Understanding the Reynolds Number: A Guide

In summary, the Reynolds number is a dimensionless parameter used to determine the type of flow (laminar or turbulent) in a fluid. In the given problem, the Reynolds number is calculated using the formula Re = ρUL/µ, where U is the velocity scale (in this case, it can be taken as V), L is the characteristic length (in this case, the distance between the two parallel plates), and µ is the fluid viscosity. The question asks for the conditions on V and G (the pressure gradient) for the Reynolds number to be small, which would indicate a laminar flow. This can be achieved by keeping the velocity and pressure gradient low, or by increasing the viscosity of the fluid.
  • #1
motherh
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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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  • #3
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.
 

What is the Reynolds Number?

The Reynolds Number is a dimensionless quantity used to determine the type of flow (either laminar or turbulent) of a fluid over a surface. It is calculated by dividing the inertial forces of the fluid by the viscous forces.

How is the Reynolds Number calculated?

The Reynolds Number is calculated by multiplying the velocity of the fluid by the characteristic length of the surface and dividing it by the kinematic viscosity of the fluid. The formula is Re = (ρvL)/μ, where ρ is the density of the fluid, v is the velocity, L is the characteristic length, and μ is the dynamic viscosity.

What is the significance of the Reynolds Number?

The Reynolds Number is significant because it helps determine the type of flow a fluid will have over a surface. If the Reynolds Number is less than 2300, the flow is considered laminar and if it is greater than 4000, the flow is considered turbulent. This information is important for designing and predicting the behavior of fluids in various systems.

What are some applications of the Reynolds Number?

The Reynolds Number is used in various fields such as aerodynamics, hydrodynamics, and fluid mechanics. It is used to study the flow of air over airplane wings, the flow of water in pipes, and the flow of blood in blood vessels, among many others. It is also important in designing and optimizing industrial processes such as oil pipelines and chemical reactors.

How can the Reynolds Number be controlled?

The Reynolds Number can be controlled by changing the velocity, characteristic length, or viscosity of the fluid. For example, decreasing the velocity or increasing the viscosity can reduce the Reynolds Number and lead to laminar flow. Additionally, by changing the shape or size of a surface, the characteristic length can be altered and therefore change the Reynolds Number.

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