Insofar as pressure is a form of energy, pressure energy increases gravity.
Gravitational collapse
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Well, I don't know about you, but I learned that pressure is force per unit of area. That (conventionally) gives it units of Newtons per square metre. That looks like: kg.m[sup]-1[/sup].s[sup]-2[/sup].
Energy looks like: kg.m[sup]2[/sup].s[sup]-2[/sup].
Now, (a) force is the time derivative of momentum, which is mv for a classical test particle with a rest mass, m. We want to know what is this force over some unit of area.
Ed: there we have it. The units say that pressure needs to be multiplied by cubic metres, i.e. volume, to be the same as energy (in units). We go from Newtons of force divided by area (pressure), then multiplied (somehow) by a volume. This volume changes because of pressure 'terms' in four dimensions (gravity attracts).
Energy looks like: kg.m[sup]2[/sup].s[sup]-2[/sup].
Now, (a) force is the time derivative of momentum, which is mv for a classical test particle with a rest mass, m. We want to know what is this force over some unit of area.
Ed: there we have it. The units say that pressure needs to be multiplied by cubic metres, i.e. volume, to be the same as energy (in units). We go from Newtons of force divided by area (pressure), then multiplied (somehow) by a volume. This volume changes because of pressure 'terms' in four dimensions (gravity attracts).
It may be known as 'Fermi pressure' but it's better to understand the details associated with electron degeneracy pressure and neutron degeneracy pressure and the limits they set for stabilizing gravitational collapse. For some reason gravitational collapse is one of the more interesting subjects for me. It ends in some really interesting 'fundamental objects'. Chandrasekhar Limit would be associated with the limit set by neutron degeneracy.
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Yes. So, where are you going with this?
Well, based on an assumption that 'physical units' are really heuristic devices that help us to understand things like forces, pressure, changes in volume etc, and especially in balancing equations. Most equations relate some kind of motion to such heuristics as 'energy'.Russ_Watters said:
Anyway, clearly to get energy out of pressure you need a factor of m[sup]3[/sup]. So where does it come from? According to John Baez, the RHS of Einstein's equation has four pressure terms, one for each of the t,x,y, and z directions. To make the RHS have units of 'energy', it gets multiplied by the volume (of a system of test particles) at t = 0.
CHRIS.Q
Registered Senior Member
Well, if did not reach this speed, then what will happen?
I think it would be like throwing a stone up into the air. There will be a point it will stop and return.
In this case it will then fall into the black hole.
In the case of earth, an object would slow, stop, and fall back down. In the case of a BH, once you've passed the event horizon and the closer you approach the center (the singularity) the stronger the gravitational force becomes, so nothing, including light, can follow any path except towards the center.
That's not a sentence. You neglected to include your point.
Yes (sort of). So what? Is this a blog? Are you a bot? This seems like a random bunch of unconnected observations with no point. Also, you are misusing the word "heuristics".
From the volume of what you are trying to determine the pressure energy of. Ie, if you have a tank of compressed air, that's the volume of the tank.
Read the second one, "Pressure as Energy Density": http://hyperphysics.phy-astr.gsu.edu/hbase/press.html
Ok. Maybe you should just put that in a blog?
Still searching in vain for a point.
As Baez' artilcle also makes clear, you need to restore certain constants, since (naively) multiplying pressure by volume only makes sense in three dimensions.
The momentum flow in the t direction is just all the matter contained in the volume (of the system of test particles)., so should have units of kg.m[sup]-3[/sup].
We see that pressure needs to be divided by (m.s[sup]-1[/sup])[sup]2[/sup], given by the square of the speed of light.. Then G scaled by an appropriate constant converts everything on the RHS to s[sup]-2[/sup].
The momentum flow in the t direction is just all the matter contained in the volume (of the system of test particles)., so should have units of kg.m[sup]-3[/sup].
We see that pressure needs to be divided by (m.s[sup]-1[/sup])[sup]2[/sup], given by the square of the speed of light.. Then G scaled by an appropriate constant converts everything on the RHS to s[sup]-2[/sup].
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He's just trolling, ignore him.
What do you think a heuristic is?RW said:
Look, you said pressure is a form of energy. What's that about? So what if that's what you think pressure is? Who should care?
P.S. Accusations of trolling are somewhat ironic, coming from the Toxic Trout.
