Can some one please tell me how I work out how much water 15 meters of 1/2 inch copper tube will hold. Thanks.
claymore Mon 25/08/08 07:34
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You will need to know (measure) the internal diameter of the pipe.
Assume it to be 10mm (D=10mm) – the internal cross sectional area is given by:-
2 x π x r x r = 2 x 3.142 x 0.005 x 0.005 = 0.000157 square metres
Multiply this by the length of the tube (15) to give a volume of 0.002355 cubic metres, or 2.355 litres.
It is early in the morning, so perhaps someone could check my maths.
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A simpler formula is pi r2 h
3.142 x 6(radius of inside of pipe assuming wall thickness of 1.5mm) squared x height(in your case 15000mm) = 1696680cubic mm, or 1.69 litres.
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Yes Hymie, there is a flaw in your maths. You have multiplied by a 2 that shouldn't be there. I think you have confused Pi r squared (area) with 2 Pi r (circimference).
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My excuse that it was early in the morning, was just an excuse for the fact that I’m useless at maths.
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Weigh the tube empty. Then fill up tube with water and weigh again. Subtract the first calculation from the second. This will give the nett weight of water. Or a simpler method is to take a shorter length of pipe and scale up.
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Mmm... I make it 1.9 litres, assuming that the inside diameter of a 1/2" pipe is 9mm. ... but then.... I support Labour so....
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. . . I get a volume of 0.95 litre for an id of 9mm?
Most copper tubing designated as "1/2 inch" will have an inside diameter equal to or exceeding 1/2 inch which varies with wall thickness and is not necessarily consistent along its length. Therefore I have assumed a 1/2 inch inside diameter for the following discussion:
Volume pertains to a three dimensional space as within a box, sphere or other containment. For a circle, (the cross section of tubing) the two dimensional area subsumed can be found by multiplying the radius (half the inside diameter) by the radius and multiplying the product (r²) by pi (π = ~ 3.1416). Multiplying this by the third dimension, (length), specifies the volume.
First convert dimensions to common (equivalent) units
1/2 inch diameter = 1.27 cm (centimeters)
15 metres length = 1500 cm
Plug variables into the formula for volume of a cylinder:
π x radius² x length = volume
(remember that radius = diameter / 2)
π x 0.635cm² x 1500cm = 1900cm³ = 1.9 litres
Your “1/2 inch” copper tubing might hold more or less water than that. Given the inconsistency of copper tubing interiors I found rov’s methods worthy of serious consideration . . . or you could fill the tube and drain the water into a measuring beaker.
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Would someone please help me to point out where I've gone wrong. Using above formula I get 3.1416 x 1.27 = 3.99cm (circumference of circle) x 0.635 (radius) = 2.53cm (square cm circle area) x 1500 = 3800 cubic cm = 3.8 litres. Grr... I seem to end up with double of mibsies result.
I couldn't give a hoot about a cylinder's volume before this Q, but now it is driving me crazy.
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Got it thanks. I forgot to square the radius.
Sorry to have hi-jacked your thread claymore.
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The volume (three dimensional space) of a rectangle is equal to the area of one face (any face will do) times its extention in the third dimension.
volume = (height x width) x depth
For a cylinder the face corresponds to the two dimensional area of the cross-section (a circle). Multiply this by the extension in the third dimension, height (or length) gives the volume.
The area subsumed by a circle equals pi x radius x radius or π r²
Remember this: The area of a circle equals π r squared
No! π r'nt squared. π r round. Cornbread r squared!
don’t mind me
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Just out of interest claymore, why do you want to know?????
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(The bore diameter of what is referred to 1/2" pipe is typically ca 15 mm but it does vary depending on the standard, copper, stainless steel, medium or heavy weight mild steel. Hence if an accurate figure is required best to measure)
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Question Author
New judge , I have built a solar hot water heater using the said 15 mtrs of copper tubing , just wondering if it would hold enough water for a good cuppa.
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Thanks claymore.
I'm just a curious (some say nosey) old ******!
Incidentally, I make it 1.7 litres as well (pi times the radiius (6mm) squared times 15 metres).
So enough for about three decent sized mugs.
The only problem I see is that I cannot imagine the heater will raise the temperature of the water to a sufficient level to brew the tea. Ideally it should be boiling. If it does perchance approach boiling you will have trouble with expansion etc. and may have to install a safety device or an expansion vessel.
You might have to settle for instant coffee or cocoa.
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