Boiler Calculations

I have a 2 5/8" seamless copper boiler tube, 0.041" thick.

This appears to be 19 gauge, which is on the thin side for boiler designs using tubing of about 3" diameter.

Using Tubal Cain's formula thickness=pressure x diameter/2xUTS for a seamless tube I get maximum pressures of: 979 PSI for the cold test and 118 psi for working pressure with hot steam. (using UTS for annealed coper of 31360 psi/square inch cold and 3,800 at the temperature of steam at 120psi).

Safety factors are built in to the above, so this suggests that the tube I have would be perfectly satisfactory for a boiler of working pressure 60 or even 90 psi to be cold tested to 120psi for a 'Tich' sized engine..

Can someone check these calculations for me?

I have built a satisfactory centre tube boiler with cross-tubes boiler of slightly larger size so i'm confident I can braze up such a boiler if it's worth doing so.

many thanks,

Neil

Neil,

It is oft said that a little knowledge is a dangerous thing.

Whilst Tubal Cain's formula is perfectly correct for an elastic material e.g. steel, copper only behaves this way to about 6000 psi,.Above this the strains become large and permanent, i.e. the copper becomes a plastic material. If you pressed your tube to 900 psi it would be deformed like a barrel if it survived the stresses at the end plates. For model boilers it would be safe to say that a maximum stress of around 5000psi at a test of twice working will give a reasonable factor of safety of about 1.2 against permanent deformation.

My own calculation allowing also for longitudinal stress in the shell gives an allowable working pressure of 80psi for this tube although I would consider it a bit thin for practical purposes at 19 gauge, as it will be very susceptible to mechanical damage (you would probably deform it with finger pressure after soldering) and I would rather see a minimum thickness of 16 gauge or 10 gauge for a tractor boiler.

Regards

Eddie

Niel

I concur with what Eddie has said.

The formula you give is from the standard formula for hoop stress in thin cylinders where stress = (pressure x shell radius) / shell thickness.

I was very surprised see UTS in your formula.

Using UTS does not provide any safety margin and to my way of thinking is more akin to burst pressures calculations.

As Eddie indicates, the safety margin is in what you use as your design stress, so thickness = working pressure x dia / 2 x design stress.

For example, pressure vessel codes typically use a design stress equal to material yield stress/1.5 for steel at ambient temperatures.

To check under hydrostatic test, you could use your test pressure and design stress of say 90% yield stress for steel. Eddie indicates that for copper a stress of 5000 psi would be suitable to use at your test pressure.

Unless there is something in Tubal Cain's book I am missing. hope my ramblings help.

Nigel

Edited By tractionengine42 on 27/10/2012 10:38:51

Hi Neil

The formula given by K N Harris in his book "Model Boilers and Boilermaking" (recommended by Edgar Westbury) p.31 is as follows:

T = P x D / 2t or P = 2T x t / D

Where;

T = thickness of shell in inches,

P = working pressure

D = internal diameter of shell

t = maximum safe stress of shell material in lbs / in² (he gives 3125 lb/in² allowing for a safety factor of 8)

Therefore:

P = 2 x 0.041 x 3.125 / 2.543 = 265.25 / 2.543 = 100.77psi

I can't guarantee the accuracy of this but Edgar Westbury says:

"Written by a practical engineer with a lifetimes experience of full size and model steam engines it gives a reliable guidance on the design and construction of small boilers."

Regards

Terry

Thanks all,

> It is oft said that a little knowledge is a dangerous thing.

Which is why I asked!

Eddie, Nigel - II feared I would terrify a few folks. The 979 psi is what comes out as the failure pressure cold, not what I would propose to test it to! that's why I sugegsted working pressuire 60, cold test 60. On treflection I think cold testing to 180si (for 90psi working) cuts the safety margin too much (only 5 times).

You have spotted an error for me though, TC says use 30% of the UTS to limit deformation to 0.1% (for copper), but suggests using not more than 15% of the UTS to allow for the high working temperature. This would give a maximum test pressure of = 146PSI.

I had already realised it isn't thick enough to have the mechanical strength for a traction engine boiler. It would have to be something like a small loco, steam crane or a stationary boiler.

Terry - The K.N. Harris figure of a working pressure of 100psi seems not far off the 118 the Tubal Cain forula gives, as different formulae appear to use safety margins differing by about 40%.

As TEST pressure needs to be twice WORKING pressure the 120 test/60 working psi seems to err on the side of caution whichever set of figures is used, and the application need to be one where.the boiler isn't a structural element of the design.

Neil

Hi Neil

Harris says that the swp (safe working pessure) should allow for a safety factor of between 6 and 10 and settles on 8 as a "good all round factor" and I would tend to use this higher figure especially as Michael said any defects affects the overall performance. After all safety is more important than cost.

Best regards

Terry

Stub mandrel,

You mentioned that you were using seamless copper tube, i have got some 50mm copper pipe from a redundant HVAC installation, would this be appropriate material for a boiler?

MT

Hello Fred,

Phew, this is an old thread!

I haven't made use of the tube yet (Stub mandrel is my old account), my plan is to use it for a a small scotch boiler at just 30psi, rough design below.

In five years I haven't increased my expertise in boiler design, others can offer you better advice than me.

Neil