ABSTRACT

Osbourne Reynolds experiment is used to investigate the characteristics of the flow of the liquid in the pipe which is also used to determine the Reynolds Number for each type of flow. The apparatus is desgn to determine the Reynolds Number for each type of flow in the pipe and also to calculate the range for the laminar, transition and turbulence flow where the calculation is used to prove the Reynolds Number is dimesionless by using its formula. For both objectives, running the experiment with different volume flow rate of water is involved. In this experiment, the time taken to collect the amount of water is 10 seconds. At the same time, characteristics of flow is also observed. From the data collected, the calculation is to estimate the range for each type of flow, laminar, transition or turbulence. To prove the Reynolds Number is dimensionless, calculating using the formula was done and it is proven that the Reynolds Number is dimesionless.

INTRODUCTION

This experiment is conducted mainly to study the criterion of laminar, transition and turbulent flow. In fluid mechanics, internal flow is defined as a flow for which the fluid is confine by a surface.

The apparatus used in this experiment is the Osborne Reynolds apparatus. This apparatus are consists of water resources for the system supply, dye input injection unit fix head water input and water output unit to determine water flow rate, a tank with stones, fix head water input, dye input injection and water output unit. . The apparatus is used to demonstrate the critical velocity based on the nature of the two modes of motion flowing in a tube whether it is laminar, transition and turbulent. We can observe laminar, transition, and turbulent flow by varying the flow rate. The water output unit is used to calculate the flow rate. The dye input injection is used to visualise the flow patterns. The dye can be controlled and adjusted to improve the quality of the flow patterns. The stone acts as baffles to minimize flow disturbances. The glass tube is where we observe the flow patterns.

OBJECTIVES

The objectives of this experiment is

1. To observe the characteristics of laminar, transition and turbulent flow

2. To prove that the Reynolds number is dimensionless by using the formula

THEORY

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations. 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. They are also used to characterize different flow regimes within a similar fluid, such as laminar, transition and turbulent flow. Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion as for the turbulent flow, it occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities. The Reynolds number can be used to determine type of flow whether it is laminar, transition, or turbulence. The flow is,

The Reynolds number is widely used dimensionless parameters in fluid mechanics.

Reynolds number formula:

Reynolds number R is independent of pressure.

Laminar flow is the flow of a fluid moving with a moderate speed has fluid layers moving past other layers as if some sheets are moving over other layers. In Laminar Flow viscous shear stresses act between these layers of the fluid which defines the velocity distribution among these layers of flow. The flow is denoted a steady flow condition where all streamlines follow parallel paths, there being no interaction between shear planes.

As for the transitional flow is a mixture of laminar and turbulent flow with turbulence inthe center of the pipe, and laminar flow near the edges.

Meanwhile, as for the turbulence flow speed of the otherwise calm layers increases, these smoothly moving layers start moving randomly, and with further increase in flow velocity, the flow of fluid particles becomes completely random and no such laminar layers exist anymore. Turbulent flow denotes an unsteady flow condition where streamlines interact causing shear plane collapse and mixing of the fluid.

APPARATUS

Figure 1: Osborne Reynold’s Demostration Unit.

1. Dye Reservoir2. Dye Injector3. Head Tank4. Observation Tube5. Water Inlet Valve, V16. Bell Mouth7. Water Outlet Valve, V28. Overflow Valve

PROCEDURES

1. Dye injector was lowered until it is seen in the glass tube.2. The inlet valve, V1 was opened and water was allowed to enter stilling tank.3. A small overflow spillage was ensured through the over flow tube to maintain a constant level.4. Water was allowed to settle for a few minutes.5. The flow control valve was opened fractionally to let water flow through the visualizing tube.6. The dye control needle valve was slowly adjusted until a slow flow with dye injection was achieved.7. The water inlet valve, V1 and outlet valve, V2 was regulate until a straight identifiable dye line was achieved. The flow was laminar.8. The flow rate was measured using volumetric method.9. The experiment was repeated by regulating water inlet valve, V1 and outlet valve, V2 to produce transitional and turbulent flow.

