Which expression defines Reynolds number in terms of fluid properties and dimensions?

• A. Re = ρ V D / μ
• B. Re = μ / (ρ V D)
• C. Re = ρ g h / μ
• D. Re = V / ν

Answer: (A)

Reynolds number measures the balance between inertial forces and viscous forces in a flow. It is defined as Re = (ρ V L) / μ, where ρ is density, V is flow velocity, L is a characteristic length (like pipe diameter), and μ is dynamic viscosity. This formula shows how increasing velocity or a larger characteristic size raises Re, while higher viscosity lowers it. The expression with ρ V D / μ matches this definition exactly, since D serves as the characteristic length.

If you rewrite with kinematic viscosity ν = μ/ρ, you get Re = V D / ν, which is equivalent. However, V / ν lacks the length scale and is not dimensionless on its own, so it’s not a correct standalone form.

The other form replaces the viscous term with μ in the numerator, which would invert the ratio of inertial to viscous effects and does not define a dimensionless Reynolds number. Using ρ g h introduces a gravitational head term and is not a Reynolds number expression.