1Which of these has the same dimensions as pressure?
Pressure and stress both have the dimensions [M L⁻¹ T⁻²].
Properties of matterClass 11, Mechanical Properties of Fluids
Dimensional formula of Pressure
[M L-1 T-2]
Force per unit area. It has the same dimension as stress and energy per unit volume.
How to get the dimensional formula of pressure
- Start from the definition: pressure = force / area.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- area = length × length, so area is [L] × [L] = [L2].
- Put in the dimension of each part: [M L T-2] / [L2].
- Add the powers of each base quantity: [M L-1 T-2].
Quantities with the dimensions [M L⁻¹ T⁻²]
Equal dimensions do not make them the same quantity. Compare pressure with the others in the full grid.
Three questions on pressure
2What is the SI unit of pressure?
The SI unit of pressure is the pascal (Pa).
3Which one has different dimensions from the others?
Velocity gradient is [T⁻¹]. The other three are all [M L⁻¹ T⁻²].
An equation that uses pressure
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
P V = n R TPV[M L2 T-2]=nRT[M L2 T-2]Dimensionally consistentEvery term is [M L2 T-2]
Pressure: quick answers
What is the dimensional formula of pressure?
The dimensional formula of pressure is [M L⁻¹ T⁻²]. It comes from pressure = force / area.
What is the SI unit of pressure?
The SI unit of pressure is the pascal (Pa).
Which quantities have the same dimensions as pressure?
Pressure shares [M L⁻¹ T⁻²] with energy density, stress, strain energy density, Young's modulus, bulk modulus, shear modulus. Equal dimensions do not make them the same quantity.