ABSTRACT

In this experiment, the characteristics of the flow in a fluid in a pipe were measured by using Reynolds number. The objective for this experiment were to compute Reynolds number (Re) and to observe laminar, transitional, and turbulent flow.

There were several steps taken to conduct the experiment. Inlet valve, V1, was opened to allow water to enter the stilling tank and was allowed to settle for a few minutes before flowing into the visualisation tube. Dye was injected into the stream to identify the current flow in the tube. Water inlet valve, V1, and outlet valve, V2, were regulated until a straight identifiable dye line is achieved. The flow rate at the outlet valve, V2, was measured using volumetric method. Constant the time taken for each collected volume of water and replicate it 3 times. The experiment was repeated in the same manner but regulate V1 and V2 to produce transitional and turbulent flow.

The result of Reynolds number obtained from the experiment were 177 for laminar flow, 2826.36 for transitional flow and 4098 for turbulent flow.

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TABLE OF CONTENT

INDEX PAGE

INTRODUCTION 3

OBJECTIVES 4

THEORY 5

DIAGRAM AND DESCRIPTON OF APPARATUS 6

PROCEDURES 8

RESULTS AND DISCUSSION 9

SAMPLE CALCULATIONS 12

CONCLUSION 12

RECOMMENDATION 13

REFERENCES 13

APPENDICES 14

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INTRODUCTION

Reynolds number, denoted as Re, is said to be a dimensionless quantity that

is used to help predict similar flow patterns in different fluid flow situations. For flow

in a pipe or a sphere moving in a fluid the diameter is generally used today. Other

shapes (such as rectangular pipes or non-spherical objects) have an equivalent

diameter defined. For fluids of variable density (e.g. compressible gasses) or

variable viscosity (non-Newtonian fluids) special rules apply. The velocity may also

be a matter of convention in some circumstances, notably stirred vessels.

The Reynolds number is defined as the ratio of inertial forces

to viscous forces and consequently quantifies the relative importance of these two

types of forces for given flow conditions. Reynolds numbers frequently arise when

performing scaling of fluid dynamics problems, and as such can be used to

determine dynamic similitude between two different cases of fluid flow. They are also

used to characterize different flow regimes within a similar fluid, such

as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where

viscous forces are dominant, and is characterized by smooth, constant fluid motion;

turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces,

which tend to produce chaotic eddies, vortices and other flow instabilities.

In practice, matching the Reynolds number is not on its own sufficient to

guarantee similitude. Fluid flow is generally chaotic, and very small changes to

shape and surface roughness can result in very different flows. Nevertheless,

Reynolds numbers are a very important guide and are widely used.

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The Reynolds experiment is conducted to observe and determine the type of

flow of a water stream in a glass tube and to determine its Reynolds number. This

experiment is done by injecting red dye into the stream and the flow of the red dye is

observed. To calculate the Reynolds number of the water stream, the volume of the

outflow water stream is measured using a measuring cylinder at a constant time

taken. With the given and obtained information, all are then used into the formula;

ℜ= ρνdμ

OBJECTIVE

The purpose of the Reynolds experiment is to illustrate laminar, transitional

(intermittently turbulent), and fully turbulent pipe flows along with the conditions

under which these types of flow occur, to compute Reynolds number (Re), and to

prove that the Reynolds number is dimensionless.

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THEORY

Reynolds number can be defined for a number of different situations where a

fluid is in relative motion to a surface. The definitions generally include the fluid

properties of density, ρ and viscosity, μ, plus a velocity, ν, and a characteristic length

or characteristic dimension, d. This dimension is a matter of convention for example

a radius or diameters are equally valid for spheres or circles, but one is chosen by

convention.

The critical velocity, v averaged over the cross section at which laminar pipe

flow changes to transitional flow, or transitional flow changes to turbulent flow, is

believed to be a function primarily of the pipe diameter, d, the fluid density, ρ, and

the fluid dynamic viscosity, μ. In mathematical terms,

V=V (d , ρ, μ)

Using dimensional reasoning, one can show that the relation among the

parameters must be;

ℜ= ρνdμ = dimensionless parameter

It is a ratio of the inertial (destabilizing) force to the viscous damping

(stabilizing) force. As Re increases, the inertial forces grow relatively larger, and the

flow gets destabilized into full-blown turbulence.

