What does this mean? (equation for viscous flows)

[vktsn0303]

While reading a textbook on viscous flows, I came across the following interpretation of an equation:

where, v is the vertical component of the free stream velocity and y is the vertical distance from the surface of a solid and Re is the reynolds number.

Can someone please help me understand what this interpretation means?
Thanks in advance

 

[BvU]

The funny O means 'is of the order of'
My interpretation would be: if the reynolds number quadruples, v and y become approximately half as big

Often the funny O is used instead of 'is proportional to' ($\propto$) if the reasoning aims to justify ignoring certain terms. But I don't know if that is true in your context.

 

[boneh3ad]

The order symbol expresses a concept similar to proportionality but not quite the same. It's a statement of how one function grows relative to another. In this case, $v$ and $y$ grow as $Re^{-1/2}$. In other words, $v$ and $y$ are bounded by $Re^{-1/2}$ multiplied by some factor as they grow. This can imply proportionality but does not necessarily. Essentially, proportionality is a stronger constraint.

 

[OrangeDog]

The "O" is called "big O notation". It means "on the order of magnitude of" Your average student body size for a college campus might be O(10^4) (between 10,000 and 99,999 students), but your average classroom size might be O(10^1) (10 to 99), for example.

 

[rupeshmishra1990]

This is called viscous flow.In this when you go upward from a fixed surface the velocity of the layer of liquid increases.At the bottom layer velocity would be zero and at top velocity of layer would be maximum.Reynold number shows that upto a specific value of Reynold number flow would be viscous and beyond that number flow would become transit and the turbulent flow.see the images below.

imgaes2

image1