During Ugraduate study we were taught that When Re<2500 then the flow is laminar when it is >4000 the flow is turbulent and could be any (laminar or turbulent) inbetween. Recently I realized some consideration for turbulent flows where Re (10^4). I am really confused, what is the criteria for flow classification as laminar or turbulent.

for flow in 'pipe' Re>2500 flow is turbulent but for flow over 'plate' Re>10e4 is turbulent.

The transition from laminat turbulent is not clear cut, and can occur 'typically' between Re 2000 to Re 4000. This is just the generalisation that most text books use and is really a guideline based on simple plate or pipe theory. Transition is not well understood nor the mechanisms behind it. In reality turbulent flow can occur at very low Re numbers as well as high. Similarly Laminar flow can occur at very high Re numbers (eg highly accelerated flow). It all depends on the nature of the flow!

The main difference is, as John said, in "pipe" and "plate" flow. Reynolds number is computed in different ways for them - for pipe/channel flows pipe diameter is used as reference length and for plate flows usually its the length of the plate (or some dimension of the body for general external aerodynamics). But if you'll use half pipe diameter for fully developed pipe flow and boundary layer thickness for plate flow, you'll get nearly the same critical values of Reynolds number.

Actually if you use the boundary layer thickness for the flat plate case you'll get R~500 since the boundary layer thickness depends upon the square root of the Reynolds number. This is much smaller than you'll get for a pipe flow. However the actual (global) Reynolds number for the flat plate is bigger (~10^5) than that of a pipe flow.

To my mind it's not "much smaller" - for pipe flow basing on radius instead of diameter (to compare with BL thickness) you'll get Re~1000, that's nearly the same order. The difference can be regarded to different flow nature (plane vs. axisymmetric).

2300 for pipe flow could be thought of as the lowest Reynolds number at which a disturbance can induce turbulenent flow ! the upper limit depends on how carefully you can conduct the experiment ! -AJAY

Well, as far as I remember 2300 is not the lowest number - most textbooks report it as "most typical for engineering applications". The same can be said for the plate flow - there is some typical critical value but the limits also depend on the experimental conditions.

In the plate flow case it's relatively difficult to stop transition above the critical Reynolds number since the flow becomes linearly unstable to infinitessimal disturbances. In pipe flow the situation is different since the flow is (believed to be) linearly stable at all Reynolds numbers and hence transition requires finite amplitude forcing effects such as surface roughness. This shows up in the range of Reynolds numbers that are observed in experiments; i.e. the Reynolds number can be anywhere in the range 2000 - 13000.