The Reynolds experiment used to demonstrate the critical velocity based on

the nature of the two modes of motion flowing in a tube, i. e. laminar and turbulent.

Reynolds investigated these two fluid motions. Fluid motion was found to be laminar

for Re numbers below 2000 and turbulent flows for Re greater than 4000. Thus, the

critical velocity, v will be directly proportional to the mass flow rate, m.

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DIAGRAM AND DESCRIPTION OF APPARATUS

Reynolds flow apparatus: dye injector, stilling tank, glass tube

300 ml measuring cylinder

A stopwatch

Color dye

Figure 1: Schematic diagram of an Osbourne Reynolds apparatus

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Figure 2: Osbourne Reynolds flow apparatus

The apparatus is set up by filling the dye reservoir with color dye liquid. Dye reservoir

is connected to the flow control valve to ensure the flow of dye liquid can be

controlled. From the injection needle, we can observed that the liquid dye is flowing

through the glass tube and is based on the velocity of the fluid. Laminar, transitional

and turbulent flow should be obtained. The water flows out from the outlet valve is

collected and the time is taken to determine the flow rate.

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Dye reservoir

Flow control valve

Injection needle

Glass tube

Water outlet valve

Safety and precautions

This apparatus should be in a separate room or away from other experiments

because any vibration from them or students bumping/leaning on the counter will

cause errors.

EXPERIMENTAL PROCEDURE

EXPERIMENT A

1. The dye injector is lowered until it is seen in the glass tube.

2. The inlet valve, V1 is opened and water is allowed to enter stilling tank.

3. A small overflow spillage through the over flow tube is ensured to maintain a

constant level.

4. Water is allowed to settle for a few minutes.

5. The flow control valve is opened fractionally to let water flow through the

visualizing tube.

6. The dye control needle valve is slowly adjusted until a slow flow with dye

injection is achieved.

7. The water inlet valve, V1 and outlet valve, V2 is regulated until a straight

identifiable dye line is achieved. The flow will be laminar.

8. The flow rate is measured using volumetric method.

9. The experiment is repeated by regulating water inlet valve, V1 and outlet

valve, V2 to produce transitional and turbulent flow.

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RESULTS

VOLUME

(L)

TIME

(s)

FLOWRATE,

Q (L/s)

FLOWRATE, Q

(m3/s)

Re= ρvdμ =

Q XDA X μ

TYPES OF

FLOW

0.058

0.058

0.058

30

30

30

1.933 x 10 -3

1.933 x 10 -3

1.933 x 10 -3

1.933 x 10 -6

1.933 x 10 -6

1.933 x 10 -6

177.00

177.00

177.00

LAMINAR

FLOW

Re < 2100Reavg =

177

0.168

0.146

0.148

5

5

5

0.0336

0.0292

0.0296

3.35 x 10-5

2,92 x 10-5

2.96 x 10-5

3083.00

2679.68

2716.40

TRANSITION

FLOW

2100< Re <

4000

Reavg =

2826.36

0.220

0.226

0.224

5

5

5

0.0440

0.0452

0.0448

4.4 x 10-5

4.52 x 10-5

4.48x 10-5

4037

4148

4111.3

TURBULENT

FLOW

Re > 4000Re avg =

4098

Given: Diameter, D = 0.0156 m

Area, A = 1.91 x 10-4 m2

Viscosity , v = 25 kg/m.s

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Kinematic = 0.89 x 10-6 m2/s

DISCUSSION

The results taken shows the Reynolds number of each set of flow. The

Reynolds number can be defined for a number of different situations where a fluid is

in relative motion to a surface.

This Osbourne Reynolds experiment used to demonstrate the critical velocity

based on the nature of the two modes of motion flowing in a tube. Laminar flow,

transitional flow as well as turbulent flow have different value of Reynolds Number.

The table above shows the results obtained from sets of experiment done with

the flowmeter apparatus. Apparently, we repeat the experiment to get the average

Reynolds Number that we want hence approving the expectation and theory with the

result we get.

