Question

In: Mechanical Engineering

Define the Reynolds number for pipe flow, film flow, annulus flow and particle motion in a...

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

motion in a fluid.

Solutions

Expert Solution

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, Dh 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, Do is inside diameter of the outer pipe, Di 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, Vp = velocity of the particle for the fluid velocity, Dp is diameter of the particle, μ = Dynamic viscosity


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