Got A Mathematics Question

[Ian b]

I am trying to work out how much liquid I will have in a plastic tube 25 mtrs long and 3mm inside diameter.

[jim360]

Assuming it's all filled then you can get 25000*3*3*pi/4 cubic millimetres inside. That's of order 600 litres but I haven't checked the exact answer. Easy to enter into a calculator though.

[jim360]

Sorry -- of order 125 litres (forgot to divide by four).

[Reg1900]

As a general rule area of cross section X length.

[Svejk]

That seems a lot, jim. Sure you haven't put a decimal point in the wrong place?

[tonyav]

Heres a formula, gawd knows how it works though.
http://www.web-formulas.com/Math_Formulas/Geometry_Volume_of_Cylinder.aspx

[jim360]

You know what? I'm having a bad "let's try to get the answer without thinking" time today... 125 is not 600/4 for example. That just looks so bad. Oh well. Put the numbers into a calculator and it will be right at least.

[jim360]

And svejk -- you're right too. Can't even remember how many mm^3 ina llitre today. Ho hum.

[Prudie]

The volume will be pi x 1.5 x 1.5 x 25000 in cubic mm
Ian are you sure your dimensions are correct - a 25 metre tube with a diameter of only 3mm is a very long tiny tube, almost like a capillary, very hard to get any liquid in at all.

[Jonathan-Joe]

Internal radius = 1.5 mm
Length = 25000 mm
Volume = cross section area x length
= (pi)x(1.5)^2 x 25000 = 1767143.5868 cu mm
= 176 millilitres (0.176 litres)

[Jonathan-Joe]

Sorry, rounded down. Take 177 millilitres, 0.177 litres.

[Prudie]

There are a million (1000 000) cubic mm in a litre so that should be 1.77 litres

[Jonathan-Joe]

A typo rather than error; a "3" somehow strayed into my result,
It should read
Volume = (pi)x(1.5)^2 x 25000 = 176714.5868 cu mm
= 176 millilitres (0.176 litres)

[KARL]

There is an easy way to look at this, as always in the metric system, one which leaves no room for getting confused (unless one is determined to get into a twist). A litre is a cubic decimetre (a decimetre is correctly known as "dm", probably christened dcmtr by some in the UK to go with mtrs instead of m and kgms instead of kg) - it is a tenth of a metre.

In this example the cross section is (0.015)² x 3.14159=0.000706858dm² (you begin to see how tiny the volume of even this long tube really is). Multiply this by 250dm (the length of the tube) to get the volume. The result is 0.1767dm³ (cudcmtrs in the UK ?) or litres.

[Prudie]

whether you work it out in mm, m or dm (which nobody uses) the result is - you won't get much liquid in :-)

[ToraToraTora]

I just type 75000*3.142/1000 into google = 235.65 (litres)

[ToraToraTora]

nope that's wrong, its (3.142 * 1.5 * 1.5 * 75000)/1000
530ltrs seems a lot!

[Svejk]

3mm is the thickness of a pound coin.(ttt)

[ToraToraTora]

yes I can't see where I'm wrong though, volume of a cylinder is pi R squared x h! so 1.5 * 1.5 * 3.142 * 25. Ah that's more like it 176 litres. I was doing 75 above doh!

[Jonathan-Joe]

We are often told, including on AB, how simple metric units are? So how come people are so confused by the units used in this simple calculation?