Fluid Mechanics Development Length

[Enzo]

Hey all

I wasn't 100% sure whether to ask this in the general forums or the homework forums, it's more of a theory question rather than straight-up calculation question. If this is the wrong forum, please notify me and I'll repost this in the homework forum.

I've recently done a fluid mechanics laboratory where we measured the different head losses of oil in a pipe system, taking readings of head loss at 18 intervals. We did this test 5 times, varying the velocity at which the fluid travels, thus altering the Reynolds number.

A discussion question for this report is to discuss the development length of the fluid over the 5 tests.

My data leads me to the conclusion that turbulent flow (or namely, high Re flow), which has a lower overall darcy friction factor, has a significantly shorter development length than laminar flow.

Intuitively, I would say that the fluids development length would be greater when it's turbulent flow rather than laminar, seeing that turbulent flow would require more force?

I guess the question that I'm asking is, what do they specifically mean by development length in terms of turbulent flow? I imagine development length in terms of laminar flow would mean how much length would the flow need to stabilize itself into wholly laminar flow?

The formulas for theoretical development lengths are:
Laminar: L' = Re*0.06*Diameter(pipe)
Turbulent: L' = Re^(1/6)*4.4*Diameter(pipe)

Thanks for any help!

 

[FredGarvin]

The developed length is the length of pipe required for the velocity profile to establish and maintain relatively unchanged. Assuming that the pipe geometry or surface does not change, the velocity profile is now only a function of radial distance from the pipe centerline.

Turbulent flows take much longer to reach fully developed flows.

 

[Enzo]

Turbulent flows take much longer to reach fully developed flows.

Understood

But given the formulas:

Laminar: L' = Re*0.06*Diameter(pipe)
Turbulent: L' = Re^(1/6)*4.4*Diameter(pipe)

And two values for reynolds numbers: Re=2000, Re=5000

I'm left with:

Laminar L' = (2000)*0.06*0.02m= 2.4m
Turbulent L' = (5000^1/6)*4.4*0.02 = 0.36m

Which matches roughly the data I have, but doesn't agree with the general theory?

 

[FredGarvin]

I would venture a guess that your Re=2000 flow is not as "low" of a Reynolds number flow as you think. I would think that there are a couple of things that can be argued:

1) The Re=2000 is, depending on your rule of thumb followed, is awfully close to transitional flow. When someone talks about "low Reynolds numbers" they are usually referring to numbers like 100, 500 or so.

2) There is nothing saying that, even though you are at a Re=2000, that you can't have turbulent flow. Imperfections in the pipe, etc... can all cause wrinkles in the perfect set up.

I would suggest running your lower Reynolds number case at a much lower number and see if the theory starts to agree.

 

[gmax137]

Those two formulas "cross" at Re of about 200 (wait...OK, at Re = 173). So, for Re>200 we see the formula for laminar flow is higher than the turbulent one. What does that mean? What's the basis for these formulas?

 

[ank_gl]

In turbulent flows, boundary layer grows faster & hence flow develops faster. Your results are based on formulas which are empirical relation, & are correct.

 

[FredGarvin]

Those two formulas "cross" at Re of about 200 (wait...OK, at Re = 173). So, for Re>200 we see the formula for laminar flow is higher than the turbulent one. What does that mean? What's the basis for these formulas?

Most relations like that are based on experience and a lot of experimental data.

 

[ank_gl]

Those two formulas "cross" at Re of about 200 (wait...OK, at Re = 173). So, for Re>200 we see the formula for laminar flow is higher than the turbulent one. What does that mean?

It means that you don't use the formula for turbulent flow at Re=200

 

[gmax137]

It means that you don't use the formula for turbulent flow at Re=200

Exactly - I was kind of hoping that Enzo, the OP, would fill in that blank.

 

[Enzo]

Thanks for the help fellas, definitely makes things a lot clearer. I guess I was just having trouble understanding why the gradient for development length for laminar flow was greater than the one for turbulent. And once again, physics forum clears things up