LAB REPORT Osbourne Reynolds Apparatus

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.

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, . The value of being influenced by the roughness of the pipe wall. For smooth pipes in this region but for very rough pipes.Example. The dimensionless unit Reynolds number (Re) = vd/ 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 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.

AIMS

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

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

the density of the fluidkg/m3vthe velocity of the flow of the fluidm/sdDiameter of pipemthe coefficient of viscosity of the fluidNs/m2

He arrived at a dimensionless constant (Reynolds number)

(Re)=vd/

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

[Figure 1- Osbourne Reynolds Apparatus]METHODOLOGY / PROCEDURE

Setting up the apparatusThe 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 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 RotationNo. Of Reading (mL)Average Reading (m3)Reynolds NumberDescription

12224232.3 x 10-5613.3Laminar

24846444.6 x 10-51220.56Laminar

35256525.333 x 10-51415.06Laminar

47264777.1 x 10-51866.14Laminar

57674767.533 x 10-51998.81Laminar

68088888.533 x 10-52210.10Transition

79276788.2 x 10-52175.79Transition

810090989.6 x 10-52547.26Transition

911092981 x 10-42653.40Transition

101061241181.16 x 10-43077.94Transition

111281341341.32 x 10-43520.49Transition

121241381441.3533 x 10-43590.05Transition

131381481481.4467 x 10-43820.9Transition

14174156152160.674264.27Turbulent

CALCULATIONS

Bell mounted glass tube (length =790 mm, diameter=16mm) Therefore the area,A = d/4 = 2.0110-4 mReynolds number (dimensionless constant)

Q = (m/s)

Q = volumetric flowrate= volume s= time

V =

V=VelocityA=Area of the pipe

Re =

Where, = density (kg/m )d = diameter (m)V = velocity (m/s) = viscosity (kg/ms)Water density, = 1000 kg/m Water viscosity, = 1.0 10kg/ms

NUMBER OF ROTATIONVELOCITY(m/s)Re =

DESCRIPTION

1V(ml)= 23 mlV(m)= 2.3 x 10 mQ = = 7.667 x 10 m/sVelocity = =0.03833 m/sRe== 613.33

Laminar


Laminar

3V(ml)= 53.33 mlV(m)= 5.333 x 10 mQ = = 1.778 x 10 m/sVelocity = =0.08844 m/sRe==1415.06

Laminar

4V(ml)= 70.33 mlV(m)= 7.033 x 10 mQ = = 2.344 x 10 m/sVelocity = =0.1166 m/sRe== 1866.14

Laminar

5V(ml)= 75.33 mlV(m)= 7.533 x 10 mQ = = 2.511x 10 m/sVelocity = =0.1249 m/sRe== 1998.81

Laminar

6V(ml)= 83.67 mlV(m)= 8.367 x 10 mQ = = 2.789 x 10 m/sVelocity = =0.1388 m/sRe== 2220.10

Transition


Transition


Transition

9V(ml)= 100 mlV(m)= 1.0 x 10mQ = = 3.333 x 10 m/sVelocity = =0.1658 m/sRe== 2653.40

Transition


Transition


Transition

12V(ml)= 135.33 mlV(m)= 1.353 x 10mQ = = 4.51 x 10 m/sVelocity = =0.2244 m/sRe== 3590.05

Transition


Transition

14V(ml)= 160.67 mlV(m)= 1.607 x 10mQ = = 5.357 x 10 m/sVelocity = =0.2665 m/sRe== 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.

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/m, the area of glass tube is 2.0110-4 m, while the viscosity of water is 1.0 10kg/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 its 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.

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

RECOMMENDATIONS

Compare with the result diagram in the laboratory, there are bit different between theresults collected. This might be some of parallax error such as the slow response duringcollecting 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. Theexperiment should be done at suitable and unshaken place. To get appropriate laminar smoothstream flow, the clip and the valve which control the injection of red dye must be regulate slowand carefully. When removing the beaker from the exit valve, we notice that some water stillenter 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.

REFERENCE

Online Journal1) High-Reynolds number Rayleigh-Taylor turbulenceAuthors:D. Livescu;J. R. Ristorcelli;R. A. Gore;S. H. Deana;W. H. Cabot;A. W. CookDOI:10.1080/14685240902870448Published in:Journal of Turbulence, Volume10, N132009First 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 andT. Alziary DeRoquefortLaboratoire d'Etudes Arodynamiques et Thermiques, Laboratoire Associ au C.N.R.S. 191, Centre d'Etudes Arodynamiques et Thermiques, 43 Route de l'Arodrome, 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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LAB REPORT Osbourne Reynolds Apparatus