Minor Losses Laminar Flow

Phoenix911 has you covered on this one. Good luck.

Thanks for the information Phoenix.

I was working with that book.

In the next link I have a calculation for the friction losses estimation, following the Example 4-8 (Page 4-4) of Crane in laminar flow conditions.

http://s000.tinyupload.com/index.php?file_id=51313779563384522282

What I can understand is how the minor losses are calculated for laminar flow. On that "Example 4-8" it was calculated the k factor for a globe valve, using the formula k1=340*fT. The ft are the values on the page A-26, but that table indicates that "the pipe friction data is for flow in zone of complete turbulence", despite the example is for laminar flow. Is it Ok to use that ft value.

For the case I am analyzing I have a very low Reynolds number =1.2 , and very low velocity 0.34 ft/s, and for 39.4 ft of piping a have a K(pipe)=323, and for one elbow I have a K(elbow)=0.45

My concern is that value of 0.45 it appears to low for me (the friction associated to piping will be 323/0.45 = 718 times the elbow friction). Do you have any idea why this happens if it is true?

I have wrote heat exchanger programs and use some of the calculations from crane for flows.

One thing I notice, and I did this with actually empirically testing of the heat exchangers to test the accuracy of my program is that the formulas in Cranes work for medium flows rate, but extremely high flows and extreme low flow rates, it does follow too good.

Sorry, I don't have a quanitive number on what's a high/low flow rate, but it was over 20 years ago and I forgot and don't have it in front of me,

I'll look over your link.

Can you give more information? Reynolds number = 1.2, velocity 0.34 ft/s and K(pipe) = 323 could be due to various combinations of flow, diameter and viscosity. Also what is the fluid?

By K(pipe) do you mean as in Δh = K(pipe)*V²/(2*g)?

I don't think hs = ∑(k*v^2/2g) is correct for laminar flow. According to my old copy of Perry (5^th edition) data is meagre, but some tests showed loss (no. of vel heads) is fairly constant as Reynolds goes from 2000 to 500, but then increases rapidly. Maybe later edition (or the internet) has better data. I have a WRc report on sewage sludge flow which says headloss increases by a factor (1 + 2000/N_Re) but it's based on a limited number of tests and might not apply too well to other fluids. Of course if the Reynolds No. and velocity are very low the velocity head is small so even if you allow for a lot of it it doesn't amount to much.

For turbulent flow I prefer to use hs = ∑(k*v^2/2g) rather than the equivalent length approach, as the latter gives fitting loss varying with the pipe friction factor, which doesn't seem logical. However, it might have some merit for laminar, as the high friction factor f = 16/ N_Re (in Δh = 4*f*L/D*V²/(2*g) ) leads to a higher fittings loss. Whether it's accurate I wouldn't know offhand. Also note that the Crane paper uses Δh = f*L/D*V²/(2*g) so f = 64/ N_Re.

You have thus far not mentioned anything about the actual rheology of this fluid being pumped...does it have any unusual characteristic? What does the viscosity curve look like? Is it at room temperature?

Your low flow situation is 20.4 ft/min, and while low, is not zero (although I am sure you surmised that by now. If you are trying to keep zones in this liquid from mixing, I am afraid you will be completely disappointed. The discontinuities of the surfaces where each section of pipe transitions to a pipe fitting will induce eddy currents in the fluid, and mix between boundary layers and the center of bulk flow.

Good luck whatever this secretive thing is, unless it contains some heretofore unseen malevolent intent. With all the Super Heroes out there in the movies these days, one never knows when a new villain will emerge, LOL. Ω

Osborne Reynolds' work of 1875 is standard text these days in many publications. Try Kempe's Engineers' Yearbook, any edition, or Perry, "The Chemical Engineer's Handbook", any edition.

Check , Chemical engineering book by Ron Darby, As crane handbook would not give good result in case of low Reynolds number. Use the 3k method

The real part of this:

(1) even when using the best approximation for laminar flow and data from the engineering books, you may find that it all comes down to how the connections to the fittings are made, i.e. - welded, threaded, clamped, etc. Also depends on the curvature of the curved fittings, the inside (smooth vs. rough casting) profile, and unknowns.

(2) you may end up with a fair idea of what the pressure profile under flow in your system looks like, but you will probably not know the precise behavior of the system until you actually have it built, and run it. IMHO that is the nature of the beast.

Any liquid piping system operating at this absurd low velocity is operating in a way that is far from normal engineering practice. Modern chemical plant Piping systems are designed for turbulent flow not laminar.

Modern liquid piping systems must balance reasonable pressure drops with energy expenditure of pumping systems. This is ALWAYS in the turbulent flow regime .

http://www.engineeringtoolbox.com/flow-velocity-water-pipes-d_385.html

To wonder and pontificate about equivalent "k" factors for very slow laminar flow seems to be a waste of time ....

But he didn't say it's water. Progressive cavity pumps are used to transfer eg dewatered sewage sludge at say 20% DS to a skip. That can result in very low Reynolds numbers, and pressure loss ~ 10bar in quite moderate lengths of pipe.

And he didn't say it was a semi solid like sewage sludge either.

The point is that it is a mistake using the Crane 410 methodology and "k" factors on bizarre semi-solids service that in no way is similar to turbulent flow liquid service.

This is a lot like pounding nails using a big pipe wrench..... and then complaining about the wrench.

With the velocity and Reynolds no. given in #3 it's something much stiffer than water!

I agree Crane isn't much use here. For the example I gave the pump pressure is more down to experience than calculation, as the viscosity is unlikely to be known at all accurately, but I was trying to help with his question. We still need more information.

The vast majority of fluid flow situations are turbulent, but you can't say ALWAYS, there are plenty of exceptions.

BTW the WRc report I mentioned relates to sewage sludge, typically 5-6% DS, not dewatered cake, but I included it as a bit of background information.