Q: What are the dimensions of Reynolds number ?

Sol: $\large R = \frac{\rho v_o D}{\eta} $

(ρ is density of the fluid, v_{0} is the critical velocity, D is diameter through which the fluid is flowing and η is the coefficient of viscosity of the fluid)

$\large R = \frac{[ML^{-3}][LT^{-1}][L]}{[ML^{-1}T^{-1}]} = [M^0 L^0 T^0]$

R is dimensionless.