It may be helpful to indicate this (qualitatively) by using a marker pen to show the approximate direction and (relative) magnitude of the two stresses. The actual magnitudes can be estimated by evaluating the pressure, wall thickness and radius. The pressure can be obtained using a (water) manometer. The radius is obviously easy to obtain (with a tape measure), while there are several ways to estimate the wall thickness - for example, by weighing the balloon (before inflation) and using the approximate density of the rubber. A typical value for the pressure is about 0.01 MPa (~0.1 atm.). The wall thickness is commonly about 10 µm, while the radius of a suitably large balloon is around 100 mm. Using the equations in the figure above, the hoop and axial stresses are thus about 20 MPa and 10 MPa.
Pressure Measurement
The inner pressure of the large cylindrical balloon can be measured by using a simple manometer arrangement.
(picture will be here)
Fig.1 Apparatus for measurement of pressure
- Inflate the balloon using a bicycle pump. This must be done while the bung is placed in the end of the U-tube, in order to ensure that the manometer fluid (blue coloured water) is not ejected by the pressure pulses associated with operation of the pump. Once the balloon is inflated, the tap should be closed, so that air cannot escape from the balloon, and the bung should be gently removed in order to allow trapped air out and the internal pressure to equalise.
- Estimate the balloon radius using callipers to measure the diameter d = 2r .
- Measure the height difference in the manometer. Then release a small amount of air from the balloon by opening the tap for a short period, and make further measurements of size and height difference. Repeat this operation several times, until the balloon has reached its uninflated size.
- the pressure can be related to the height difference, h, using:
P = h ρ g (1)
where ρ is the density of the liquid and g is the acceleration due to gravity.