Reynolds Experiment

Summary: The main objective of this experiment was to manifold the classical experiments conducted by Professor Osborne Reynolds concerning fluid flow condition. Flows are of different types. They are: laminar, turbulent and transitional. The behavior of a fluid, particularly with regard to energy loss, is quite dependent on whether the flow is laminar or turbulent. For this reason, we want to have a means of predicting the type of flow without actually observing it. It can be shown experimentally and verified analytically that the character of a flow in a round pipe depends on four variables: fluid density ρ, fluid viscosity μ, pipe diameter D, and average velocity of flow v. Osborne Reynolds was the first to demonstrate that laminar or turbulent flow can be predicted if the magnitude of a dimensionless number, now called the Reynolds number is known. It is actually the ratio of the inertia force on the element of fluid to the viscous force. The inertia force is developed from Newton’s second law of motion. On the other hand, the viscous force is related to the product of the shear stress times area. Flows having large Reynolds numbers, typically because of high velocity or low viscosity, tend to be turbulent. Those fluids having high viscosity or moving at low velocities will have low Reynolds numbers and will tend to be laminar. For practical applications in pipe flow we find that if the Reynolds number for the flow is less than 2000, the flow will be laminar. Also, if the Reynolds number is greater than 4000, the flow can be assumed to be turbulent. In the range of Reynolds numbers between 2000 and 4000, it is impossible to predict which type of flow exists; therefore this range is called the critical or transitional region. In this experiment, using Reynolds apparatus a vegetable dye is flown through at different velocity which is of almost same density and concentration as that of the fluid. In steady flow condition fluid flow rates was observed through a visualization pipe and a valve at the discharge end was used to control the flow. The visual flow conditions were observed for various flow rates in steady flow condition. And from collected data Reynolds Number was calculated using the Reynolds Number equation. Reynolds number was found to be varied from 141.8 to 4884.84. The values calculated from this experiment for different flows were about similar to the visual dye conditions observed. Although some deviations that have taken place were due to the experimental error.

EXPERIMENTAL SETUP: The apparatus used in this experiment are:  Hydraulic Bench  Osborne Reynolds’ Apparatus  Measuring Cylinder  Stopwatch  Vegetable dye  Thermometer

Observed data: Internal diameter of visualization pipe =11𝑚𝑚 = .011𝑚 Temperature of water =29℃ Density of water at 29◦C = 995.96 (From interpolation in table A.1) Viscosity of water at 29◦C =. 8164 × 10−3 (From interpolation)

Table 01: Table for the observed data like volume of water collected, time & visual dye conditions of Reynolds experiment is given below: No of observation

Time (sec)

Visual dye condition

1

Volume of water collected (cm3) 60

60

Straight

2

190

30

Straight

3

260

20

Slightly dispersed

4

260

21

Slightly dispersed

5

355

10

Dispersed

6

275

8

Dispersed

Calculated data: Table 02: Data for volumetric flow rate, Reynolds number & flow type are given below: No of observation

1

Volumetric flow rate (cm3/s) 1

Area of the tube (cm2)

Average velocity

Reynolds number

1.05

141.21

2

6.33

6.66

894.31

3

13

13.68

1835.69

4

12.38

13.03

1748.28

5

35.5

37.36

5012.85

6

34.375

36.17

4853.99

.95033

Sample Calculation: Internal diameter of visualization pipe, D = 11𝑚𝑚 = 1.1 𝑐𝑚 = .011𝑚 Area of the pipe, A=

𝜋×𝐷 2 4

=

3.1416×(1.1)2 4

𝑐𝑚2 = .95033 𝑐𝑚2

Sample calculation for observation no 5: Volume of water collected, V= 355𝑐𝑚3 Time of water collection, t = 10 𝑠𝑒𝑐 𝑉

Volumetric flow rate of water, Q = 𝑡 = Velocity, v =

𝑄 𝐴

=

35.5 .95033

355 10

𝑐𝑚 = 35.5𝑐𝑚

𝑐𝑚/𝑠𝑒𝑐 = 37.36 𝑐𝑚/𝑠𝑒𝑐

Density of water at 29℃, ρ = 995.96 𝑘𝑔/𝑚3 Viscosity of water at 29℃, μ = . 8164 × 10−3 𝑃𝑎. 𝑠𝑒𝑐 ∴ Reynolds number, Re =

𝐷𝑣𝜌 𝜇

=

.011×.3736×995.96 .8164×10−3

= 5012.85

Results & Discussions: Table 03: Results of this experiment are given below: No of observation

Volumetric flow rate (cm3/sec)

Visual dye condition

Reynolds number Re

Flow type

1

1

Straight

141.21

Laminar

2

6.33

Straight

894.31

Laminar

3

13

Slightly dispersed

1835.69

Transition

4

12.38

Slightly Dispersed

1748.28

Transition

5

35.5

Dispersed

5012.85

Turbulent

6

34.375

Dispersed

4853.99

Turbulent

 General acquisition of related ideas: The experiment was carried out to investigate the characteristic of the flow of the liquid in the pipe which is also used to determine the Reynolds Number for each state of the flow. There are three types of flow that we study in this experiment. Firstly, laminar flow which is the type of flow in which the particles move in a straight line in the form of thin parallel sheets. Laminar flow denotes a steady condition where all stream lines follow parallel paths. Under this condition, the dye will remain easily identifiable as a solid core. There is no dispersion of dye throughout the flow, except the slow dispersion due to molecular motion. Then, turbulent flow which is the type of flow in which the particles move in a zigzag pattern. Turbulent flow denotes as unsteady condition where stream lines interact causing shear plan collapse and mixing occurs. For turbulent flow, if a dye filament injected into a turbulent flow, it disperse quickly throughout the flow fluid, the lines of dye breaks into myriad entangled threads of dye As the flow rate is increased, the transition from laminar to turbulent flow is a gradual process. This zone of change is defined as transitional flow. This will appear as a wandering dye stream prior to dispersion as turbulence occurs. So, when the flow changes from laminar to turbulent or vice verse a disturbance is created, it is called as the transitional flow.

