Density and Pressure

There are several mechanical properties of materials. But some common physical properties that we encounter every day are density and pressure. There are three states of matter: solid, liquid, and gas. Both of these properties play a major role in defining the state of the material. As the density of the material increases, the fluid behavior of the material decreases. Hence, it is evident that the density of solids is far greater than liquids and gases. 

This article will enlighten you on the two important mechanical properties of materials. Moreover, while explaining density and pressure, we will also give you a brief explanation of the density of water. 

Definition of Density 

Density is a vital concept, and it cannot be neglected while explaining the properties of liquids or gases. It is represented by the Greek letter ‘rho’ and is defined as the ratio of mass to volume. Thus, if the volume of material is 1m³ and its mass is 1kg, then the density of the material is 1 kg/m³. The formula of density is as follows:

ρ=m ⁄ v

In the formula mentioned above,

= density of the object

m = mass of the object

v = volume of the object

Since density is a combination of two physical quantities: mass and volume, it can be expressed using a dimensional formula. The dimensional formula for density is [ML-³]. The SI unit for density is kg m-³. It is a scalar quantity and has magnitude but no direction. Since the liquids are incompressible, their densities stay constant at all pressures. Meanwhile, gases can be compressed. Hence, their values of density vary drastically over a range of numbers. 

The density of water is calculated at 4 degrees Celsius or 277 K and is found to be 1 kg m³. Moreover, this density is used to calculate the relative density of a substance. Relative density is defined as the ratio of the density of the substance to the density of water.

Since relative density is the ratio of the same quantities, it is dimensionless. The relative density of aluminium is 2.7 and its density is 2.7 x 10³ kg m-³, mercury has a value of 13.6 x 10³, air is 1.29, hydrogen is 9 x 10-², etc.

Definition of Pressure

If a force F is acting on a plate with a cross-section area of A, pressure is defined as the ratio of normal force acting on the body to the cross-section area of the body. The formula for pressure is as follows:

P=F ⁄ A

In the above mentioned formula, 

P = pressure acting on the object

F = the normal force

A = cross-section area of the object

Just like density, pressure is also a scalar quantity. Thus pressure doesn’t have a specific direction. The dimensional formula for pressure is [ML-¹T²]. The SI unit of pressure is Nm-² and 1 N/m² = 1 Pa where ‘Pa’ stands for Pascal. Another unit which is commonly used for pressure is atmospheric pressure (atm). The value of 1 atm = 1.013 x 105 Pa.

Effect of area on pressure

Pressure can be explained with the help of a simple example. Consider that you have a needle. When you try to insert the needle into your skin, it gets easily inserted. But a blunt object doesn’t get inserted. Another example where you can observe the application of pressure is the circus. In a circus, an artist puts a wooden plank on his chest. The elephant easily walks over the human without breaking his ribs. But if the same elephant steps on the ribs of the human being, it fractures the person’s ribs, and the person dies.

Moreover, hammering a nail into a wall is much easier than hammering a flat screw. Thus, the force and coverage area are essential parameters for determining pressure. Thus, the smaller the area of the force applied, the greater the impact of the force. Thus as the area decreases, the pressure exerted by the object increases. 

Pascal’s Law

The French Scientist Blaise Pascal observed that the pressure acting in a fluid at rest is equal at all points if the height of the points is equal. You can consider a rectangular bar element in the fluid to understand this concept. The horizontal forces acting on the bar element of fluid must be balanced or equal. If they are not equal or balanced, some net force must be acting on the fluid, which helps the fluid flow in a particular direction. Therefore, in the absence of flow, the pressure in the fluid remains the same everywhere. One of the examples of pressure difference is the flow of air. 

Conclusion

In this article, we have explained matter’s two vital mechanical properties: density and pressure. Density is defined as the ratio of mass to volume. In contrast, pressure is defined as the ratio of force acting per unit area of cross-section. Pascal’s law describes the relation between the pressure acting on stationary liquid. Towards the end, we have explained that the pressure difference is the reason behind the flow of fluids.