# Pressure in fluid (liquid)

• B
Let’s imagine a glass of water. Now, we press on the free surface of water with a spoon (just for example), will the pressure in the entire glass increase equally?

Yes. Is there some reason that isn’t clear to you?

Dale said:
Yes. Is there some reason that isn’t clear to you?
Thanks for help. I’ve been struggling to understand the term pressure because I would always think of directions… due to this definition: “it acts in all directions”. However, knowing that pressure is a scalar quantity, just like mass, I thought I should give it a different approach. Interestingly, when I did thermodynamics, the term pressure was perfectly intuitive to me (and still is when talking about gases), but with liquids it felt like a whole different story and I got lost. So I choose to apply thermodynamical approach to liquids too and that’s why I asked this question. I feel like I am slowly, but surely, connecting all information and knowledge I’ve gained so far about fluids

Field physics
When someone is thinking about pressure “acting in a direction” what they are actually thinking about is a quantity called the stress.

Stress is a tensor so it maps a vector to a vector. In this case an infinitesimal area is represented by a vector perpendicular to the area, and the stress gives the force on that area. So that is exactly what people mean by pressure acting in a direction.

Pressure is the isotropic part of the stress. So it acts in all directions because if it didn’t then it wouldn’t be pressure, it would be stress. Not all stress is isotropic, not even in a gas or a liquid. But if the stress isn’t isotropic then we don’t call it pressure. So there isn’t anything particularly magical about pressure being isotropic, that is just its definition.

Let’s imagine a glass of water. Now, we press on the free surface of water with a spoon (just for example), will the pressure in the entire glass increase equally?
If you person on the free surface with a spoon, the system will no longer be in equilibrium, and the spoon will begin descending into the fluid. The fluid at the surface of the spoon will be moving at the spoon velocity, while the fluid further away will be moving more slowly, and the fluid at the wall of the glass will not be moving. So the fluid will be deforming and, in terms of what Dale has pointed out, there will be viscous stresses developed within the deforming fluid, such that the state of stress is no longer isotropic.

Chestermiller said:
If you [press] on the free surface with a spoon [...]
The mental picture I have is of a spoon pressing down into the water without submerging. Like a tiny boat that is forced a bit into the water.

Naturally, the surface of the fluid in the rest of the glass will rise slightly due to the displaced water. Naturally, this in turn means that pressure throughout the glass increases -- once the ripples die down and a new equilibrium is reached, anyway.

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