Orifice - Soccer Ball Question

We don't do homework here.

Besides, you didn't even copy the problem correctly.

Just how big IS a "0.3 diameter soccer ball"?

And air is compressible.

Yes, external forces would force air out....

sorry, units for diameter is meters, i.e. 0.3m.

Tough question.

If the air is incompressible, then the 20kPa pressure would have to come from tension in the skin of the soccer ball. However, you are not given the elastic modulus of the skin material. Therefore, one could assume that the skin is assumed to be inextensible -- an assumption that is less unrealistic than the assumption that air is incompressible.

If the skin is rigid, and the air is not compressible, then any leak will reduce the pressure very rapidly: letting out a few molecules should be enough to equalize pressure with ambient. (When a tank is tested by using a non-compressible fluid, the rupture is relatively uneventful for this reason.)

Perhaps you can ask the teacher for the characteristics of the skin material. In practice, the skin of a soccer ball is relatively stiff (not very stretchy) and the air inside is quite compressible, giving the ball its bouncy quality. Perhaps your teacher is asking you to model the ball as you would a balloon, where the internal pressure is created mainly skin stretch, and less so by the compressibility of the gas.

But in any case, something must give the ball its springy quality -- either a springy medium enclosed (like a real soccer ball) or a springy skin and a non-compressible medium (like a water balloon). Your teacher can clarify. Also ask for clarification of "noticeably softer." Does this mean that a gauge needle would be noticed to be in a different position, or that the ball yields differently to a squeeze, or responds differently to a kick of a skilled and perceptive player?

Thanks Mr Fry