Flow Regimes

In 1883, Osborn Reynolds conducted a classical experiment, illustrated in Fig. 6-1, in which he measured the pressure drop as a function of flow rate for water in a tube. He found that at low flow rates the pressure drop was directly proportional to the flow rate, but as the flow rate was increased a point was reached where the relation was no longer linear and the "noise" or scatter in the data increased considerably. At still higher flow rates the data became more reproducible, but the relationship between pressure drop and flow rate became almost quadratic instead of linear.

To investigate this phenomenon further, Reynolds introduced a trace of dye into the flow to observe what was happening. At the low flow rates where the linear relationship was observed, the dye was seen to remain a coherent, rather smooth thread throughout most of the tube. However, where the data scatter occurred, the dye trace was seen to be rather unstable, and it broke up after a short distance. At still higher flow rates, where the quadratic relationship was observed, the dye dispersed almost immediately into a uniform "cloud" throughout the tube. The stable flow observed initially was termed laminar flow, because it was observed that the fluid elements moved in smooth layers or "lamella" relative to each other with no mixing. The unstable flow pattern, characterized by a high degree of

Figure 6-1 Reynolds' experiment.

mixing between the fluid elements, was termed turbulent flow. Although the transition from laminar to turbulent flow occurs rather abruptly, there is nevertheless a transition region where the flow is unstable but not thoroughly mixed.

Careful study of various fluids in tubes of different sizes has indicated that laminar flow in a tube persists up to a point where the value of the Reynolds number (NRe = DVp/i) is about 2000, and turbulent flow occurs when NRe is greater than about 4000, with a transition region in between. Actually, unstable flow (turbulence) occurs when disturbances to the flow are amplified, whereas laminar flow occurs when these disturbances are damped out. Because turbulent flow cannot occur unless there are disturbances, studies have been conducted on systems in which extreme care has been taken to eliminate any disturbances due to irregularities in the boundary surfaces, sudden changes in direction, vibrations, etc. Under these conditions, it has been possible to sustain laminar flow in a tube to a Reynolds number of the order of 100,000 or more. However, under all but the most unusual conditions there are sufficient natural disturbances in all practical systems that turbulence begins in a pipe at a Reynolds number of about 2000.

The physical significance of the Reynolds number can be appreciated better if it is rearranged as


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