Explain the pressure terms in Bernoullis Equation


by StartlerBoy
Tags: bernoullis, equation, explain, pressure, terms
potatoecannon
potatoecannon is offline
#19
Oct5-10, 01:35 PM
P: 28
Greetings all,

Okay, I just lost a long detailed reply, but I'll try again (shortform).
I like the answers I read here - I'd just like to rephrase it how I understand it, and maybe that will aid StartlerBoy.

First: There is no such thing as "dynamic" pressure, and no conversion between potential and kinetic energy occures through the Bernoulli equation.

Please don't crucify me for that statment - hear me out.

A fluid (or gas) is made up of many particles moving in straight-line trajectories. The average particle speed is a function of temperature, and in a stationary fluid the NET direction of all particles is zero. (This velocity is related to the speed of sound in the fluid).
The boundary (pipe wall) is made up of particles vibrating within their bonds, and their vibrations also correspond to the material's temperature.
If the average temperature of the boundary and the fluid are the same, the net energy exchanged during fluid particle collisions with the wall is zero, and the particles rebound with the same energy they had before the collision.

The "static" pressure felt by the pipe is the average rate of momentum being reflected.
This varies by density (more particles in system = more boundary collisions / second), particle mass, particle velocity (function of temp), and the angle-of-impact with the boundary.
-Only the velocity component normal to the pipe surface is reflected, the parallel component is not affected.

If the same fluid is flowing through the pipe now (same streamline - example of a pipe off a water tower), the average particle velocity has not changed. The "flow velocity" is the net velocity of all the fluid particles.
Because the average direction of the particles' motion is parallel to the pipe wall, the average angle of impact of particles bouncing off the boundary will be lower (less "normal" to the surface).
With all other variables the same, decreasing the average impact angle will decrease the normal component of momentum that must be reflected, thus reducing the percieved "Static pressure".

The "dynamic pressure" is a defined quantity - the non-random component of the total fluid's particle motion, or the amount of particle momentum that must be randomized to reachive stagnant conditions.


To summarize:
Total pressure is a measure of average fluid particle speed and the fluid density.
Static pressure is the random component of the fluid particles' momentum.
Dynamic pressure is the non-random component - the net momentum after integrating.

And the Bernoulli equation provides a method to calculate the change in randomness of the bulk fluid particles' motion. Neat, actually.


I realize you also wanted a discussion of why laminar flow accellerates through a contracting boundary, but this post is long enough.

Cheers


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