橡胶气球大小与内外压强差关系

Study on the relationship between balloon size and pressure

球面液体膜的拉普拉斯定律指出,球面膜内外的压力差与球的半径成反比.但是对于橡胶制成的气球,实验测得的内外压强差Δp和球的直径d之间的变化关系比较复杂:只在中间半径区域近似地满足球面膜的拉普拉斯定律,但吹气球的起始阶段和后面气球被吹得很大时并不满足该关系.本文对这一现象进行了模拟分析,并结合橡胶高分子材料弹性性质数据,模拟结果很好地符合实验结果,定量地得到了Δp随d增加先迅速增加后缓慢降低又逐渐增加的实验现象.

For a spherical liquid ball,the Laplace equation indicates that the internal and external pressure differenceΔp is inversely proportional to the radius of the liquid ball.But for a rubber balloon,the measured relationship betweenΔp and the diameter d had a very complex behavior,and the Laplace equation was only satisfied approximately in the intermediate radius region.A numerical analysis was done based on the real data for rubber macromolecule material,and the same behavior betweenΔp and the diameter d was obtained.