If p is the density and η is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Rₑ is :

Solution

Physics sir · 3 steps

Reynolds number compares inertia to viscosity, so the inertia terms go on top and η goes below.

1. What it measures. Reynolds number is the ratio of inertial force to viscous force in a flowing fluid. Inertia grows with density ρ, speed v and pipe size d. Viscous drag grows with η.

   Rₑ = (inertial force)/(viscous force) = (ρ v d)/η

2. Check the units. ρ v d has units kg m⁻³ × m s⁻¹ × m = kg m⁻¹ s⁻¹. That is exactly the unit of η, so Rₑ is a pure number, as it must be.

   Option	Units	Physics
   (a) (η d)/(ρ v)	m², not dimensionless	wrong
   (b) (ρ v)/(η d)	m⁻², not dimensionless	wrong
   (c) (ρ v d)/η	dimensionless	faster or denser flow gives larger Rₑ
   (d) η/(ρ v d)	dimensionless	inverted: more viscosity would raise Rₑ

3. So. The correct formula is Rₑ = (ρ v d)/η, option (c).

The idea to keep. Reynolds number must be dimensionless and must rise as flow gets faster and fall as the fluid gets thicker. Large Rₑ means turbulent flow, small Rₑ means streamline flow.

Answer from the NTA final answer key. Solution by PrepWiser.