1Which is the dimensional formula of pressure gradient?
Pressure gradient works out to [M L⁻² T⁻²].
Properties of matterClass 11, Mechanical Properties of Fluids
Dimensional formula of Pressure gradient
[M L-2 T-2]
How fast the pressure changes with distance. It drives the flow of a fluid.
How to get the dimensional formula of pressure gradient
- Start from the definition: pressure gradient = pressure / length.
- 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].
- pressure = force / area, so pressure is [M L T-2] / [L2] = [M L-1 T-2].
- Put in the dimension of each part: [M L-1 T-2] / [L].
- Add the powers of each base quantity: [M L-2 T-2].
Three questions on pressure gradient
2What is the SI unit of pressure gradient?
The SI unit of pressure gradient is the pascal per metre (Pa/m).
3Do pressure gradient and Young's modulus have the same dimensions?
Pressure gradient is [M L⁻² T⁻²] but Young's modulus is [M L⁻¹ T⁻²].
Pressure gradient: quick answers
What is the dimensional formula of pressure gradient?
The dimensional formula of pressure gradient is [M L⁻² T⁻²]. It comes from pressure gradient = pressure / length.
What is the SI unit of pressure gradient?
The SI unit of pressure gradient is the pascal per metre (Pa/m).
Is pressure gradient dimensionless?
No. Pressure gradient has the dimensions [M L⁻² T⁻²].