The dimensional formula of Pressure is
[ M1 L-1 T-2 ]
where [M] [L] and [T] are the fundamental quantities: Mass, Length, and Time.
From the above formula, it’s clear that the dimension of pressure is 1, -1, and -2.
Derivation of Dimensional Formula of Pressure
We can derive this formula using the definition of pressure.
In physics, we can define force as the total measure of the force exerted on a unit area. Hence, Hence, mathematically,
Pressure = Force / Area
We know, Force = mass * acceleration and Area = length * breadth. So, our formula becomes
Pressure = ( mass * acceleration ) / ( length * breadth )
- acceleration = speed / time
- speed = distance / time
- so, acceleration = distance / time2
Pressure = ( mass * (distance / time2 ) / ( length * breadth ) Pressure = ( mass * distance ) / ( time2 * length * breadth ) Pressure = mass1 * distance1 * time-2 * length-1 * breadth-1
Dimensionally, we use
- [M] for mass
- [L] for distance, length, and breadth
- [T] for time
Now, the formula becomes
Pressure = [M1] * [L1] * [T-2] * [L-1] * [L-1] Pressure = [M1] * [L-1] * [T-2]
Hence, the dimensional formula of Pressure becomes [ M1 L-1 T-2 ].