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fun math (about circumference of a tubular)

Since previously I have been dealing with lot of calculation of a tubular member, there is an interesting yet fun discovery (which I believe some people may have found it too) where you can find more than one way to calculate the cross-section area of the tubular member.

You see when you have a tubular member or a pipe, the area of the cross-sectional circle can be measured by using the equation

A = π r^2…..(1)

This is a common equation for calculating the area considering the tubular member is rigid.

The circumference of the circle (C) can be calculated as

C = 2 π r…..(2)

In a real application, we deal with a lot of tubular member which has an inner diameter (id) and outer diameter (od).

tubular
When we calculate the cross-section area of this tubular, the equation (1) becomes

A = π r.outer^2 – π r.inner^2

where r is the radius of the tubular member

or

A = (π/4) (od^2 – id^2)

For example,

with od = 6 mm,

id = 5 mm

The cross-section area will be

A = (π/4) (6^2 – 5^2) = 8.639 mm^2

In other analysis, we can calculate the cross-section area by breaking off the tubular such that

A = (thickness of tubular) * (the circumference of outer tubular member)

tubular2

t = thickness of tubular

Substituting parameter provided from the example, we can get

A = (0.5 ((od) – (id))) * (2 π r.outer)

A = (0.5 (6 – 5)) * (2 π (6/2)) = 9.425 mm^2

In logical thinking, both ways of calculating the cross-section area should have been resulting the same.

There is a deviation around,

δ = (9.425 – 8.639) / 8.639 = 9.09 %

Quite interesting, isn’t it ?

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