# Why is horizontal pressure the same as vertical pressure in a static fluid?

In a static fluid, I know that because it is not moving, the pressure from the top equals the pressure from the bottom.

Also, using the same logic, the pressure from the sides must be the same.

Why are the pressures in all directions equal? It seems like pressure from the sides would be able to be different than pressure from the top.

• Let's look at an infinitesimal sized box of fluid. If the pressure on the opposite sides didn't balance, the fluid would accelerate. The fluid is static, so the pressure on the pairs of sides in the tiny box mustf be equal. – zeta-band Jun 17 at 22:02
• In addition to the comment from @zeta-band, note that for an object that actually has a "substantial" size, the pressure on the bottom of an object in a static fluid is greater than the pressure on top of that object. In other words, be careful regarding how you define pressure if you are talking about something that is not a mathematical point. – David White Jun 17 at 22:06
• @zeta-band, I know that the opposite sides balance. What I'm wondering is why the pressure from the top is the same as the pressure from the right. – 63677 Jun 17 at 22:10
• @zeta-band, you didn't really answer the OP question. Why is there no directional dependence in the stress and strain tensors. – ggcg Jun 17 at 22:21