Pressure in fluid (liquid)

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In summary, pressure in a fluid (liquid) is defined as the force exerted by the fluid per unit area on a surface. It is influenced by factors such as the depth of the fluid, the density of the liquid, and the gravitational force acting on it. Pressure increases with depth due to the weight of the fluid above, leading to a greater force on lower surfaces. The formula for calculating pressure in a liquid is given by P = ρgh, where P is pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the depth of the fluid. Understanding fluid pressure is crucial in various applications, including hydraulics, engineering, and natural phenomena.
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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?
 
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Yes. Is there some reason that isn’t clear to you?
 
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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
 
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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.
 
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adjurovich said:
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.
 
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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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FAQ: Pressure in fluid (liquid)

What is fluid pressure?

Fluid pressure is the force exerted by a fluid per unit area on a surface. It is caused by the weight of the fluid above the surface and acts in all directions. In liquids, pressure increases with depth due to the weight of the liquid above, and it can be measured in units such as pascals (Pa), atmospheres (atm), or pounds per square inch (psi).

How is fluid pressure calculated?

Fluid pressure can be calculated using the formula: P = ρgh, where P is the pressure, ρ (rho) is the density of the fluid, g is the acceleration due to gravity, and h is the height (or depth) of the fluid column above the point where the pressure is being measured. This formula indicates that pressure increases with depth in a fluid.

What factors affect fluid pressure?

Fluid pressure is primarily affected by the density of the fluid, the gravitational acceleration, and the depth of the fluid. Additionally, temperature can affect the density of the fluid, which in turn can influence the pressure. In non-static conditions, factors such as fluid motion and viscosity can also play a role in the pressure experienced within the fluid.

How does fluid pressure change with depth?

Fluid pressure increases linearly with depth in a liquid. As you go deeper into a fluid, the weight of the fluid above increases, resulting in higher pressure. This relationship is described by the hydrostatic pressure equation, and it shows that for every meter of depth in water, the pressure increases by approximately 9.81 kPa (kilopascals).

What is the difference between absolute pressure and gauge pressure?

Absolute pressure is the total pressure measured relative to a perfect vacuum, while gauge pressure is the pressure measured relative to atmospheric pressure. Gauge pressure can be positive or negative, depending on whether the pressure is above or below atmospheric pressure. For example, a gauge pressure of 0 indicates that the pressure is equal to atmospheric pressure, while a negative gauge pressure indicates a vacuum condition.

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