# What does this mean? (equation for viscous flows)

While reading a text book 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.

BvU
Homework Helper
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.

Gold Member
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.

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.

Randy Beikmann
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

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