Fluid pressure close to an accelerating plate
Fluid pressure close to an accelerating plate
(OP)
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
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





RE: Fluid pressure close to an accelerating plate
Independent events are seldomly independent.
RE: Fluid pressure close to an accelerating plate
So I think I understand that the expression ρ * V^2 / 2 is dynamic pressure, but what about / 2 / g * Shape Factor ?
Thanks.
RE: Fluid pressure close to an accelerating plate
you need the 2g if you're working with weight density. No 2g if mass density.
http://www.grc.nasa.gov/WWW/k-12/airplane/shaped.h...
Independent events are seldomly independent.
RE: Fluid pressure close to an accelerating plate
RE: Fluid pressure close to an accelerating plate
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
RE: Fluid pressure close to an accelerating plate
TTFN

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RE: Fluid pressure close to an accelerating plate
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.
RE: Fluid pressure close to an accelerating plate
http://bbaa6.mecc.polimi.it/uploads/validati/pst25...
TTFN

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RE: Fluid pressure close to an accelerating plate
http://www.researchgate.net/publication/228925889_...
http://www.ewp.rpi.edu/hartford/~ferraj7/ET/Other/...
http://www.hindawi.com/journals/jam/2012/465972/
TTFN

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RE: Fluid pressure close to an accelerating plate
RE: Fluid pressure close to an accelerating plate
RE: Fluid pressure close to an accelerating plate
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
RE: Fluid pressure close to an accelerating plate
Independent events are seldomly independent.
RE: Fluid pressure close to an accelerating plate
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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