Physics - Fluid Question with Solution | TestHub

Let ${\mathrm{P}}_0=$ atmospheric pressure, ${\mathrm{P}}_1$ and ${\mathrm{P}}_2=$ pressures inside the two bubbles.

$${\mathrm{P}}_1-{\mathrm{P}}_0=\frac{4\mathrm{S}}{{\mathrm{r}}_1},{\mathrm{P}}_2-{\mathrm{P}}_0=\frac{4\mathrm{S}}{{\mathrm{r}}_2}\text{ or }{\mathrm{P}}_2-{\mathrm{P}}_1=\frac{4\mathrm{S}}{{\mathrm{r}}_2}-\frac{4\mathrm{S}}{{\mathrm{r}}_1}$$

= pressure difference across the common surface. Let $\mathrm{r}=$ radius of curvature of the common surface.

$$\therefore {\mathrm{P}}_2-{\mathrm{P}}_1=\frac{4\mathrm{S}}{\mathrm{r}}\therefore \frac{4\mathrm{S}}{\mathrm{r}}=\frac{4\mathrm{S}}{{\mathrm{r}}_2}-\frac{4\mathrm{S}}{{\mathrm{r}}_1}$$