1Which is the dimensional formula of coefficient of viscosity?
Coefficient of viscosity works out to [M L⁻¹ T⁻¹].
Properties of matterClass 11, Mechanical Properties of Fluids
Dimensional formula of Coefficient of viscosity
[M L-1 T-1]
From F = ηA v/d, force times distance over area times velocity. The CGS unit is the poise.
How to get the dimensional formula of coefficient of viscosity
- Start from the definition: coefficient of viscosity = force × length / (area × velocity).
- 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] × [L] / ([L2] × [L T-1]).
- Add the powers of each base quantity: [M L-1 T-1].
Three questions on coefficient of viscosity
2What is the SI unit of coefficient of viscosity?
The SI unit of coefficient of viscosity is the pascal second (Pa s).
3Do coefficient of viscosity and stress have the same dimensions?
Coefficient of viscosity is [M L⁻¹ T⁻¹] but stress is [M L⁻¹ T⁻²].
An equation that uses coefficient of viscosity
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
F = 6 π η r vF[M L T-2]=6 pi eta r v[M L T-2]Dimensionally consistentEvery term is [M L T-2]
r = lengthv = velocity
Coefficient of viscosity: quick answers
What is the dimensional formula of coefficient of viscosity?
The dimensional formula of coefficient of viscosity is [M L⁻¹ T⁻¹]. It comes from coefficient of viscosity = force × length / (area × velocity).
What is the SI unit of coefficient of viscosity?
The SI unit of coefficient of viscosity is the pascal second (Pa s).
Is coefficient of viscosity dimensionless?
No. Coefficient of viscosity has the dimensions [M L⁻¹ T⁻¹].