Fluid Flow Problem

Because it is so small as to be negligible?

Poiseuille's law is applicable. Since it is a vertical tube and the flow is due to gravity alone, head loss equals elevation change.

http://hyperphysics.phy-astr.gsu.edu/Hbase/ppois.html

bioramani

I've read about the Poiseuille flow, and I don't get how you can use that as an argument here. One of the results of the Poiseuille flow is that the velocity is proportional to the partial derivative of the preassure with respect to eleveation.

The velocity isn't zero here(obviously) that means that the partial derivative of the preassure with respect to elevation isn't zero. This leads to that there is a preassure difference between the ends of the pipe, hence the head loss should also depend on this according to Bernoulis equation with the friction correction?

PWSlack: What is the argument you use to justify saying that the preassure difference is negligible?

The Fanning's equation for friction loss is:

ΔP = 4 f L v² ρ/(2 g_c D)

f- Fanning's friction factor = 16/N_Re = 16 μ/D v ρ

This leads to ΔP = 32 μ L v/(g_c D²)

The ΔP = vertical height of the pipe.

bioramani

It wasn't an argument. It was a question intended to draw a valid answer out of another reader.

If the pipe is open at both end, at the athmospheric pressure, the pressure difference is 0

Not quite. That is true only for a horizontal pipe. If the pipe is vertical the pressure difference is equal to the hydrostatic head of the fluid in the pipe.

bioramani

This is so wrong... Come on!!??? You can only say this if the fluid is not flowing(hydrostatic), but here the problem is with friction loss so obviously the fluid is flowing...

If the pipe is open the preassure at both ends is equal to the atmospheric preassure at both ends, and this is nearly allmost the same because we tend to say that the atmospheric preassure doesn't change with hight.

That is exactly the point. If we have tappings at both ends and measure the pressure difference it will be equal to to the fluid height which is the friction drop in the pipe. bioramani

Are you saying Rheolog is wrong?

Rheolog is correct in that the atmospheric pressure is same at both ends. As you mentioned in your reply to the post on atmomosphric pressure variation due to altitude, for small differences this can be ignored.

If the pipe were to be horizontal there is no pressure difference causing flow. On the other hand if the pipe were inclined, the hydrostatic head causes flow. If no other force were acting, the flow will be as per Fanning's equation.

I am sure that we are all clear about the phenomenon. Maybe it is the terminology that is different.

bioramani

Hi Guest,

If the pipe is open the preassure at both ends is equal to the atmospheric preassure at both ends, and this is nearly allmost the same because we tend to say that the "atmospheric preassure doesn't change with hight".

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There is a lot of assumptions here but, not knowing the exact details of whether the pipe is vertical or horizontal, we do not know the length either, we have to make a 'guess''.

Now, you say that 'atmospheric pressure is the same with differing height'?

Well, it is not like that!

'Atmospheric pressure', also known as 'gravity' does fall (is less) as you go higher above sea level. Have you tried to use a garden water hose to rinse the roof and gutter? Did you notice the pressure was noticeably lower?

(If the pipe or container was horizontal the pressure at both ends would be the same. I quote the details below and the web address'.)

http://www.usatoday.com/weather/wbarocx.htm

[(The weight of the air pressing down on the Earth, the ocean and on the air below causes air pressure. Earth's gravity, of course, causes the downward force that we know as "weight." Since the pressure depends upon the amount of air above the point where you're measuring the pressure, the pressure decreases as you go higher.] [Air pressure is related to its density, which is related to the air's temperature and height above the Earth's surface. (Related: Understanding air density).]

Take care and join now! It is a great place.

Dear babybear, it is good to contribute, and I think you are very smart. But I've learned that the atmospheric preassure is 101kPa. Now, in the excercise the pipe is vertical and 1m and in the next excercise 2 meters. The atmospheric preassure does not change much in one or two meters, the preassure change: density * hight*g=1,2*2*9,81=23,544 Pa is nowhere near 101000 Pa, I mean if we use 3 significant numbers it won't even the slightest inpact...

Hello Guest,

I guess you are about right. I have not checked your figures because I don't have time now. However with regard to the pipe. I have not seen any ref' to it. What post did you see it mentioned on please?

There is so many ways across the world to measure atmospheric pressure! Pa I am getting used to but if used all the time it is easier.[p]

Take care

Are you asking about the details of the pipe?, those are in the picture in the first post.

Hello Guest,

Just a thought, perhaps it is because 'the friction head loss equals the difference in elevation + the difference in pressure divided by *g, which constantly varies depending on how high you are above sea level, hence the differing gravity.

This is going to be constant at any given *g? Which is why it was deemed not necessary to explain, perhaps?

I am not that familiar with Tribology so if you get back so if you get back to me do not quote fancy Math please. Those kind of equations I may get used to again but it will take time. ;=) OK? No offence.

I would have also thought that the whole equation varies depending on the kind of tube, glass, brass, steel, plastic etc, that the flow is moving in? Just a thought as I said.

Take care