1Which of these has the same dimensions as velocity gradient?
Velocity gradient and activity both have the dimensions [T⁻¹].
Properties of matterClass 11, Mechanical Properties of Fluids
Dimensional formula of Velocity gradient
[T-1]
How fast the speed of a fluid changes across the layers. It has the dimension of frequency, and viscosity is the ratio of shear stress to it.
How to get the dimensional formula of velocity gradient
- Start from the definition: velocity gradient = velocity / length.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- Put in the dimension of each part: [L T-1] / [L].
- Add the powers of each base quantity: [T-1].
Quantities with the dimensions [T⁻¹]
Equal dimensions do not make them the same quantity. Compare velocity gradient with the others in the full grid.
Three questions on velocity gradient
2What is the SI unit of velocity gradient?
The SI unit of velocity gradient is the per second (s⁻¹).
3Which one has different dimensions from the others?
Poisson's ratio is [M⁰ L⁰ T⁰]. The other three are all [T⁻¹].
Velocity gradient: quick answers
What is the dimensional formula of velocity gradient?
The dimensional formula of velocity gradient is [T⁻¹]. It comes from velocity gradient = velocity / length.
What is the SI unit of velocity gradient?
The SI unit of velocity gradient is the per second (s⁻¹).
Which quantities have the same dimensions as velocity gradient?
Velocity gradient shares [T⁻¹] with angular velocity, frequency, angular frequency, decay constant, activity. Equal dimensions do not make them the same quantity.