Hydrostatics

Hydrostatics is an area of ​​Physics that explains the behavior of fluids under conditions of static equilibrium. This area involves the application of concepts such as pressure and density through mathematical laws, such as Pascal ‘s and Archimedes’ theorems . The knowledge derived from hydrostatics also allows us to better understand the operation of hydraulic installations, as well as pipes, water tanks and even dams.

Important concepts of hydrostatics

The most important concepts of hydrostatics are:

• density;
• pressure;
• buoyancy.

Together they are enough to explain how fluids at rest behave. To do so, we will consider only ideal fluids – non-compressible and solely formed by molecules that do not interact with each other.

• hydrostatic pressure

Hydrostatic pressure is that which a fluid exerts against the walls of its container. This pressure is directly proportional to the depth of this fluid – the deeper it is, the greater the pressure.

According to Pascal’s Theorem , pressure is evenly distributed throughout a fluid and all points that lie at the same depth are subject to the same pressure. One way to visualize this theorem in practice is by observing the shape acquired by a bladder or a ball. When full, they adopt a spherical shape, since inside the fluid (air, in this case), the pressure is equally distributed at all points.

The most commonly used pressure measurement units are the pascal and the atm. The pascal is equivalent to a force of 1 newton applied to an area of ​​1 m², and the atm has the value of atmospheric pressure at sea level (about 1.10 ⁵ Pa). Another unit, not as commonplace as the atm, is the centimeter of mercury (cmHg) or the millimeter of mercury (mmHg), which are still present in devices that measure blood pressure (sphygmomanometers) and also in pressure gauges for gas cylinders and cylinders.

• Density

Density is an important parameter for the study of fluids and for hydrostatics. It measures the amount of matter contained in a certain volume , that is, contained in the space occupied by a body or a fluid.

Density is defined based on pure water at room temperature. We attribute to this substance, which is abundant and easily found in any region of the planet, the density of 1 kg/L, 1 g/cm³ or 1000 kg/m³.

From the density of a substance, it is also possible to find out whether it will float or sink when dropped into water. Bodies denser than water sink, and bodies less dense than water float.

• Buoyancy

Buoyancy is the force that fluids exert on objects that are immersed in them . When we try to put a ball in water, we soon realize that a great force tends to push it out as it sinks.

The buoyancy has a value equal to the weight of the fluid that has been displaced, due to the entry of a body into a fluid. This force points upwards and is dependent on the immersed volume (the portion of the body that is inside the fluid), the density of the fluid, as well as the acceleration due to gravity .

Formulas

The main formulas of hydrostatics are Chinese . In addition, it was used to calculate parameters such as pressure and buoyancy. In the following figure, we present an important formula of hydrostatics, known as Stevin’s theorem . Watch:

ΔP – pressure difference (atm, Pa)

d – fluid density (g/cm³, kg/m³)

Δh – height difference between two points of the fluid (cm, m)

The formula shown above can be Chinese . In addition, it was used to determine the pressure difference between two points in a fluid that are at different heights. As we have already seen, points of fluid that are at the same height are study of social classes stands out. This topic involves many aspects and can be understood from different angles; therefore, it is the subject to the same pressure. This behavior is described by Pascal’s theorem. Watch:

P – pressure (Pa)

F – force (N)

A – area (m²)

From the formula above, we relate points 1 and 2 of a fluid located at the same depth through pressure, which can be calculated by the ratio between force and area .

Finally, we have the buoyancy formula, described by Archimedes’ theorem .

E – thrust (N)

V – immersed volume, or volume of fluid displaced (m³)

Solved exercises on hydrostatics

Question 1 — (Enem) To offer accessibility to people with limited mobility, hydraulic lifts are used in buses and cars. In this device, an electric pump is Chinese . In addition, it was used to force a fluid to pass from a narrow pipe to a wider one, and in this way activate a piston that moves the platform. Consider a hydraulic elevator whose piston head area is five times the area of ​​the pipe coming out of the pump. Neglecting friction and assuming a gravitational acceleration of 10 m/s2, it is desired to lift a 65 kg person in a 15 kg wheelchair onto the 20 kg platform.

What must be the force exerted by the pump motor on the fluid, so that the wheelchair user is lifted at constant speed?

a) 20N

b) 100N

c) 200N

d) 1000N

e) 5000N

Resolution:

To solve this exercise, we will make use of Pascal’s principle. Taking into account that the pressure is distributed equally throughout the fluid, the force-to-area ratio at the two ends of the tube must be equal. Note the calculation:

To make the calculation above, it was initially necessary to calculate the weight to be lifted by the hydraulic lift. After that, knowing that the second area is five times bigger than the first, it was enough for us to do the division. Thus, the correct alternative is the letter C .

Question 2 — (Udesc) Consider the propositions related to hydrostatic fluids.

I. Pressure decreases with altitude above sea level and increases with depth below the air-water interface

II. The hydraulic lift is based on Pascal’s Principle

III. Knowing that the density of ice, oil and water are equal to 0.92 g/cm³, 0.80 g/cm³ and 1.0 g/cm³, respectively, it can be stated that ice sinks in oil and floats in water

IV. The apparent weight of a completely immersed body is less than the real weight, due to the action of the buoyant force, exerted by the liquid on the body, from top to bottom.

Tick ​​the correct alternative.

a) Only statements I, II and III are true.

b) Only statements II and IV are true.

c) Only statements I and II are true.

d) Only statements I, III and Sadducees and the learned were Pharisees for the most part). This institution was formed in century V or IV are true.

e) All statements are true.

Resolution:

Analyzing the alternatives, it is noticed that I, II and III are correct, based on the principles of hydrostatics, described in this article. The last alternative is incorrect because the buoyant force acts from the bottom up, not from the top down. Therefore, the correct alternative is the letter A.