Fluid pressure close to an accelerating plate 3

[Crispy2]

Hi all,

I need to calculate the pressure in a fluid at some fixed distance from a flat plate which is accelerating (normal to its surface) through a fluid.
If you assume the plate to be infinite (i.e. a rigid half-space), then I think the problem can be formalised as a one dimensional problem:

Imagine a rigid, semi-infinite, one-dimensional pipe, with one end which is capped. This could be visualised as a test-tube of infinite height. The pipe is filled with an idealised inviscid fluid of density Rho and bulk modulus B. The pipe is subjected to a constant acceleration A, parallel to its length. How can I calculate the pressure in the fluid at a point along the length of the pipe which is a constant distance X from the capped end?

Does anyone have any ideas or experience with this kind of problem?
Thank you in advance

 

[BigInch]

[ρ] * V^2 / 2 / g * Shape Factor

Independent events are seldomly independent.

 

[Crispy2]

Thanks for your reply BigInch. Could you please explain that formula? I can't seem to find it elsewhere.
So I think I understand that the expression ρ * V^2 / 2 is dynamic pressure, but what about / 2 / g * Shape Factor ?

Thanks.

 

[BigInch]

I think a shape factor for a flat square plate is something like 1.28

you need the 2g if you're working with weight density. No 2g if mass density.

http://www.grc.nasa.gov/

http://WWW/k-12/airplane/shaped.html

Independent events are seldomly independent.

 

[btrueblood]

Uh, I think Biginch may have misunderstood the question, or else I have. Is the fluid moving with respect to the pipe, or do the fluid and pipe move (accelerate) in unison? If the latter, wouldn't the correct equation be (rho)*(acceleration)*(distance from capped end)?

 

[Crispy2]

Thanks btrueblood, I think you're right. I reckon the pressure in the fluid should be a function of the acceleration.

Let me rephrase the same problem in a different way. In the project I'm working on we've come across a situation which can be approximated as the following:
Consider a flat plate with infinite breadth and height. This plate has a constant acceleration, forwards, in the direction normal to its surface. The plate is submerged fully in an infinite expanse of fluid, all points of which are initially at rest. The effect of gravity can be ignored.

As the plate advances through the fluid, a pressure gradient is generated in the fluid close to the plate, and this fluid pressure decreases as a function of X, where X = distance in front of the plate.

(My original post was an attempt to simplify the above situation to a one-dimensional problem involving the acceleration of an infinite capped tube containing a fluid. I think these two problems are equivalent. My apologies if that's not true!)

Basically I've been trying find an expression which described the pressure in the fluid in front of the accelerating plate as a function of X (the distance from the plate). My instinct originally was to use (rho)*(acceleration)*(distance), as you suggested, but if (distance) = X = (distance from the plate), then the predicted fluid pressure increases away from the plate, when actually it should decrease.

Thanks again

 

[IRstuff]

You've set up an unrealistic situations that may not result anything meaningful for a real situation. Your infinitely large accelerating plane will result in all of the fluid above the plane accelerating along with the plane, assuming that the fluid is incompressible. Because you made the plane infinite, the fluid does not have a chance to move radially outward to get around the plate, which would result in a bump in the surface of the fluid, where the upward moving fluid is drawn back down by gravity to flow around the plate. The limiting case would be the pressure front in front of a wing.

TTFN
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[BigInch]

I don't believe that I misunderstand anything, but I did try to make sense out of,
Consider a flat plate with infinite breadth and height. This plate has a constant acceleration, forwards, in the direction normal to its surface. The plate is submerged fully in an infinite expanse of fluid, all points of which are initially at rest. The effect of gravity can be ignored.
Which doesn't make any sense. That describes one infinite wall moving forward in an infinite expanse of fluid (I presume equally infinite). What the heck is that?

So I take a plate of finite dimension in an infinite expanse of fluid, in the following,

Force to acceleration relationship is F=MA. Pressure is Force/Area, so Pressure = MA * Area. That's the Force, or pressure responsible for moving the fluid, ie. changing its velocity. That's the acceleration it took to get the fluid to its current velocity.

Acceleration is the change in velocity over a given time, (V2-V1)/T
So to find force and then pressure, you must have a change in velocity. What's the change in velocity in this case. It is the change in the fluid's velocity from its initial free stream velocity to the velocity it has when it impacts the plate, 0, zero. The ideal force on the plate is the force necessary to change the velocity of the fluid from free stream velocity to zero. Considering turbulence requires another factor, the 1.28 shape factor, or drage coefficient for fluid impacting a perpendicular square plate.

If both fluid and plate are moving then it is nothing more than considering their relative (forward) velocities, the velocity of one object in relation to the other, V object a - V object b.
Pressure in the fluid in front of the plate is proportional to the fluid's accelerations occuring in the vicinity of that point.

Draw some streamlines and figure the time the fluid would need to get out of the way of the plate by following those streamlines as the plate moves forward into the fluid at some given constant velocity. Once those fluid particle velocities are known along the streamlines, you can calculate the pressures between any of two adjacent points on a streamline.

Independent events are seldomly independent.

 

[IRstuff]

I think what you're looking is usually tied in with bluff or blunt bodies in a fluid flow found in fluid dynamics texts and articles. to wit:

http://bbaa6.mecc.polimi.it/uploads/validati/pst25.pdf

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[IRstuff]

Actually, better yet, look for "square cylinder" in the context of flow.

http://www.researchgate.net/publica...ethod_for_simulating_flow_around_bluff_bodies

http://www.ewp.rpi.edu/hartford/~ferraj7/ET/Other/References/Gawronski/Rodi_JWEIA_1997b.pdf

http://www.hindawi.com/journals/jam/2012/465972/

TTFN
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[btrueblood]

I thought of a tectonic plate, sub-sea, when reading the OP question. He's not talking about flow around a plate, therefore it's static pressure due to acceleration of a fluid column, not fluid dynamic drag around a bluff body. You can argue about how (un)likely the scenario is, but if you're going to post a one-line answer then do so for the stated problem, don't invent your own problem and then say you haven't misunderstood something. Especially when you are held in high regard by most of us here as knowing a thing or two about fluids. This post is in specific reply to BigInch's first reply and his subsequent strident denials of wrong doing. Tried, convicted. I hereby sentence him to be exiled from the USA, and forced to live in someplace sunny, like Spain.

 

[Crispy2]

Thank you all for your help, I really appreciate it.

 

[MikeHalloran]

Google "shkval".

Any associated papers may be difficult to acquire, depending on where you are, for reasons that will become obvious, but the technology seems to be where you are trying to go.



Mike Halloran
Pembroke Pines, FL, USA

 

[BigInch]

Acceleration of a fluid onto a plate, or acceleration of a plate in a fluid is relative. Air moving across fix wing, wing moving though fixed air = same answer, but I have to admit that tectonic plates never came into my mind, so OK. I don't get it, never did and probably never will.

Independent events are seldomly independent.

 

[IRstuff]

"I need to calculate the pressure in a fluid at some fixed distance from a flat plate which is accelerating (normal to its surface) through a fluid."

I believe that BI's description from 29 Mar 13 1:38 is appropriate. I think the infinite plate approach was a red herring.

TTFN
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