# Stevin’s Law

Stevin’s Law, also called Stevin’s Theorem, is a physical rule that deals with the pressure in liquids, depending on their density and depth. This is a very important study, which allows us to understand blood circulation, submarines, oil plants, aquariums and many other uses. In this article, learn about the formulas, characteristics and see the resolution of entrance exam questions about Stevin’s Law.

## Definition of Stevin’s Law

Stevin’s Theorem is considered the fundamental law of hydrostatics , the science that studies the forces and physical entities that act on a liquid in a state of static equilibrium. The main function of Stevin’s Law is to explain how atmospheric pressure acts on a liquid material.

According to studies proposed by Belgian scientist Simon Stevin (1548–1620), when a fluid is placed in a container, the pressure exerted on this liquid depends exclusively on the height of the liquid column. From this, he created a formula that will be presented in the next topic.

### Stevin’s Law Formula

Upon realizing that the height of the liquid column is decisive for the pressure, Stevin looked for other quantities that were related to this value. His studies indicate that the density of the liquid and the acceleration of gravity are also important factors in determining this pressure value.

In this way, the scientist developed the following formula:

#### p = ρ⋅g⋅h, where

p = pressure exerted on the liquid, measured in Pascals (Pa)

ρ = density of the liquid, can also be represented by d. Quantity in kg/ m3

h = height of the liquid column, measured in meters

When two points of the liquid are observed (A and B), it is common for the heights of the columns to be different. In these cases, the pressure exerted on the material will be given by:

Δp = ρ⋅g⋅Δh

Δh = height variation = h A – h B

#### Δp = pressure variation

A direct consequence of this formula is that the closer the observed point is to the surface, the lower the pressure exerted on it. And, similarly, the deeper the observed region, the greater the pressure found.

See the application of the formula in a question from the State University of Amazonas (UEA), year 2022.

Some waterproof watches have a print on their dial informing them of the maximum pressure or depth that these instruments can withstand underwater. Generally, this information refers to gauge pressure, that is, the pressure that only the liquid exerts on the watch. In the figure, you can see the information that the watch can withstand up to 3 atm of pressure.

Knowing that 1 atm = 10⁵ Pa and that the density of water is 10³ kg/m³, the maximum depth that can be dived with this watch in a region where g = 10 m/s², without it being damaged, is

a) 0.3m

b) 3m

c) 30m

d) 15m

e) 150m

From the statement, we have that the watch supports a maximum gauge pressure given by:

p=3 atm

Now, we will find the pressure in Pa:

p=3⋅10⁵ Pa

With this, it is possible to calculate the maximum depth through the relationship with the maximum gauge pressure:

p = ρ⋅g⋅h

3⋅10⁵ = 10³⋅10⋅h

h = 30 m

## Utilities of Stevin’s Theorem

### Communicating vessels

Since the pressure at all points of the liquid depends exclusively on the height, the shape of the container makes no difference to the pressure value. Thus, in vessels that communicate and have different shapes, the pressure will be the same when the height is the same.

From other physics principles, it can also be observed that the same pressure distributed in the liquid favors that all communicating vessels have the same liquid level, as shown in the figure below.

### Pascal’s theorem

Stevin’s Law led to the formation of another physical theorem, Pascal’s Theorem. In this case, it is determined that all pressure variations experienced at a point in the liquid will be equally transmitted within it and the container in which it is located.

Taking points A and B in the container below, if a force is applied, with pressure variation Δp A in A, this will propagate throughout the material equally. Thus, in B Δp B will occur , where Δp A = Δp B .

In everyday life, this can be used in hydraulic presses, generally for lifting heavy objects. A system of communicating vessels is created: on one side is the free surface of the liquid and on the other, the carriage. A hydraulic press applies pressure to the liquid surface, this pressure will be transmitted throughout the content and the object on the opposite side is lifted.