Question

7. Viscous force on sphere is F=6n n dv, where n
(eeta ) is the coefficient of viscosity.d is diameter of
the sphere, and v is velocity. Find dimensional formula
for n​

Answer 1

......ÂÑ$WÊR......

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