Pressure at a point in a liquid

The plunger of a syringe exerts a pressure on the fluid that is transmitted to all points in the fluid.

In Physics we study a very interesting branch: Hydrostatics, responsible for studying the properties that are linked to fluids (remembering that a fluid can be a gas or a liquid), which, in turn, are subject to the action of the force of gravity. It is interesting to note that a fluid is a substance that can flow, that is, it does not have its own shape and always assumes the shape of any container in which it is inserted.

Some fluids play a key role in our daily lives. Some of them, vital, circulate in our body. In automobiles, there are fluids in the tires, in the fuel tank, in the braking and steering systems, in the air conditioning system, etc.

According to the figure below, we can see that when a liquid contained in an open container is at rest, a point located inside it is pressed by the liquid column above it, which is also pressed by the atmosphere. Taking this into account, let us calculate, or rather determine, the total pressure p at point P, situated at a depth h , in an equilibrium liquid.

As we mentioned earlier, point P is being pressured by both the liquid column above it and the atmosphere. In this way, we can determine the total pressure exerted at point P by adding the atmospheric pressure, that is, the pressure that the air exerts on the liquid, with the pressure of the liquid column of height h . In this way, we have:

P=P atm   + P column
P=P atm   + μ . g. H

It is practical to consider the origin of the frame of reference at the surface of the liquid and orient it downwards, measuring the water column as depth. The graph of pressure P versus depth h is straight, as shown in the figure below. Note that when the height is h = 0, the pressure exerted on the surface of the liquid is the atmospheric pressure itself, so we have: P = P atm .

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