ABSTRACT / SUMMARY

Osbourne Reynolds experiment is used 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. The design of the apparatus allowed studying the characteristic of the flow of the fluid in the pipe, the behaviour of the flow and also to calculate the range for the laminar and turbulent flow where the calculation is used to prove the Reynolds number is dimensionless by using the Reynolds Number formula. For the first and second objectives, it involve running the Osborne Reynolds equipment with different of water volume flow rate. In this experiment we fix the time, which is 5 second to collect the amount of water. At the same time we also observe the characteristic of the flow, there are laminar, transition and turbulent flow. From the data collected we made calculation to estimate the range for laminar and turbulent flow. To prove that the Reynolds number is dimensionless, we calculate by using the units only and using the appropriate formula, it is proved that the Reynolds number is dimensionless

INTRODUCTION

The apparatus used here to demonstrate ‘critical velocity’ is based on that used by Professor Reynolds who demonstrated the nature of the two modes of motion flowing in a tube, example laminar and turbulent. The unit is designed to be mounted on P6100 hydraulic Bench and the quantity of water flowing through it can be measured and timed using the Hydraulic Bench Volumetric Tank and a suitable stopwatch. A bell mounted glass tube 790mm long overall by 16mm bore is mounted horizontally and concentrically in a much larger diameter tube fitted with baffles. A uniform supply of water can then be made to flow along the 16mm bore tube.

The unit is fitted with a constant head tank and the flow rate which can be varied by adjustment to the head tank height, can be measured using the volumetric tank.

A dye injector is situated at the entrance to the 16 mm bore tube and thus it is possible to detect whether the flow is streamline or turbulent.

Critical velocities and Reynolds number

Reynolds obtained the loss of pressure head in a pipe at different flow rates by measuring the loss head (hf) over a known length of pipe (l), from this slope of the hydraulic gradient (i) was obtained.

i=hfl

When Reynolds plotted the results of his investigation of how energy head loss varied with the velocity of flow, he obtained two distinct regions separated by a transition zone. In the laminar region the energy loss per unit length of pipe is directly proportional to the mean velocity. In the turbulent flow region the energy loss per unit length of pipe is proportional to the mean velocity raised to some power, ƞ. The value of ƞ being influenced by the roughness of the pipe wall.

hflα v1.7 For smooth pipes in this region but

hflα v2 for very rough pipes.

Examplehflα v1.7¿2.¿. The dimensionless unit Reynolds number (Re) = ρvd/μ and has a value

below 2000 for laminar flow and above 4000 for turbulent flow (when any consistent set of units is used) – the transition zone lying in the region of Re 2000 – 4000 (example ‘lower

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critical velocity’ LCV at Reynolds number of 2000 and ‘upper critical velocity’ UCV at a Reynolds number of 4000)

Note that the value of Re obtained in experiments made with ‘increasing’ rates of flow will depend on the degree of care which has been taken to eliminate disturbance in the supply and along the pipe. On the other hand, experiment made with ‘decreasing’ flow rates will show a value of Re which is very much less dependent on initial disturbance.

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AIMS

The objective of this laboratory experiment is to demonstrate the differences between laminar, turbulent, and transitional fluid flow, and the Reynolds’s numbers at which each occurs.

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THEORY

Laminar and turbulent flow

Professor Osborne Reynolds (1842-1912) first realized that there was a ‘critical velocity’ at which the law relating loss of pressure energy and velocity in pipe flow changed. He first demonstrated this with his famous ‘Color Band’ (on the die-line) experiment. This consisted of injecting a line jet of dye into the flow of water visible through a transparent pipe. At low velocities the dye-line was unbroken, but as the velocity of the flow through the pipe was increased, the dye-line broke up and eddies were seen to form. From this and further experiments, he came to the conclusion that there are two distinct types of flow:-

1. Streamline or Laminar Flow (Latin lamina = layer of thin sheet). The fluid moves in layers without irregular fluctuation in velocity. Laminar flow occurs at low Reynolds Numbers. (The flow of oil in bearing is Laminar).

