In my experiments I am filling a 10inch rubber balloon with 600ml of water and then applying compressive force downwards and then recording pressure and flow. I would like to know how much external force I have applied.
I know the radius of the ballon (assume to be a sphere before), and the 2 radii of the ellipsoid after the deformation. I also know the pressure before and after the deformation with the volume in the balloon constant. I think there is probably a simple equation for this.
All I have thought of so far is using the Laplace equation to calculate the wall tension but this doesn’t seem to be quite right as I want the force towards the centre not around the circumference. I have also thought of maybe applying the hertz contact theory equation assuming a large radius bead in contact with the ballon as a last resort. However I realise this is a wrong assumption, not curved surface, and don’t know what the Young’s modulus of the balloon filled with water Or could this all be simplified with the use of a stress strain curve for an elastic material? If so I am not sure what value I should use for the slope. Or pehaps just F=P*A using the A as the internal surface area of the sphere or ellipsoid?
If there is any more information needed please feel free to ask, and I have provided a visual aid below. Your comments and feedback will be greatly appreciated.
