# Direction of excess pressure inside air bubble

What is the "direction" of excess pressure (or capillary pressure) inside an air bubble submerged in a fluid? Does it tend to act outwards towards fluid (from inside the bubble) or vice versa? My intuitions tell me it acts outwards, but from what I've seen in a solution to a question, it assumes the pressure to be acting inwards (from fluid to bubble). Or am I misunderstanding the question? For reference, the question

## 1 Answer

Pressure is a scalar and doesn't have a direction. However the force generated by the pressure does have a direction because it is the product of the pressure and the vector area:

$$d\mathbf F = P\,d\mathbf A$$

So the question is then about the direction of the force not the pressure, and that's simpler to understand. The pressure of the air inside the bubble exerts a force on the bubble surface that acts outwards, and the pressure of the water outside the bubble exerts a force on the bubble surface that acts inwards.

• Yes I know that. I was talking about the direction of the force, but I thought it was implied. I know that the force due to hydrostatic pressure acts on the bubble due to the fluid. My question was whether the force due to excess pressure is due to the air inside the bubble or vice versa? Please go the the question I linked in my question, and tell me whether the equation he wrote is correct or not. Thanks in advance. – Arka Seth Jan 8 '19 at 9:40
• @ArkaSeth you have three forces acting: the force due pressure inside the bubble acts outwards, the force due to the surface tension in the bubble wall acts inwards and the force due pressure inside the bubble acts inwards. The direction of the net force depends on the sum of the three forces. At equilibrium the net force is zero. – John Rennie Jan 8 '19 at 9:45
• thank you. I got what I wanted to know now. The equation that I linked is correct. – Arka Seth Jan 8 '19 at 9:50