2. Turbulent flow. This results in the fluid particles moving in irregular patterns carrying an exchange of momentum from one portion of the fluid to another.

Reynolds investigated these two different types of motion and concluded that the parameters which were involved in the flow characteristics were

Ρ the density of the fluid kg/m3

v the velocity of the flow of the fluid m/sd Diameter of pipe mμ the coefficient of viscosity of the fluid Ns/m2

He arrived at a dimensionless constant (Reynolds number)

(Re)=ρvd/μ

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The value of which was concerned with the fluid motion. Fluid motion was found to be laminar for Re numbers below 2000 and turbulent flows for Re greater than 4000.

APPARATUS

1) OSBOURNE REYNOLDS APPARTUS – [Figure 1]

Consist of:-

Dye Injection Vessel Water Inlet Dye Injector Clear Acrylic Tube Baffles Glass tube 16mm Boro P6100 Hydraulic Bench Feet on P6248 Base Locate on P6100 Overflow pipe Discharge from Glass Tube Inlet to flow Apparatus Position Locking Collet Variable Height header tank (Inlet to Flow Apparatus)

2) Beaker3) Measuring Cylinder4) Stopwatch

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[Figure 1- Osbourne Reynolds Apparatus]

METHODOLOGY / PROCEDURE

Setting up the apparatus

The Hydraulic Bench (P6100) is mounted on the apparatus at the locating spigots of the working surfaces so that the unit straddles the weir trough and the outlet feeds into measuring tank. P6100 Hydraulic Bench at the variable height header tank is connected to the water supply which it is mounted on its support stand. The water supply was turned on and ensured that all the air in the systems displaced prior to proceeding with the investigation. The water flow is regulating to give a steady flow in the system with water just trickling out of the header tank overflow. The water level in the flow system must be above the inner bell mouthed glass tube.

Measuring flow-rate

The flow rate of water is measured through the apparatus and achieved by using the Hydraulic Bench volumetric measuring tank or smaller graduated vessel (not supplied), which is used to collect the known quantity of water.

Demonstration of the difference between laminar and turbulent

This experiment demonstrated the visually laminar (streamline) flow and its transition to turbulent flow at a particular velocity.

1. The apparatus is set up with the dye reservoir is fitted and filled, and with a steady flow of water through the inner tube.

2. The small cock on the base of reservoir is opened to permit dye to flow from the nozzle at the entrance to the channel. The colored dye will be visible along the passage. If the dye accumulates around the nozzle, the velocity of the water flow in

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the passage has to be increased or regulate the flow from the dye reservoir. The adjustments of the dye flow are made up by using the tube outlet tap.

3. The stream will be visible along the whole length of the passage under laminar flow conditions. If it not so, the water flow is reduced until continuous stream of dye is visible along the passage.

4. The water flow rate is increased by raising the height of the variable head tank and the condition of the fluid in the channel carefully note, for example, the streamline and turbulent. The height of head tank is increased until instability of water flow leading to the break up of the dye system is occurred.

5. The break up position in the passage is noted and the corresponding value of the flow rate is measured by timing the collection of known amount of water in the volumetric measuring tank.

6. The dose is maintain and the observation of the passage is continued further increasing the flow rate until the whole system is turbulent with no visible dye stream at any point.

RESULTS

No. Of Rotation No. Of Reading (mL)

Average Reading (m3)

Reynolds Number

Description

1222423

2.3 x 10-5 613.3 Laminar

2484644

4.6 x 10-5 1220.56 Laminar

3525652

5.333 x 10-5 1415.06 Laminar

4726477

7.1 x 10-5 1866.14 Laminar

5767476

7.533 x 10-5 1998.81 Laminar

6808888

8.533 x 10-5 2210.10 Transition

7927678

8.2 x 10-5 2175.79 Transition

81009098

9.6 x 10-5 2547.26 Transition

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91109298

1 x 10-4 2653.40 Transition

10106124118

1.16 x 10-4 3077.94 Transition

11128134134

1.32 x 10-4 3520.49 Transition

12124138144

1.3533 x 10-4 3590.05 Transition

13138148148

1.4467 x 10-4 3820.9 Transition

14174156152

160.67 4264.27 Turbulent

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CALCULATIONS

Bell mounted glass tube (length =790 mm, diameter=16mm)