Seconded. In fact I would reword it as "pressure is absolutely not a form of energy". Quite the point I unsuccessfully tried to drive home in another thread, before quitting there in disgust. Obviously there is as linkage between the two, via e.g. material dependent bulk or Young's moduli - but they are functionally quite different creatures. As for the oxymoronic term "pressure energy" used in that hyperphysics article linked to in #29, the author needs his/her head read. There is no such thing as "pressure energy", and the absurd 'derivation' there giving P = Energy/Volume is rubbish. The nearest legitimate thing is the differential relation dW = PdV (needing refining re isothermal vs adiabatic etc.), where it is obvious P is not an energy term. And just because pressure appears in the Bernoulli equation 'on an equal footing' dimensionallly wise with KE and PE terms does not make it 'a form of energy'! There is a certain contagious madness in the air here at SF.
This is your thread. You asked the question, you brought up the issue of pressure, you're steering the thread. You have to supply the point. I tried to provide a relevant answer to your question, but you aren't doing anything with it, you just stated a bunch of random observations that don't include a point.
Sorry guys, this is basic fluid dynamics and thermodynamics. And Hyperphysics is a pretty well respected site. How many other sources would it take to show you that "pressure energy" is a real concept? Yes, that really is what Bernoulli's principle is about:
http://en.wikipedia.org/wiki/Bernoulli's_principle
Ultimately, the math is what counts, so do you recognize what the three terms are in Bernoulli's equation? Do you recognize the equation is a conservation of energy statement?
Or in thermo:
http://en.wikipedia.org/wiki/Work_(thermodynamics)
Do you recognize what an air motor does? The output is rotational kinetic energy. The input must be a form of energy too...
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To which I agree (proviso as assumed there friction is negligible). Notice - two energy terms - KE & PE, not three. Pressure enters the Bernoulli formula, but not as an energy density, but as a factor in energy change. How could it be otherwise, when by definition pressure = force/area, which is clearly not an energy density. Sure, one can as the hyperphysics twit did, arbitrarily multiply top and bottom by a distance and formally obtain an 'energy density'. There is though zero physical justification for doing so, just as there is none in claiming that since torque = force x moment-arm = force x distance, therefore torque 'is a form of energy' since energy = force x distance! Slight problem with cross vs dot products, but who cares about such trivialities it seems.
You misunderstand. The term 'pressure' here refers to dynamic pressure q = 1/2rho v^2, and is really KE density by another name (see further below in that article). When it comes to BE, be careful of nomenclature. There are several versions and variants of those again, using differing terminology.
Yes, but evidently you are having trouble sorting out static and dynamic pressure terminology as used in various versions of BE.
Pressure or more generally stress is an essential factor involved in elastic or hydraulic or pneumatic or hydrodynamic energy, but is not energy of itself. That should have been sorted out early on in secondary school. A wiki article listing forms of energy:
https://en.wikipedia.org/wiki/Forms_of_energy
Search in vain for the 'pressure energy' entry.
There is nothing in the above that lends support to the notion that pressure - static pressure - 'is a form of energy'. It aint. It's an essential participant, as equally is strain, in mechanical stored elastic/hydraulic/pneumatic energy. As discussed already.
Sure, but the point is?
Posting from a cell phone so cant quote...
You can't mix terms with different units: the other two in Bernoulli's are energy density, so the third must be too. And by the way, what you called energy terms also have pressure names: velocity pressure and gravitational head (pressure). So you basically just accidentally agreed with me. Why are you accepting some forms of pressure energy and energy density ("kinetic energy density") but not others in the same equation?
Regarding units, YOU should check again: divide energy (N-m) by volume (m^3) and what do you get? By definition: energy density, which for compressed air happens to also be pressure.
And the point of the last line was that the input of an air motor has to be a form of energy: what name would you give it?
You can't mix terms with different units: the other two in Bernoulli's are energy density, so the third must be too. And by the way, what you called energy terms also have pressure names: velocity pressure and gravitational head (pressure). So you basically just accidentally agreed with me. Why are you accepting some forms of pressure energy and energy density ("kinetic energy density") but not others in the same equation?
Regarding units, YOU should check again: divide energy (N-m) by volume (m^3) and what do you get? By definition: energy density, which for compressed air happens to also be pressure.
And the point of the last line was that the input of an air motor has to be a form of energy: what name would you give it?
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If the input to your air motor is 100psi air, and the ambient environment is 100psi air, how much energy can you extract from that 100psi "form of energy?"
Absolute pressure is not a form of energy. A pressure _differential_ is a form of potential energy, and a mass flow is that pressure differential expressed as kinetic energy.