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Old Dec 11th 2018, 10:34 PM   #1
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Question viscosity and Reynold

When velocity of the liquid is less than the critical velocity, then the flow of the liquid is mainly governed by viscosity. When the velocity is greater than critical velocity, it is mainly governed by density not viscosity.

How is this true?
How Sir Reynold concluded it?

plz someone help me out.
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Old Dec 12th 2018, 02:19 AM   #2
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You can think of a fluid as being a big collection of mass parcels. The parcels are a bit sticky and tend to drag each other along (viscous forces) but also have motion and push into each other (inertial forces).

What experimenters noticed is that if you take a fluid (a liquid or a gas) and push the fluid through a tube, there is a flow velocity where the behaviour of the fluid changes. This critical velocity changes from fluid to fluid.

When the velocity is low, the fluid passes through the tube in a laminar fashion, which is generally quite ordered and smooth. In this regime, the viscous force between mass parcels in the fluid is dominant, so parts of the flow tend to drag each other around and consequently travel together.

However, when the velocity is high, the fluid passes through the tube in a turbulent fashion, which is generally messy and chaotic with vortices and other local effects. This is because the mass parcels have greater inertial forces, so they push each other around rather than drag each other around.

There is also a transition zone where this behaviour starts to become more prevalent, so it's not an immediate "cut-off point".

Reynolds figured out a measure which reasonably determines whether a fluid acts in a laminar or turbulent manner, which is the Reynolds number:

$\displaystyle Re = \frac{\text{Inertial force}}{\text{Viscous force}} = \frac{uL}{\nu}$

where u is the fluid velocity, L is a characteristic dimension of the flow (such as a pipe diameter) and $\displaystyle \nu $ is the kinematic viscosity.

If the Reynolds number starts to exceed around 50000, you can expect a transition from laminar to turbulent flow.

Last edited by benit13; Dec 12th 2018 at 05:33 AM.
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