Re: Water flow in rectangular ("pipe") profiles 1

[sush54]

Gentlemen:

I'm more than a little out of my field here so please bear with me. We have a proprietary job that requires some unusal fixes.

By way of example, let's assume we have a 5' high vertical pipe with inner dimensions of 1-1/4" X 1-1/4" (1.5625" square inch cross section).

Water supplied at the bottom by a magnetic centrifigal pump--7' max. lift. Top is open.

Now, let's change this "pipes" cross section to various rectangular profiles, keeping the same 1.5625" total cross section, ie;

5/8" X 2-1/2"
5/16" X 5"
1/16" X 25"

As the "pipe" narrows more and more towards a "slot" the square inch cross section remains the same, but the relative internal surface area of the pipe increases dramatically.

Questions:

1. As the profile progresses towards a narrow "slot", does maximum lift figure for the pump decline?

2. Does the outward force exerted against the pipe wall increase? Would it be greatest at the bottom?

3. In the case of the 1/16" profile, there will only be a little more than 2 quarts of water in the the full pipe. Does the weight of the water have any or much bearing on the force exerted against the bottom of the pipe wall?


4. What role does friction play and what are the calculations for determining the forces at work? (Layman)

(Using the 1/16" example, if I were to hazard a guess, I'd say that as the water column rises, friction resistance begins to generate increasing pressure which would tend to cause maximum deflection at the flat center of the "pipe". I envision that since the left and right sides are rigidly sealed at the edges, they would tend to go concave as the center begins to bow out. Anything resembling reality here?)

Yours truly,
Sush54

 

[quark]

I will try to answer some of your questions at the moment.

1. The pressure exerted by a liquid column depends upon the height of the liquid column and independant of the area of cross section. So the answer for your first question is No. It remains constant.

2. The pressure exerted by the liquid column remains same in all the configurations. So the answer to the first part of your second question will also be a No. Infact, as you are reducing the surface area the force gets reduced.
Yes, the force will be maximum at the bottom.

3. Weight of water column is w x a x h, where w is specific weight of fluid, a is area of cross section and h is height of liquid column. So weight remains constant(and so volume) if you keep cross sectional area constant. Yes, weight of water does influence the force at the bottom (because it is the only factor which exerts force.

4. My gut feeling is that when you narrow the pipe at one plane yet keeping the cross section constant, pressure drop will increase due to increased turbulence. (You may have viscous flow where the passage is narrower and turbulent flow where it is wider. This may result in vortex formation)
But I have to confirm this from the experts of this forum or from books.

Regards,





Eng-Tips.com : Solving your problems before you get them.

 

[sush54]

Thanks quark;

I think I wasn't exactly clear in describing the situation. The cross sectional configuration is constant throughout. 1/16" X 25" We have a very tight size restriction in one plane so we have to build our own flat "pipe" which will probably wind up having that 1/16" slot, 2' wide. An initial test showed some strong forces being exerted against the bottom center and I was hoping for some help in determining what, why and how much to expect should it of necessity grow wider and longer with possibly a still smaller slot.

Yours truly,
sush54

 

[arto]

You need to use the "hydraulic diameter" Dh =4A/P
[A = cross-sectional flow area; P = wetted perimeter]to do your flow calculations.

 

[sush54]

ah, something to work with...

So I multiply .0625 X 25" and I get 1.5625 square inches cross sectional flow area. Times 4=6.25
divided by the wetted perimeter of 50.125" and I get a hydraulic diameter of .0312

How do I use that figure relative to to my problem? (Layman)

sush54

 

[arto]

No, 4A/P = 4*1.5625/50.125 = 0.125"


Get Crane #410

http://www.cranevalve.com/tech.htm

or a fluids book

 

[MikeHydroPhys]

University of Wales M_D_Stagg
BSc_Wales 1969 U. C. W. Aberystwyth
Interflow MSc

57 BRAMPTON WAY PORTISHEAD BS20 6YW England Eu
3D Fluid Shear Molecular Physical Mechanics Earth Plane Critical InterfaceDesign

ART ~ DESIGN COMPLEX
INTERFACE PLANE ENERGY



MikeHydroPhys(Structure) Thursday, 25 March 2004
For
SUSH54 (Materials)