Therefore the area,A = πd²/4 = 2.01×10-4 m²

Reynolds number (dimensionless constant)

Q = ѵs (m³/s)

Q = volumetric flowrateѴ= volume s= time

V = QA

V=VelocityA=Area of the pipe

Re = ρvdμ

Where,

ρ = density (kg/m³ )

d = diameter (m)

V = velocity (m/s)

µ = viscosity (kg/ms)

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Water density,ρ = 1000 kg/m³

Water viscosity, µ = 1.0× 10 ³kg/msˉ

NUMBER

OF

ROTATION

VELOCITY

(m/s)Re = ρvdμ

DESCRIPTION

1 V(ml)= 23 ml

V(m³)= 2.3 x 10 ⁵ m³ˉ

Q = 2.3x 10 ˉ ⁵m ³

3 s

= 7.667 x 10 ⁶ m³/sˉ

Velocity = 7.667 x 10 ˉ ⁶ m

3

s2.01×10 ˉ ⁴m2

=0.03833 m/s

Re=1000(0.03833)(0.016)

1.0×10 ˉ ³ .

= 613.33 Laminar

2 V(ml)= 46 ml

V(m³)= 4.6 x 10 ⁵ m³ˉ

Q = 4.6 x10 ˉ ⁵m ³

3 s

= 1.533 x 10 ⁵ m³/sˉ

Velocity = 1.533 x 10ˉ ⁵m

3

s2.01×10 ˉ ⁴m2

=0.07629 m/s

Re=1000(0.07629)(0.016)

1.0×10 ˉ ³ .

= 1220.56 Laminar

3 V(ml)= 53.33 ml

V(m³)= 5.333 x 10 ⁵ m³ˉ

Q = 5.333 x 10ˉ ⁵m³

3 s

= 1.778 x 10 ⁵ m³/sˉ

Velocity = 1.778 x 10ˉ ⁵m

3

s2.01×10 ˉ ⁴m2

=0.08844 m/s

Re=1000(0.08844)(0.016)

1.0×10 ˉ ³ .

=1415.06 Laminar

4 V(ml)= 70.33 ml Re=1000(0.1166)(0.016)

1.0×10ˉ ³ .

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V(m³)= 7.033 x 10 ⁵ m³ˉ

Q = 7.033 x 10ˉ ⁵m³

3 s

= 2.344 x 10 ⁵ m³/sˉ

Velocity = 2.344 x10 ˉ ⁵ m

3

s2.01×10 ˉ ⁴m2

=0.1166 m/s

= 1866.14 Laminar

5 V(ml)= 75.33 ml

V(m³)= 7.533 x 10 ⁵ m³ˉ

Q = 7.533 x 10ˉ ⁵m³

3 s

= 2.511x 10 ⁵ m³/sˉ

Velocity = 2.511 x10 ˉ ⁵m

3

s2.01×10ˉ ⁴m2

=0.1249 m/s

Re=1000(0.1249)(0.016)

1.0×10 ˉ ³ .

= 1998.81 Laminar

6 V(ml)= 83.67 ml

V(m³)= 8.367 x 10 ⁵ m³ˉ

Q = 8.367 x10 ˉ ⁵m ³

3 s

= 2.789 x 10 ⁵ m³/sˉ

Velocity = 2.789x 10ˉ ⁵m

3

s2.01×10 ˉ ⁴m2

=0.1388 m/s

Re=1000(0.1388)(0.016)

1.0×10 ˉ ³ .

