Calculation vs. measurement of a manifold

I cannot give a clue on the errors of estimates. However, I learnt once that it was indeed possible for pressure to rise rather than fall in proceeding along a manifold, depending on the relative diameters of manifold and takeoff lines. So, sometimes, contrary to conventional wisdom, the first takeoff pipes in a manifold can get less flow rate than the average.

I don't like to admit it but, in my experience, calculations on relatively simple systems of known length, known fittings, etc are only within ten percent if you are lucky. When it comes to local complexities, such as manifolds, I don't expect you would get within ten percent unless you were very, very lucky! Maybe fifty percent is more like the appropriate figure.

I agree with 25362 in that the actual flow distribution in a manifold (i.e. relative proportions in the connected branches) is not necessarily intuitive; it sometimes seems to defy "common sense".

Brian

Hi.

The pressure loss I have calculated is approx. half the measured. I expected some difference due to the complex design, but 100% off????

But if simple systems can give 10% off, my calc may not be that surprising. But it is however very unfortunate that a trustworthy calculation is that hard (impossible) to achieve.

Btw, I think that the pressure drop 25362 is speaking about is the static pressure and it should rise only if the flow area increases. When I measure the pressure loss as P_in-P_out, I measure the static pressure under similar flow areas, and a “correct” pressure loss should be obtained.
The distribution of the flow in the manifold is exactly one of the details I was trying to calculate (only approximated) and the measured distribution was worse than calculated. This is however not surprising as it seems I cannot trust the pressure calculation (and the flow distribution is governed by the pressure distribution in the manifold).

es335
what you state about the change in static pressure is not fully correct: even with constant flow area (more precisely: in a manifold with constant cross section) there is a change in static pressure due to the change in velocity, and this in turn is varying as the mass flow rate along the manifold is changing due to the departures in the pipes connected to the manifold.
If you want to calculate the distribution of flow rates in a bank of tubes connected into an inlet and an outlet manifold, you can't dismiss that phenomenon. Moreover the behaviour (and the equations) are different for the inlet and the outlet manifold, as in the outlet the dynamic pressure of the fluid coming out at each intersection is lost in the main stream.

prex

Online tools for structural design

prex is right. For most headers , the static pressure will increase toward the dead end of the header. To roughly match this change in static pressure change, the inlet and outlet headers should be arranged in a mirror configuration ( ie, "U" shape), so the max static pressure in the inlet header is feeding the max static pressure location in the outlet header. This will minimize the tube to tube flow unbalance due to header unbalance.

There are a few tech papers on this subject from the 1960's-70's- I'll dig them up and send a followup message.

One detail that also affects this header unbalance is the style of tube to header weld- a "stick thru" weld will have a greater loss than a flush weld.

Prex:
Well, you are correct about the relation velocity-static pressure. I was assuming constant flow and changing area, but it would be more correct just to deal with the velocity.
When I described my case as a manifold it was because it was a good description, but not an accurate one. The problem I face is however difficulties in calculating the flow distribution in a tube bank with a manifold as inlet an outlet. Sorry, I should have written that before.
The fluid is also water (and not air as you might assume if you take the word manifold literally) so no compressibility effects are present as with some exhaust manifolds.
I cannot see why the equations should be different for the inlet and the outlet. What equations are you thinking about? The physics are the same! It does not matter if the flowrate in the individual tubes change, the physics hence the equations does not change. Only the values of the parameters in the equations.
The problem is not difficult as such. It is only a question of balancing the pressure losses as the inlet feeds the whole design and the outlet is for the whole design also. The problem as I see it, is the minor losses and a correct estimation of them. And that is not easy.

It just bugs me that the calculation is so far from being correct.


Davefitz
Maybe my problem is losses from weldings and bore holes. I have not taken that in account. It seems however unlikely that can raise the pressure loss with a factor of 2, but it definitely should have an impact.

here are some references that are useful for determining the flow unbalance in manifolds/ headers:

Bajura, RA "A model for flow distr...: trans ASME 98-A-4,473-479 Oct 76

Acrivos, A Chem Eng Sci V10 p112 1959

Keffer, JF J Fluid Mech 15 p 481 & , 1963

Bajura, RA, Jones, EH J Fluid Eng-T ASME 98(4)654-666 1976

Ahn, H KSME Int J 12(1):87-95 feb 98

Hager,WH P I Mech Eng C-J Mech 201(6):439-448 1987

Greskovi, EJ , Obara, J T Ind Eng chem proc DD 7(4):593 1968

Yes, the physics is the same, but in the inlet header the pressure change across a tube departure is, with constant cross section, proportional to M[ignore]&Delta[/ignore];M where M is the flow rate in the header and [ignore]&Delta[/ignore];M is the flow rate going out in the tube, whereas for the outlet header the pressure change across a tube arrival is proportional to 2M[ignore]&Delta[/ignore];M.
This comes from the application of the momentum equation, assuming also the tubes are connected at right angles to the headers.
Don't ask me details about the derivation: this was a work I did in a very far past and I have no more documents at hand. As part of this work the distribution of flow rates in a bank of tubes was calculated quite correctly with the basic relationships above.
What I want to underline is that the problem is not trivial, but also that the calculations should be able to give better results than what you quote: I hope you'll find the correct equations in one of the references quoted by davefitz.

prex

Online tools for structural design

correction for one reference:

Bajura, RA "a model for flow..."trans ASME V93-ser A-no 1, pp 7-12, Jan 71

Most manifold flow distribution/pressure loss procedures, replace evenly distributed lateral flow areas by a continuous slot of manifold length and a width calculated from the sum of lateral flow areas and slot length. The efficiency of conversion from dynamic to static pressure due to velocity decrease in a distributing manifold and the efficiency of static pressure decrease in the direction of flow in a collecting manifold due to velocity increase are represented by fixed pressure regain coefficients.
The lateral flow pressure loss is calculated from fixed loss coefficients (turning loss, inlet loss, outlet loss, friction loss, bend losses etc).
Static pressure difference between distributing and collecting manifold is the driving force for lateral flow.
So if in a U-flow configuration the static pressure increase in the distributing manifold is the same (in magnitude and form) as the static pressure decrease in the collecting manifold, the flow distribution will be completely even.
Whether the maximum flow goes through the first or the last lateral connection of a manifold depends on the interaction between lateral pressure loss and static to dynamic pressure conversion in the manifold(s).
The assumption of all fixed (flow independant) resistance coefficients is not correct for splitting and joining flows. This (and the continuous slot approximation) puts a limit on the achievable accuracy of manifold pressure loss calculations.
James B. Riggs (Ind. Eng. Chem. Res. 1987, 26, 129-133 or Chemical Engineering 1988, 10, 95-98) suggests the use of a worst case analysis to estimate uncertainty in design, assuming you know all resistance coefficients within 95% confidence, however you probably don't have this information.
I suggest the following procedure to get an uncertainty estimate:
J.B.Riggs uses a momentum coefficient to take account of the dynamic to static conversion which ranges between 0.8 and 1.3 for a distributing and between 1.5 and 2.2 for a collecting manifold.
Use these ranges of the momentum coefficients (and perhaps uncertainty ranges of all other resistance coefficients) to perform an uncertainty analysis and thus get an idea of the overall accuracy of prediction.

(Of course you can use procedures of others. They all use similar coefficients as J.B. Riggs, sometimes with slightly different definitions and always with different names. In the end most published coefficients originate from the same sources)

Walter Kramer