lehpron
Posts: 6846
Joined: Tue Jul 10, 2001 3:42 am

### Question About Fluid Flow In A Pipe

say there is a large pipe with a smaller pipe within it, the flow in the smaller pipe is much slower than the outer one. Now say the little pipe ends and empties into the outer pipe which doesn't change it's size.

Is the overall resulting flow moving slower or negligible to the outer pipe's original flow?
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delta-flyer
Posts: 2631
Joined: Mon Jul 30, 2001 9:47 am

### RE: Question About Fluid Flow In A Pipe

The average speed would be slightly slower - it's basically the continuity equation. You can of course complicate the problem by considering boundary effects, the wall thickness of the inner pipe, etc., but both these effects would cause reduction of the speed after the flows join.

Pete
"In God we trust, everyone else bring data"

lehpron
Posts: 6846
Joined: Tue Jul 10, 2001 3:42 am

### RE: Question About Fluid Flow In A Pipe

So I'm guessing the inner flow would be forced to accelerate? I am familiar with the eqn, just a friend is borrowing my fluids text and their out of state. it is m-dot-1 plus m-dot-2 equals m-dot-3?

By m-dot I think I mean mass flow as in area times velocity times density.

But what I do not know is how to figure where downstream the flow is more or less uniform. If the outer flow is fast enough then I gguess the distance is pretty short.

oh yeah, happy 4th! i totally forgot.
The meaning of life is curiosity; we were put on this planet to explore opportunities.

777236ER
Posts: 12213
Joined: Sat Aug 18, 2001 7:10 am

### RE: Question About Fluid Flow In A Pipe

Yeah, it's continunity.

The mass flow rate (dm/dt) is just ρAU, and continunity states that the mass flow rate into a system has to equal the mass flow rate out.

In this case, (ρAU)1 + (ρAU)2 = (ρAU)final. If the fluids are the same, then A1U1 + A2U2 = AfinalUfinal

Which gives, Ufinal= (1/dfinal2)(d12U1+d22U2)
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DC10GUY
Posts: 2590
Joined: Fri Feb 18, 2000 5:52 am

### RE: Question About Fluid Flow In A Pipe

I would say that PSI would determine flow.
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lehpron
Posts: 6846
Joined: Tue Jul 10, 2001 3:42 am

### RE: Question About Fluid Flow In A Pipe

shall I assume U is velocity? We here (accross the pond) use it to mean potential energy, so initially I did not understand your eqn. How do you guys use V?

and d is diameter. Gotcha, thanx!

Optional question, what if the area in the larger pipe approached infinity (got extremely large), does the smaller pipe flow then not affect anything down stream? Imagine a duct outside of a car with no other purpose but to slow air coming in and through it. What happens to that air on the otherside of the duct? Speed up?

Again, that is optional, thanks for the replies.
The meaning of life is curiosity; we were put on this planet to explore opportunities.

777236ER
Posts: 12213
Joined: Sat Aug 18, 2001 7:10 am

### RE: Question About Fluid Flow In A Pipe

U is velocity, yeah.

Continuity holds for anything, that is mass flow rate in = mass flow rate out.

If the area of the larger pipe appropached infinity, the mass flow rate in would be infinity + the mass flow rate of the smaller pipe, which is negligible. So the mass flow rate out, downstream, would be infinite (the mass flow rate of the larger pipe.)

Of course none of this takes into account viscous effects etc.

Imagine a duct outside of a car with no other purpose but to slow air coming in and through it. What happens to that air on the otherside of the duct? Speed up?

Effectivly yes, in reality it's so tiny as to be negligible. In reality, turbulence around the pipe would probably slow the air around the pipe down more than continunity would theoretically speed it up.
Your bone's got a little machine

WellHung
Posts: 3299
Joined: Mon Feb 23, 2004 8:50 pm

### RE: Question About Fluid Flow In A Pipe

Fluid flow in a pipe? We'll report back to you after this weekend.

Signed,
Jcs17 and Aa61hvy

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