Recently, I had a "discussion" regarding length, radius and their effects on airflow. I used Ohm's law to explain the principle (yes, I know it is for a circuit, but I was trying to keep things simple since Poiseuille's law is analogous to Ohm's but more complicated to explain).
Here's my explanation...

The simplest model for the flow of a fluid through a pipe is contained in Bernoulli's equation, which is simply an application of the law of conservation of mechanical energy to a moving fluid:

1)P+pgh+ pv^2/2= constant


here P is the pressure of the fluid, r its density, h its height and v its velocity. Air , when traveling down an intake pipe, behaves like a fluid and laminar flow is an issue. The laminar flow through a pipe is described by the Hagen-Poiseuille law, stating that the flow rate (F = volume of fluid flowing per unit time) is proportional to the pressure difference Dp between the ends of the pipe and the fourth power of its radius r and inversly proportional to the length (what was that about length not having an effect?)

2) F= 3.14 (Delta)pr^4/ 8ul

Because the flowrate F and the pressure p are proportional to each other (Eq. 2) - as are current and voltage in Ohm's law- it is convenient to write Eq. 2 in a form analogous to Ohm's law by introducing the flow resistance R , defined as:


3) R= p/F= 8uL/3.14r^4

I am wondering if this is right? Are there factors that I am missing? I am assuming that air is a Newtonian fluid and therefore, should obey these laws? Anyone with a more advanced physics backround care to comment and post the right equations, if these are indeed the wrong ones.
Thanks!

 

you have to consider shear force from the surface on the intake. plus it may not be laminar flow. the air that goes through the filter is likely to Reynold's number higher than laminar flow. i didn't do so hot in fluid mechanics, but i believe that with the air originating from the filter, Pouseuille flow is not correct in describing the flow in the intake. gotta run but ill thinkg about this tomorrow. nite

 

I can acutally help you in this. I am a civil engineer and I work in hydrology & hydraulics. Water flow equations are essentially the same as air flow equations. The only difference is when the flow becomes pressure flow. Water is considered an incompressable fluid, and air can be compressed.

Secret AP1 is correct, the air that is going through an intake tube can't be considered laminar flow because of the speed it's flowing at.

And fluid flow can't be compared to Ohm's law either.

 

[QUOTE]Originally posted by Big Ben
I can acutally help you in this. I am a civil engineer and I work in hydrology & hydraulics. Water flow equations are essentially the same as air flow equations. The only difference is when the flow becomes pressure flow. Water is considered an incompressable fluid, and air can be compressed.

Secret AP1 is correct, the air that is going through an intake tube can't be considered laminar flow because of the speed it's flowing at.

 

There are some similarities between the two. But they only are similar in a mathematical sense. Just like many formulas for motions and momentums use a variable squared divided by 2. (v^2)/2g or (mv^2)/2, etc.

 

hmmm, I guess wondering about is this:
Ohm described a resistance to the flow of electrons in a wire, and Poiseuille described the flow of water (or any Newtonian fluid) through a pipe. Now, in Ohm's law the voltage and current are propotional to one another, much like flowrate and pressure and propotional to one another. Therefore, there is resistance to the flow of fluid in a pipe that is analogous to the the resitance to the flow of electrons in wire. The principle is the same, the relationship between those factors is present...true?

Second, I agree that the airflow through the filter wouldn't be laminar (that would be like water flowing through a pipe filled with pebbles) but once it reached the intake pipe, wouldn't laminar flow be present?

 

So Ben or AP1,
Would The Darcy-Weisbach Equation describe the flow at the filter?

 

So the DWE states:
hf=f*L/D*V^2/2g

where hf is the head loss due to friction, calculated from: a friction factor f, the ratio of the length to diameter of the pipe L/D, the velocity of the flow V, and the standard constant for acceleration due to gravity g.

So as L increases the loss due to friction increases? If that is the case, then a longer, thinner intake tube is not ideal... correct? Which is analogous (not the same, but the same principleto the Ohm's law, in which length/diameter adversly effect flow...right?

Here's a link that helps (I think)
http://www.chemicalprocessing.com/web_firs...A6?OpenDocument

 

In fluid flow, there is head loss and friction loss. Those are the two main losses. Head loss is from a size change, bend, or from another head of fluid joining the main one. (like 2 pipes coming into one)

In current flow, the whole cross sectional area of the wire is causing a friction loss. The friction in a wire causes the electrons to dramatically heat the wire. And I believe that the resistance is different at different temps. This is how any heating element works. Lots of curent is being shoved through a highly resistive piece of metal. So it gets very hot.

I really don't know. I'd have to look it up. An aerospace engineer would know though.

 

The Darcy-Weisbach Equation describes head loss?
I posted on a physics discussion board and I'm waiting for their response.