After preparing the experimental setup and gathering some knowledge about the proceedings, we started the experiment. We observed that the red eye line change with the increasing of water flow rate. The shape change from thin threads to slightly swirling which still contains smooth thin threads and then fully swirling. We can say that this change is from laminar flow to transitional flow and then to turbulent flow and it does not occur suddenly. We must control the water inlet valve and outlet valve until the flow formed. For lower critical velocity, it is the velocity at which laminar flow stops and for upper critical velocity it is where a turbulent flow starts. The results obtained (volumetric flow rate & Reynolds number) from our experiment are interpreted below:

 Interpretation of results: Observation no 1 & 2: For the first two observations, the flow rates were very small (1 and 6.33 cm3/sec respectively). The jet of colored water was observed to flow intact along with the mainstream and no cross mixing occurred. The water was flowing in straight lines and the flow was laminar. The experimentally obtained Reynolds numbers for these two observations were 141.21 & 894.31 respectively. Observation no 3 & 4: For these two observations, the flow rates were moderate (13 and 12.38 cm3/sec respectively). The line of dye was not smooth and the width of the streak line was changing in both cases. The streak line width was changing periodically from top to bottom indicating that the flow was wavy and was in transition region. The experimentally obtained Reynolds numbers were 1835.69 & 1748.28 which was in accordance with our observations. Observation no 5 & 6: For these two observations, the flow rates were large (35.5 and 34.375 cm3/sec respectively). The steak line was observed in dispersed condition. The dye was falling with great velocity. The movement of dye was understood in the path of flow. Visual dye condition indicates that the flow was turbulent which was supported by our calculated values of Reynolds Number- 5012.85 & 4853.99.  Comparison between theoretical & experimental results: As our main objective was to compare the Reynolds number (Re) with the observed flow type we will check it now. The three fluid flow conditions – laminar, transitional, turbulent flow can be detected by calculating Reynolds Number. It has been internationally recognized that:   

A flow having Reynolds number less than 2100 is defined as laminar flow. The flow is called a transitional flow if it has Reynolds number between 2100 and 4000. A flow having Reynolds number more than 4000 is a turbulent flow. Our experimentally obtained Reynolds number and observation of dye shows the flow to

be Laminar for Re = 141.21-894.31  Transition for Re = 1748.28-1835.69 ( experimental error here )  Turbulent for Re = 5012.85-4853.99 It can be said from above discussions that our experimental results support the theory provided by Osborne Reynolds within some experimental errors obtained in observation no 3 & 4.

 Precautionary measures & probable causes of error: The experiment was done very carefully and responsibly to reproduce the actual fluid flow phenomena observed by Professor Osborne Reynolds. The application of Reynolds number in determining the flow condition is definitely convenient and precise. The accuracy of the result depended much on the determination of velocity of flow. The precautionary measures & probable causes of error are listed below: The experiment was done at suitable and unshaken place. To get appropriate laminar smooth stream flow, the clip and the valve which control the injection of red dye was regulated slowly and carefully. Constant water level mechanism maintained a constant water-head during the experiment. A vegetable dye having a density similar to water was used in the apparatus. Heavier or lighter dyes would have resulted in differences between fluid velocity and dye velocity resulting in artificial visualization of flow conditions. If concentrated dyes were used, rapid coloration of the water in the setup tank would have occurred resulting in loss of definition. The viscosity and density of the dye was near to that of the fluid but not exactly the same. For this reason when the dye mixed up with the water they differed a little in the velocity as their density and viscosity is different. Though glass-marbles were used to eliminate the effect of bubbling, it was not possible to fully eradicate that. The observation tube was dirty and in spite of close observations, it was difficult to be sure about the original visual flow conditions. There might be some parallax error such as the slow response during collecting the water, the position of eyes during taking the value of water volume, time taken for the volume of water and regulating the valve which control the flow rate of water unstably. Although for the reasons stated above, exact values of Reynolds number could not be calculated, it may be concluded that, the experiment was technically correct and the objective of reproducing the classical experiment conducted by professor Osborne Reynolds related to the fluid flow at different conditions and demonstrating various flow regimes was fulfilled.  Recommendations: Based on this experiment, there are many ways to improve the experiment and obtain the best results which are given below: Firstly, the experiment should be repeated three times in order to get average readings. This will reduce the deviation from theoretical results.(Observation no 3 & 4) While conducting the experiment, there were some errors such as the slow response when collecting the water in the beaker once we get the flow regime. Besides, the slow response to start the time taken for the volume of water and regulating the valve which control the flow

rate of water. So, the person in charged should be more alert and focus during the experiment in order to obtain the accurate result. There were also some parallax errors while conducting the experiment. For instant, the position of the eyes during taking the value of water volume is not in the same level with the readings. Therefore, the readings taken from the beaker should be taken at eye level which is perpendicular to our eyes to avoid parallax error. The experiment should be done at suitable and unshaken place which was followed during conducting our experiment. Also, to get appropriate laminar smooth stream flow, the clip and the valve which control the injection of blue dye must be regulated slowly and carefully. When removing the beaker from the exit valve, we noticed that some water still enter the beaker. So, to avoid this it is better to take same person who guard the stop watch and the collecting beaker. Last but not least, we must study the lab manual that have been given to us before start up the experiment. We also can improve our skill and knowledge to ensure that experiment can be done smoothly.