Suggested Response - Q5

*/** A carbon dioxide collection balloon may be considered a cylinder of 8 m in length and 3 m in diameter. If the internal pressure is 5 kPa (g), what will be the total force, and the net force, on the inside surfaces of the balloon? Atmospheric pressure is 95 kPa.

Response:

This is an application of the definition of pressure, namely a force applied over an area:

P r e s s u r e space P space equals space fraction numerator F o r c e space F over denominator A r e a space A end fraction

Re-arranging for force F gives:

F o r c e space F space equals space P r e s s u r e space P space cross times space A r e a space A 

The area, or more precisely, the surface area of a cylinder is given as the sum of the area of each end (a circle) and the wall surface of the cylinder:

T o t a l space a r e a space equals space 2 space cross times space fraction numerator pi d squared over denominator 4 end fraction space plus space pi d l

T o t a l space a r e a space equals space 2 space cross times space fraction numerator pi space cross times space 3 squared over denominator 4 end fraction space plus space left parenthesis pi space cross times space 3 space cross times space 8 right parenthesis

T o t a l space a r e a space equals space 14.1 space plus space 75.4 space equals space 89.5 space m squared

We need to ask ourselves which value of internal CO2 pressure we will use? The value given is a gauge pressure of 5 kPa. If we represent this pressure as an absolute pressure, this will give the total force due to the CO2 and the effect of atmospheric pressure (which is of course acting on both sides of the balloon, inside and outside).

P subscript A b s o l u t e space end subscript equals space P subscript G a u g e end subscript space plus space space P subscript A t m o s p h e r i c space end subscript equals space 5 space plus space 95 space equals space 100 space k P a

Substituting these values of area and absolute pressure gives us:

T o t a l space F o r c e space F space equals space 100 space cross times space 10 cubed space cross times space 89.5 space equals space 8 comma 950 comma 000 space N

T o t a l space F o r c e space F space equals space 8.95 space M N

The net force on the surface of the balloon, allowing for fact that atmospheric pressure is present on both the inside and outside, is a more meaningful figure for balloon design purposes, and may be calculated as:

N e t space F o r c e space F space equals space 5 space x space 10 cubed space x space 89.5 space equals space 447 comma 550 space N space equals space 0.45 space M N

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