Question

Find the dimensional formula of coefficient of viscosity $\eta$

Answer 1

Coefficient of viscosity is defined as tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.

Mathematically,

Coefficient of viscosity (η)= Fr/Av where F = tangential force, r = distance between the layers , v = velocity.

Dimensional Formula of Force = M¹L¹T^-2

Dimensional Formula of Area= M⁰L²T⁰

Dimensional Formula of distance= M⁰L¹T⁰

Dimensional Formula of velocity= M⁰L¹T^-1

Putting these values in above equation we get,

[η]= [M¹L¹T^-2][M⁰L¹T⁰] / [M⁰L²T⁰] [M⁰L¹T^-1] = [M¹L^-1T^-1]

Dimensional Formula of Coefficient of viscosity (η)=[M¹L^-1T^-1]
SI unit of Coefficient of viscosity (η) is Pascal-second