For first set of experiment, we recorded the volume of liquid collected within

30 seconds to find the flow rate of the flow. The results shows the Re avg = 177. This

value lies below Re<2000, proving that it is a laminar flow. Laminar is characterized

by streamlines and highly-ordered motion and the flow rate of the fluid is the lowest

among the three test.

Secondly, we change the flow of the fluid. This time with the increment of flow

rate that been determined manually, the Reynolds Number shows the value of Reavg=

2826. This value lies between 2000< Re<4000, hence the flow is transition flow.

The third set was done the same as the two sets before, the Reavg= 4098

which the value lies in Re>4000. The flow was decided to be the turbulent flow.

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Turbulent in the second case where it is characterized by velocity fluctuations and

highly disordered motion.

The observation that we obtained from the results for laminar is the dye that

flow has straight and smooth line, for transition the flow of dye has bursts of

fluctuations and for turbulent the dye has zigzas rapidly and randomly.

The results that we get in this experiment was approximately according to

theory of Osbourne Reyolds. Increse in flowrate effected the flow which the highest

flowrate causing the turbulent flow and vice versa.

The properties for each flow determined by the Osbourne method practically

can be differentiate using data below:

Laminar Turbulent Transition

low flowrate

Lowest Reynolds

Number

Re<2000

The ink injected

forming a visible

straight line

High flowrate

High Reynolds

value Re>4000

The ink injected

observed to be

very inconsistent

and no visible

line form

Flowrate lies between

laminar and turbulent

The Reynolds number lies

between laminar and

turbulrent flow.

2000<Re<4000

The line visible until reach

turbulent flow

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SAMPLE CALCULATION

Given Diameter = 0.0156 m

Area = 1.91x10-4 m2

Kinematic viscosity = 0.89x10-6 m2/s

Re = Qx DA x µ

Average volume=0.058+0.058+0.0583

=0.058 L

Flowrate(m3s )=0.058 L30 s

¿(1.933×10−3L /s)( 0.001m31 L ) = 1.933x10-6 m3

ℜ= (1.933 x10−6m3 /s ) (0.0156m )(1.91 x10−4m2 ) (0.89 x10−6m2/s )

=177.39

CONCLUSION

In conclusion, the results that we obtained after calculate the Reynold’s

number were 177 for laminar, 2826.36 for transitional and 4098 for turbulent. The

theories of this Reynold’s number state that if it is below than 2000, it is laminar. The

transition states occur at Reynold’s number range between 2000 and 4000.

Meanwhile, for turbulent flow the Reynold’s number is above 4000. Thus the results

obtained are similar as the theories stated. The flow of each laminar, transition and

turbulent can also be seen clearly based on the behaviour of the liquid inside the

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pipe. For laminar, the dye remained straight and parallel to the streamline as

entering the observation tube. While for transition, the dye start to mix with the

streamline and the behaviour is differ with the laminar flow. Turbulent flow shows

that the dye starts to disperse as they entered the observation tube. The theories

stated and the results and observation that we obtain from this experiment are exact

hence this experiment was considered as successful.

RECOMMENDATION

It is recommended that the water sink plug is changed to a more efficient

design so water leaks can be overcome faster and thus saving precious experiment

time. The dye used during the experiment was not thick due to the face that I could

cause a blockage to the dye injector. It turns out that a few extra drop of dye wouldn’t

turn it into a worst case scenario. So in short, use a thicker dye.

REFERENCES

Osbourne Reynolds’ experiment. (2011). Retrieved September 5, 2014, from

http://prezi.com/yia-jutherne/osborne-reynolds-experiment/

http://research.me.udel.edu/~lywang/meeg331/labs/reynolds.pdf

http://www.scribd.com/doc/39165338/Osbourne-Reynolds-Apparatus-

Experiment

www.wikipedia.org/Reynolds_number

www.engineeringtoolbox.com/reynolds-number-d_237.html

V. L. Streeter, (1962). Fluid Mechanics (3rd Edition) McGraw-Hill.

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APPENDICES

App. 1: Laminar flow App. 2: Transitional flow

App. 3: Turbulent flow

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