Understanding the Reynolds Number

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The discussion centers on understanding the Reynolds number in the context of fluid flow between two parallel plates. The user has derived the velocity profile and is seeking clarification on how to calculate the Reynolds number, specifically how to define the variables U, L, and T. It is noted that U can be taken as the velocity V of the moving plate, while L represents a characteristic length, which could be the gap height h. The user is also confused about the role of the pressure gradient G in determining conditions for a small Reynolds number. Overall, the conversation highlights the need for a clearer understanding of these variables in relation to fluid dynamics.
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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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.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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