the end of garden hose with a pretty good flow of water through it can be pushed against a flat surface, and you will feel a pull instead of a push on the hose.

 

[tsochiu]

Jeff Reid, thank for your clear explanation. Now I know that increase in dynamic pressure is more than increase in total pressure in this case.
But it raise another question, how do we know when will the dynamic pressure increase more than the total pressure?

 

[tsochiu]

I have no idea what you mean by this tsochiu?

I want to ask when will the total pressure be the same and when won't?
Also, If the wind blow toward the building, will the wind have the same total pressure with the steady air behind the building?

 

[rcgldr]

Now I know that increase in dynamic pressure is more than increase in total pressure in this case. But it raise another question, how do we know when will the dynamic pressure increase more than the total pressure?

This could be difficult depending on the situation, but my guess is that as long as the air is fairly free to move about and isn't heated significantly, such as a fan blowing air freely, or through a constant diameter pipe, the dynamic (velocity related) pressure will increase more than the total pressure.

In the case of a jet engine, the air is heated dramatically, along with burnt fuel, experiences high pressure, which is convereted into high speed as it returns to ambient pressure, depending on nozzle setting (expanding, straight, or compressing), and afterburner usage. So the static pressure is returned to ambient (as opposed to below), at high temperature, high speed, so total pressure and total energy (including temperature) is increased by quite a bit.

I want to ask when will the total pressure be the same and when won't?

Total pressure is the same when no net work is done on the air. In reality, this would be fairly rare, as it takes some amount of work to cause air to flow and overcome it's resistance a change in speed due to do momentum and viscousity

If the wind blow toward the building, will the wind have the same total pressure with the steady air behind the building?

There will be small volume of "static" (some turbulence) air with slightly higher pressure than ambient on the leading side of the building, and a larger volume of "static" air with slightly lower pressure than ambient on the trailing side of the building. This is the principle of drag and a factor into how wings generate lift. The building is peforming work on the air by slowing it down, and the air in turn reacts with a downwind force against the building.

 

[tsochiu]

Thank for your patient in answering my questions.
I have learned a lot from it.

 

[rcgldr]

Note that dynamic pressure is directional and relative to a frame of reference (it's based on kinetic energy). Here are a couple of links to how pitot - static port systems work on aircraft. The pitot is aimed into the flow of air for increased pressure, while the static port is designed so that it's pressure is very close to ambient. The "alternate" static ports experience some loss of pressure due to venturi effect, but it's minimized, and most of the pressure differential versus ambient is via the pitot port. The net result is two chambers of air within an aircraft, moving at the same speed, but with different pressures, based on the path between the chambers and the outside air.

http://en.wikipedia.org/wiki/Pitot-static_system

Note here that static port is same as ambient, and alternate static port is only slightly lower:

http://www.luizmonteiro.com/Learning_Pitot_Sim.htm