Is this a correct interpretation of pressure?

So I am told that pressure = Force per Area --> F/A..

When considering the units of Force I find that force = kg * m/s^2

When considering the units of Area I find that area = m^2

Thus the units of Pressure = kg/s^2 *1/m = d^2(mass)/dt^2 * 1/m

If I interpret this correctly that means that if one had a long glass tube

(picture below):

=========================================================================

=========================================================================

And we considered a segment of the tube

                  this is the segment:


===============|===================================|=====================

===============|===================================|=====================

and we assumed that there was matter flowing through the entire tube:

===============|===================================|=====================

* * * * * *** * * ** * * * * * * ** * * * * * * ** * * *** *

===============|===================================|=====================

Then at any given moment: the pressure in this particular segment could be given by:

The change in the rate of mass flow/length of segment:

= d^2(mass in segment)/dt^2 *1/length

Is this correct?

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@007 I love how the mass is completely non-uniform. –  Isopycnal Oscillation May 4 '13 at 2:21
Thanks! Good OP' –  frogeyedpeas May 4 '13 at 2:29
Stupid autocorrect... I meant ASCII art not OP –  frogeyedpeas May 4 '13 at 2:30

What you've done here is just dimensional analysis. But you've gone a little too far. In particular, just because two things have the same dimensions doesn't mean that they are equal. If you want to expand $F/A$ a little more, you can choose your favorite from $$F = \frac{d p}{dt} = \frac{d}{dt}(m\, v) = m\, \frac{d}{dt} v = m\, a$$ Here, $p$ is the momentum, $m$ is some amount of mass you're keeping track of, $v$ is its velocity, and $a$ the acceleration.

Now, pressure is really defined as being the force on a unit of area. So if you don't choose an area, you can't define pressure. There might be situations where there is some momentum change in a volume without the matter directly hitting a surfce. For example, with an electromagnetic force. So there could be a net force on a volume. But again, you can't call anything a pressure unless you select an area to measure it.