Understanding the Reynolds Number

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SUMMARY

The Reynolds number (Re) is a dimensionless quantity used to predict flow patterns in different fluid flow situations. In the context of the problem discussed, Re is defined as Re = ρUL/µ, where ρ is the fluid density, U is the characteristic velocity (which can be taken as V, the speed of the upper plate), L is a characteristic length (the gap height h), and µ is the dynamic viscosity of the fluid. For the flow to be considered laminar, the Reynolds number must be small, which occurs when the velocity V and the pressure gradient G are sufficiently low relative to the fluid's viscosity.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the concepts of viscosity and density
  • Knowledge of basic equations of motion for fluids
  • Ability to interpret dimensionless numbers in fluid mechanics
NEXT STEPS
  • Study the derivation and applications of the Reynolds number in fluid mechanics
  • Explore the relationship between pressure gradients and flow regimes
  • Learn about laminar vs turbulent flow characteristics
  • Investigate the effects of varying viscosity and density on flow behavior
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Students and professionals in engineering, particularly those focusing on fluid dynamics, mechanical engineering, and applied physics, will benefit from this discussion.

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Homework Statement



I don't fully understand the Reynolds number and it has arisen in a problem. It says:

Fluid with viscosity µ and density ρ fills the gap between two parallel plates at z = 0 and z = h. The upper plate at z = h moves with speed V in the x direction, while the lower plate at z = 0 is stationary. The fluid is also subject to a pressure gradient −G in the x direction.

Homework Equations



I have solved for the velocity u (no idea if this is needed for the Reynolds number bit at all) to find

u(z) = Gz(h-z)/2µ + Vz/h.

The Attempt at a Solution



The question then says:

What is the Reynolds number for this flow? What are the conditions on V and G for it to be small?

Can anybody help at all? It would be much appreciated.

All my notes really say is that Re = ρUL/µ or Re = ρL^2/µT but I don't understand the U, L or the T.
 
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That Wiki helps a little but I'm still confused by this. So the Reynolds number is given by Re = ρUL/µ? As U is the velocity scale it makes to take U as V here. But after this I don't know how G comes into the Reynolds number.
 

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