= 2220.10 Transition

7 V(ml)= 82 ml

V(m³)= 8.2 x 10 ⁵ m³ˉ

Q = 8.2 x 10ˉ ⁵m ³

3 s

= 2.733 x 10 ⁵ m³/sˉ

Velocity = 2.733x 10ˉ ⁵m

3

s2.01×10 ˉ ⁴m2

=0.1360 m/s

Re=1000(0.1360)(0.016)

1.0×10 ˉ ³ .

= 2175.79 Transition

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8 V(ml)= 96 ml

V(m³)= 9.6 x 10 ⁵ m³ˉ

Q = 9.6 x10 ˉ ⁵m ³

3 s

= 3.2 x 10 ⁵ m³/sˉ

Velocity = 3.2 x10 ˉ ⁵ m

3

s2.01×10ˉ ⁴m2

=0.1592 m/s

Re=1000(0.1592)(0.016)

1.0×10ˉ ³ .

= 2547.26 Transition

9 V(ml)= 100 ml

V(m³)= 1.0 x 10 ⁴m³ˉ

Q = 1.0x 10ˉ ⁴m ³

3 s

= 3.333 x 10 ⁵ m³/sˉ

Velocity = 2.733x 10ˉ ⁵m

3

s2.01×10 ˉ ⁴m2

=0.1658 m/s

Re=1000(0.1658)(0.016)

1.0×10 ˉ ³ .

= 2653.40 Transition

10 V(ml)= 116 ml

V(m³)= 1.16 x 10 ⁴m³ˉ

Q = 1.16 x 10 ˉ ⁴m ³

3 s

= 3.867 x 10 ⁵ m³/sˉ

Velocity = 3.867 x 10 ˉ ⁵m

3

s2.01×10 ˉ ⁴m2

=0.1924 m/s

Re=1000(0.1924)(0.016)

1.0×10 ˉ ³ .

= 3077.94 Transition

11 V(ml)= 132 ml

V(m³)= 1.32 x 10 ⁴m³ˉ

Q = 1.32 x10 ˉ ⁴m ³

3 s

= 4.4 x 10 ⁵ m³/sˉ

Velocity = 4.4 x 10ˉ ⁵m

3

s2.01×10ˉ ⁴m2

Re=1000(0.2189)(0.016)

1.0×10 ˉ ³ .

= 3502.49 Transition

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=0.2189 m/s

12 V(ml)= 135.33 ml

V(m³)= 1.353 x 10 ⁴m³ˉ

Q = 1.353 x 10ˉ ⁴m ³

3 s

= 4.51 x 10 ⁵ m³/sˉ

Velocity = 4.51 x10 ˉ ⁵m

3

s2.01×10 ˉ ⁴m2

=0.2244 m/s

Re=1000(0.2244)(0.016)

1.0×10 ˉ ³ .

= 3590.05 Transition

13 V(ml)= 144 ml

V(m³)= 1.44 x 10 ⁴m³ˉ

Q = 1.44 x10 ˉ ⁴m ³

3 s

= 4.8 x 10 ⁵ m³/sˉ

Velocity = 4.8 x 10ˉ ⁵ m

3

s2.01×10ˉ ⁴m2

=0.2388 m/s

Re=1000(0.2388)(0.016)

1.0×10 ˉ ³ .

= 3820.9 Transition

14 V(ml)= 160.67 ml

V(m³)= 1.607 x 10 ⁴m³ˉ

Q = 1.607 x 10 ˉ ⁴m ³

3 s

= 5.357 x 10 ⁵ m³/sˉ

Velocity = 5.357x 10 ˉ ⁵m

3

s2.01×10 ˉ ⁴m2

=0.2665 m/s

Re=1000(0.2665)(0.016)

1.0×10 ˉ ³ .

= 4264.27

DISCUSSION

Laminar flow- highly ordered fluid motion with smooth streamlines.

Transition flow -a flow that contains both laminar and turbulent regions.

Turbulent flow -a highly disordered fluid motion characterized by velocity and fluctuations and eddies.

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According to the Reynolds`s experiment, laminar flow will occur when a thin filament of dye injected into laminar flow appears as a single line. There is no dispersion of dye throughout the flow, except the slow dispersion due to molecular motion. While for turbulent flow, if a dye filament injected into a turbulent flow, it disperse quickly throughout the flow field, the lines of dye breaks into myriad entangled threads of dye.

