PHYSICS · Subjective · CBSE · Physics · Units and Measurements · Units and Measurements
Problem
According to Newton’s law of viscosity, the tangential force F required to maintain a velocity gradient dxdv between two parallel layers of a fluid of area A is
F=ηA(dxdv),
where η is the coefficient of viscosity.
(a) Deduce the dimensional formula of η and write its SI unit.
(b) State whether η is a base quantity or a derived quantity, giving a reason for your choice.
(c) For flow in a pipe, the Reynolds number is defined as
Re=ηρvL,
where ρ is the density of the fluid, v its mean speed, and L a characteristic length of the pipe. Using dimensional analysis, prove that the Reynolds number is dimensionless.