{"id":5606,"date":"2019-11-01T09:15:46","date_gmt":"2019-11-01T03:45:46","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=5606"},"modified":"2022-11-04T12:06:29","modified_gmt":"2022-11-04T06:36:29","slug":"dimensional-formula-of-pressure","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/dimensional-formula-of-pressure\/","title":{"rendered":"Dimensions of Pressure"},"content":{"rendered":"\n

In this article, we’ll talk about the dimensions of pressure. Here, we will look at the dimensional formula of pressure and how to find the dimensions of pressure.<\/p>\n\n\n\n

Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed. $\\frac{F}{A}$ is the basic pressure formula (Force per unit area). Pascals is the SI unit of pressure (Pa). In SI base units 1 $N\/m^2$, $1 kg\/(m\u00b7s^2)$, or $1 J\/m^3$ are the units of pressure.<\/p>\n\n\n\n

Increasing the amount of force applied to any object increases the amount of pressure applied. As a result, the greater the force, the greater the pressure applied. This effect occurs because, according to our definition, pressure varies directly with force $\\left (\\frac{F}{A}\\right )$. By reducing the area over which the force acts, you can increase the pressure caused by the same force.<\/p>\n\n\n\n

Dimensional Formula of Pressure<\/h2>\n\n\n\n

Dimensional Formula for Pressure is given by<\/p>\n\n\n\n

\"dimensional
Dimensions of Pressure<\/figcaption><\/figure>\n\n\n\n

Here<\/p>\n\n\n\n

M<\/strong> denotes Mass<\/p>\n\n\n\n

L<\/strong> denotes Length<\/p>\n\n\n\n

T<\/strong> denotes Time<\/p>\n\n\n\n

Derivation for dimensions of pressure<\/h3>\n\n\n\n

Pressure is defined as Force per unit area<\/p>\n\n\n\n

$Pressure = \\frac {Force}{Area}$<\/p>\n\n\n\n

Now<\/p>\n\n\n\n

Force is defined as<\/p>\n\n\n\n

$F= ma$<\/p>\n\n\n\n

Dimension of Mass  is $[M^1L^0T^0]$<\/p>\n\n\n\n

Dimension of acceleration is $[M^0L^1T^{-2}]$<\/p>\n\n\n\n

So the dimension of Force  will be<\/p>\n\n\n\n

$=[M^1L^0T^0] \\times [M^0L^1T^{-2}] = [M^1L^1T^{-2}]$<\/p>\n\n\n\n

Now Dimension of Area = $[M^0L^2T^0]$<\/p>\n\n\n\n

Substituting these values of dimension of Force and area, we get the dimensional formula of Pressure as<\/p>\n\n\n\n

$\\text {dimensional formula of Pressure} = \\frac { [M^1L^1T^{-2}]}{[M^0L^2T^0]} = [M^1L^{-1}T^{-2}]$<\/p>\n\n\n\n

Pressure is denoted by Letter $P$<\/p>\n\n\n\n

SI unit of pressure is Pascal or Newton\/square meter<\/p>\n\n\n\n

Try the free Quiz given below to check your knowledge of Dimension Analysis:-<\/p>\n\n\n\n

Quiz on Dimensional Analysis<\/h4>\n\n\n