Thin flat pipe section

Is bound to be subject to

1. Lateral stress in the walls due to the mass, but one presumes this may be resisted by position in a set substance and if this is free standing then the quantities must be worked out to take the load prescribed by the responses giving the dead weight by volume rising up the pipe. Can you divide flow by internal section not necessarily up the entire length ?
2. Abrasion along the central zone, I know of no way to provide a spread of pumped energy unless the entire mass is made turbulent by baffles and filtered through a textile, breaking up the laminar pattern and sending nearer to equal energy proportions along the entire width section. However Energy is the key to this, you are trying to pump the fluid through a wide section from what can only be described as a discrete source, even with a magnetic flow induction across the entire width this is going to be difficult to resolve as “even flow” without incurring too many load problems (the separation of the main velocity flow zone into a flow pattern by the above described would add a need for pressure that may be untenable in this work of yours).
3. Deflection of the system and increased flow at the central zone, possible if the pressure applied becomes high and your energy input rises to overcome the lift and friction; the more viscous the fluid the greater the distortion pressure potential, so
4. Velocity increase means more energy and the greater difference between the central zone and the extremities.
5. In a thin section low speed flow the problem will not matter as much as in a high speed system as the status is indicated by the descriptions given you previously where in a low flow rate of low pressure, low energy and slow the weight of water bearing down on the base will be your main concern and of course overcoming this by a pump.
6. You can use with a thin section capillary force and try to ease the flow upward if this is very slow by the cohesion between the molecules and the adhesion to the sides, this becomes untenable if the viscosity is high, the section is smaller and the pumping rate low and then the capillary forces tend to dominate and you might as well throw away the pump and rely on the capillary force to maintain a static state that seeps back downwards; in fact the high viscosity and thin section may cause a “leak” back down flooding the system.
7. The best persons to ask about the worst problem are likely to be radiator engineers as the high central flow and low edge zone may result in congestion from deposits and precipitates away from the clearing and eroding section. Alternate sources for information on low flows in thin section are concerned with fissures in rock, but this is less well researched than DeWiest on porous rock flow, so look through engineering geology, geohydrology, hydrogeology and soils texts and papers, but groundwater science may be a good source as you are looking for fissure flow not particulate mass, porous rock flow.
8. Suggestion: flow has to be altered from a transfer of energy at pump of a central mass with Bagnold effect of side flow shear and central core transit, to a flow wherein shear in apparent throughout the mass, ideally across the section. This can be effected by baffling such that the flow from the pump source is sent to the extremities at an early stage in transit, after this the mass will settle to a central form with less flow at the high reach sides, but this will matter less as the upper reaches have low weight mass applied, as you preceding respondents noted. Better than this is to use an induction system that calls upon the fluid properties and temperature ranges and form a magnetic flow impeller that applies across the width of the section, so you are using if this is at all feasible the physical properties of the materials and dragging the flow; works well for a flat zone, miserable for a vertical one at a long reach.
9. Can the flow be stage lifted and do you need to rely on one pump ?
10. I would consider corrosion and mass weight first for your section dimensions of material thickness, then the load imposed on lift which you will have done and then see if you can separate flow so the centre takes less stress and the sides have more flow, which I presume by now may have been your practice.
11. It might be possible to vary the section so the input is not through an even section entrance but later moves to a flat section, corrugated so the flow goes from the impeller to the zone via a unit that makes it into think and thin sections, the frequency of thick being concentrated at the extremities and the frequency of thin being concentrated in the centre, near the pump source; this gets around the baffle deflection additional energy for motion requirements.
12. I could go on a suggest variable section that adjusts with the flow and flexible elastic systems, because my daughter has got into Biology and the Japanese use rubber dam systems and I was at one time looking at geomembrane, but I will leave that, your life is complicated enough as it is, although it makes a good research project to work through.

How are you going to pin the sections, weld, does this include a flow effect from the weld ridge, does rivet and lap improve the system ? Curious. What materials, have you tried composites – FibreForce – glass fibre, carbon fibre, Nottingham Trent was looking at direct concrete steel interface in 1990.
Post Note
I was looking at an oil filled radiator this morning which is formed of thin section, plated by pressed steel into a rectangle with centre from each panel linked and thus the maximum thickness for flow is around each of the four sides, this makes both a strong system resistant to pressure load deflection and sends the flow away from the entrance zone across allthe width of the panel made of a number of rectangles. Possible ?

Best wishes
MikeHydroPhys Fluid Mechanics Flow Design Earth Interface Critical Energy