In this experiment we have to firstly is to observe the characteristic of the flow of the fluid in the pipe, which may be laminar or turbulent flow by measuring the Reynolds number and the behaviour of the flow, secondly to calculate the range for the laminar and turbulent flow and lastly to prove the Reynolds number is dimensionless by using the Reynolds number formula.

After complete preparing and setup the equipment we run this experiment. But firstly we have to calculate the area of bell mounted glass tube, the viscosity of water and the density of water. The density of water is 1000 kg/m³, the area of glass tube is 2.01×10-4 m², while the viscosity of water is 1.0× 10 ³ˉ kg/ms, this is done for easy step by step calculation.

We observe that the red dye 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’s not occurs suddenly.

CONCLUSION

As the water flow rate increase, the Reynolds number calculated also increase and the red dye line change from thin thread to swirling in shape.

Laminar flow occurs when the Reynolds number calculated is below than 2300; transitional flow occurs when Reynolds number calculated is between 2300 and 4000 while turbulent flow occurs when Reynolds number calculated is above 4000.

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It is proved that the Reynolds equation is dimensionless, no units left after the calculation

In this experiment, Osbourne Reynolds apparatus was used 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. The design of the apparatus allowed us to study the characteristic of the flow of the fluid in the pipe, the behaviour of the flow and also to calculate the range for the laminar and turbulent flow where the calculation is used to prove the Reynolds number is dimensionless by using the Reynolds Number formula.

With the data gathered, it was found that as water flow rate is increasing, the Reynolds number will automatically increase as well, and the 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. After 3 trials, our group computed a Reynolds number which is more than 4000 for every trial, thus, the flow is turbulent.

The values calculated in results section might not be exactly 100% correct due to several

reasons. 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.

Also, do this experiment at steady place, control the clip and valve carefully to get long thin of

laminar dye flow, and remove the beaker which uses to collect the amount of water at sharp when

the time is up, to avoid error flow rate error. Lastly, 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.

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RECOMMENDATIONS

Compare with the result diagram in the laboratory, there are bit different between the

results collected. This might be some of 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.

During the experiment there are several precaution steps that need to be alert. The

experiment should be 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 must be regulate slow

and carefully. When removing the beaker from the exit valve, we notice that some water still

enter the beaker because of the slow response between the person who guide the stop watch and

collecting beaker. So to avoid this parallax error, it is better to take same person who guard the stop

watch and the collecting beaker.

Lastly, do this experiment at steady place, control the clip and valve carefully to get long thin

of laminar dye flow, and remove the beaker which uses to collect the amount of water at sharp

when the time is up, to avoid error flow rate error.

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REFERENCE

Online Journal

1) High-Reynolds number Rayleigh-Taylor turbulence Authors: D. Livescu; J. R. Ristorcelli; R. A. Gore; S. H. Deana; W. H. Cabot; A. W. CookDOI: 10.1080/14685240902870448Published in: Journal of Turbulence, Volume 10, N 13 2009First Published on: 01 January 2009Subjects: Aerospace Engineering; Applied Mechanics; Astrophysics; Computational Physics; Fluid Dynamics; Fluid Mechanics; Meteorology; Oceanography; Physical Oceanography; Plasmas & Fluids; Statistical Physics;

2) Structure of a high-Reynolds-number turbulent wake in supersonic flowJ. P.  Bonnet, V.  Jayaraman and T. Alziary De  Roquefort Laboratoire d'Etudes Aérodynamiques et Thermiques, Laboratoire Associé au C.N.R.S. 191, Centre d'Etudes Aérodynamiques et Thermiques, 43 Route de l'Aérodrome, 86000 Poitiers, France.Journal of Fluid Mechanics (1984), 143:277-304 Cambridge University PressCopyright © 1984 Cambridge University Pressdoi:10.1017/S002211208400135X

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APPENDIX

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