Reynolds number basically determines the transition of fluid flow form laminar flow to turbulent flow. When the value of Reynolds number is less than 2300, laminar flow will occur and the resistance to flow will be independent of the pipe wall roughness (℮). Meanwhile, turbulent flow occurs when the value of Reynolds number is exceeding 4000.
For large viscous force, whereby Re value is less than 2300, viscous effects are great enough to damp any disturbance in the flow and the flow remains laminar. The flow is called laminar because the flow takes place in layers. Any combination of low velocity, small diameter, or high kinematic viscosity which results in Re value of less than 2300 will produce laminar flow. As Re increases, the viscous damping of flow disturbances or perturbations decreases relative to the inertial effects. Because of a lack of viscous damping, disturbances are amplified until the entire flow breaks down into in irregular motion. There is still a definite flow direction, but there is an irregular motion superimposed on the average motion. Thus, for turbulent flow in a pipe, the fluid is flowing in the downstream direction, but fluid particles have an irregular motion in addition to the average motion. The turbulent fluctuations are inherently unsteady and three dimensional. As a result, particles which pass though a given point in the flow do not follow the same path in turbulent flow even though they all are flowing generally downstream. Flows with 2000 < Re < 4000 are called transitional. The flow can be unstable and the flow switch back and forth between turbulent and laminar conditions.
APPARATUS
* A re-entrant bell mouthed glass experimental tube of 16 mm bore and approximately 790 mm long mounted horizontally in a 103 mm bore Perspex tube.
* Dye injector with needle valve control.
* Rotometer flow meter.
* Water supply from a tank with clear test section tube and “bell mouth” entrance.
EXPERIMENTAL PROCEDURES
This experiment demonstrates visually laminar (or streamline) flow and its transition to turbulent flow at a particular velocity.
- Firstly, the apparatus is set up and insert the red dye into the dye reservoir with a steady flow of water.
- The dye is allowed to flow from the nozzle at the entrance of the channel until a colored stream is visible along the passage. The velocity of water flow should be increased if the dye accumulates around the nozzle.
- Adjust the water flow until a laminar flow pattern which is a straight thin line or streamline of dye is able to be seen along the whole passage.
- Collect the volume of water that flows for 10 seconds then measure the amount of water in the volumetric measuring tank. Repeat this step 3 times to get the average and more accurate volume of water. The volume flow rate is calculated from the volume and a known time.
- The water flow rate is increased by opening the pipe vessel and the flow pattern of the fluid is observed. Repeat step 2-4 for transition and turbulent flow.
- Clean all the apparatus after the experiment is done.
RESULTS
SAMPLE CALCULATIONS
Data Given:
Times = 3 sec
Density of water, ρ = 1000 kg/m³
Viscosity, μ = 10.00 x 10-4 Ns/m²
Diameter of tube, d = 16 x 10ˉ³ m
Length, = 0.103 m
Area of cross passage, a = πd²/4
= π (16 x 10ˉ0³) / 4
= 2.0106 x 10ˉ4 m²
From experiment:
Laminar Flow:
Volume flow rate = volume/ time
= 8.4 x 10-5 m3 / 3s
= 2.8 x 10-5 m3/s
Velocity, v = (m / ρa) = volume flow rate / area
= 2.8 x 10-5 m3/s ÷ 2.0106x 10-4 m2
= 0.1393 m/s
Reynolds number, Re = ρvd / μ
= (1000 kgm-3 x 0.1393 m/s x 16 x 10-3 m) ÷ 10.00 x 10-4Ns/m2
= 2228.8
* For laminar flow Re should be less than 2300.
Transition Flow:
Volume flow rate = volume/ time
= 9.6 x 10-5 m3 ÷ 3s
= 3.2 x 10-5 m3/s
Velocity, v = (m / ρa) = volume flow rate / x area
= 3.2 x 10-5 m3/s ÷ 2.0106 x 10-4m
= 0.1592 m/s
Reynolds number, Re = ρvd / μ
= (1000 kgm-3 x 0.1592 m/s x 16x 10-3m) ÷ 10.00 ˉ4 Ns/m²
= 2547.2
*For transition flow Re should be in between 2300 and 4000
Turbulent Flow:
Volume flow rate = volume/ time
= 16.8 x 10-5 m3 ÷ 10s
= 5.60 x 10-5 m3/s
Velocity, v = (m / ρa) = volume flow rate / area
= 5.60 x 10-5 m3/s ÷ 2.0106 x 10-4m2
= 0.2785 m/s
Reynolds number, Re = ρvd / μ
= (1000kgm-3x 0.2785 m/s x 0.016m) ÷ 10.00 x 10ˉ4 Ns/m²
= 4456.0
*For turbulent flow Re should be more than 4000
DISCUSSION
It is necessary to know the differences between laminar, turbulent and transition flow before one is about to conduct this experiment. As for laminar flow, it is defined as a highly ordered fluid motion with smooth streamlines. Turbulent flow is much different with laminar, as it is a highly disordered fluid motion characterized by velocity and fluctuations and eddies, whereas transition flow is known as a flow that contains both laminar and turbulent regions.
Based on Reynolds apparatus experiment, laminar flow is obtained when a single ordered line is seen after a thin filament of dye is injected into the transparent glass tube. There is not much dispersion of dye can be observed throughout the flowing fluid. Nevertheless, the case is not the same with turbulent flow, as there is obvious dispersion of dye along the glass tube, whereby the lines of dye breaks into myriad entangled threads of dye.
Throughout the experiment, we observed that the red dye line starts flowing in a straight ordered line through the glass tube, and as the velocity increases after some time, the ordered streamlines is seen to begin to disperse at about the middle of the streamlines, but still remain the straight line at the earlier part. Next, the dispersion started to increase, indicating the turbulent flow. These observations are concluded as the streamlines is undergoing a change of type of flow, which is from laminar flow, transition flow to turbulent flow.
There are a few careless mistakes that have been done during this experiment. Most of all, the accuracy of collecting the fluid flowing out of the tube within 3 seconds is a bit inaccurate. The one who collect the fluid might not begin right when the person monitoring the stopwatch started ticking on it, and he/she might also not stop collecting exactly after the third second. Therefore, the values calculated in results section might not be exactly 100% correct.
CONCLUSION
As a conclusion, as water flow rate is increasing, the Reynolds number will automatically increase as well, and the red dye line change from straight line to swirling streamlines. Likewise, it is proven that Reynolds number is dimensionless, since no unit is representing the value of Reynolds number. Laminar flow is obtained if the Reynolds number is less than 2300; meanwhile the Reynolds number for turbulent flow is more than 4000. The Reynolds number for transition flow is in between 2300 until 4000.
RECOMMENDATIONS
There are some recommendations to make sure this experiment would attain more accurate and precise results in the future:
- Check whether the water in the tube flows in a correct way and we should also make sure that the flow is stable before measuring the flow rate by monitoring the time taken for collecting an amount of water in the volumetric measuring tank.
- Before injecting the dye into the fluid, we should make sure the dye is not too much and not too insufficient. It will be hard to stable the fluid to get a laminar flow.
- The experiment should be repeated twice to get better result.
- The person collecting the water should synchronize well with the time keeper.
REFERENCES
- Fluid Mechanics by Dr. Andrew Sleigh (J. Franzini/E. Finnemore), McGraw Hill.
- F. M. White, Fluid Mechanics (Mc-Graw Hill, Inc., New York, 1994).
-
J. Baggett and L. Trefethen, “Low-dimensional models of subcritical transition to turbulence,”Phys. Fluids 9, 1043 (1997).
APPENDICES
