Question

Define the Reynolds number for pipe flow, film flow, annulus flow and particle

motion in a fluid.

Answer 1

Reynolds Number:

Definition: The Reynolds number is a dimensionless number and it is defined as the ratio of internal forces to viscous forces within a fluid which is subjected to relative movement due to different fluid velocities. Reynolds number is defined as,

Where, ρ is density of the fluid, V = velocity of the flow, D_h is hydraulic Diameter of the pipe, μ = Dynamic viscosity of the fluid

• For pipe flow, Reynolds number is defined as,

Where, ρ is density of the fluid, V = velocity of the flow, D is hydraulic Diameter of the pipe, μ = Dynamic viscosity of the fluid

• For film flow, Reynolds number is defined as,

Where, ρ is density of the fluid, D = Diameter of the pipe, μ = Dynamic viscosity of the fluid, (m_dot) = mass flow rate, ν is kinematic viscosity

• For Annular flow, Reynolds number is defined as,

  

Where, ρ is density of the fluid, V = velocity of the flow, D_o is inside diameter of the outer pipe, D_i is outside diameter of the inner pipe, μ = Dynamic viscosity of the fluid

• For Particle motion in a fluid, Reynolds number is defined as,

Where, ρ is density of the fluid, V_p = velocity of the particle for the fluid velocity, D_p is diameter of the particle, μ = Dynamic viscosity