RESULTS

i) Laminar Flow

Volume (L) Time (s) Flow rate, Q

(L/s)

Flow rate, Q

(m³/s)

Reynold’s Number

0.035 10 0.0035 0.0000035 321.19

0.032 10 0.0032 0.0000032 293.66

0.023 10 0.0023 0.0000023 234.82

ii) Transitional Flow

Volume (L) Time (s) Flow rate, Q

(L/s)

Flow rate, Q

(m³/s)

Reynold’s Number

0.232 10 0.0232 0.0000232 2129.06

0.248 10 0.0248 0.0000248 2275.89

0.289 10 0.0289 0.0000289 2652.16

iii) Turbulent Flow

Volume (L) Time (s) Flow rate, Q

(L/s)

Flow rate, Q

(m³/s)

Reynold’s Number

0.600 10 0.060 0.000060 5506.21

0.620 10 0.062 0.000062 5689.75

0.680 10 0.068 0.000068 6240.37

D = 0.0156 m

A = 0.000191 m²

V = 0.0000089 m²/s

CALCULATION

Using formula,

Where,

Thus,

i) Laminar Flow

Re = 0.0000035 × 0.0156 0.000191 × 0.0000089

= 321.19

ii) Transitional Flow

Re = 0.0000232 × 0.0156 0.000191 × 0.0000089

= 2129.06

iii) Turbulent Flow

Re = 0.00006 × 0.00156 0.000191 × 0.0000089 =

DISCUSSION

It is necessary to know the difference 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. Turbulent flow is a highly disordered fluid motion characterized by velocity and fluctuations and eddies, whereas transition flow is known as a flow that contain both laminar and turbulent flow.

Based on the Osbourne Reynolds experiment, laminar flows is obtained when a single line of red dye is seen after a thin film of dye is injected into the glass tube. However, for turbulent flow, there is a huge dispersion of dye along the glass tube, whereby the lines of dye breaks into a highly tangled threads of dye.

For laminar flow, from the conducted experiment, the Reynold’s numbers calculated are 321.19, 293.66 and 234.82. On average, the value is somewhere 283. Thus, it obeys the condition of a laminar flow which its Reynold’s number is less than 2100 (Re < 2100). This represents that laminar flow is a steady flow where all streamlines follow parallel paths and there being no interaction or mixing between shear planes. Under this condition the dye observed will remain as a solid, straight and easily identified. In today’s application, this type of flow is widely used in surgery, nursery, diagnostic and treatment.

Throughout the experiment, we observed that the red dye line starts flowing in a straight ordered line at small velocity. However, as the velocity increases over time, the ordered line seem to dispersed everywhere along the streamline but still remain as straight line at the earlier part. This indicate a transition flow. Later on, as the velocity increases, the dispersion of dye starts to be huge, indicating a turbulent flow. These observation are concluded as the streamline is undergoing change of type flow from laminar flow, transition flow and turbulent flow.

Meanwhile, for transitional flow, we get these Reynold’s numbers of 2129.06, 2275.89 and 2652.16. On average, the value becomes around 2352. Thus, it can be said that this value represents a transitional flow. (2100 < Re < 4000). Transitional flow is actually a mixture of laminar and turbulent flows with turbulence in the centre of the pipe and laminar flow near the edges. Each of these flows behaves in different manners in terms of their frictional energy loss while flowing nd have different equations that predict their behaviors. It is applied in some working areas encompassing reentry vehicles, scramjets, tactical and ballistic missiles and much more.

Lastly, for the turbulent flow, the Reynold’s number are as follows; 5506.21, 5689.79 and 6240.37. On average, these values become 5812.12. Thus, it clearly proves the condition of a turbulent flow (Re > 4000). This large scale denotes an unsteady flow condition where streamlines interact causing shear plane collapse and mixing of the fluid. In this condition the

dye observed will become disperse in the water and mix with the water. The dye will not be identified this time. The use of turbulent flow for on-line sample clean-up of urine samples is one of the applications nowadays.

CONCLUSIONS

As a conclusion, as water flow rate is increasing, the Reynolds number will increased, and the dispersion of the red dye line changing, indicating there is an existence of different type of flow along the glass tube streamline. From the calculation, it is proven that Reynold’s number is dimensionless. For laminar flow, the Reynold’s number is proven to be less than 2300, transition flow is between 2300 to 4000 while turbulent is proven to be more than 4000.

RECOMMENDATIONS

There are some recommendations to make sure this experiment would obtained more accurate results.

Check whether the water in the tube flows in a correct way and we should also make sure the flow is table before considering the type flow and collecting the fluid flow out and time recorded.

Before injecting the dye into the fluid, make sure the dye is sufficient in order to get a stable, straight ordered line laminar flow.

The person collecting the fluid flowing out and taking the reading should be the same person.

The experiment should be repeated twice in order to get more accurate result.

REFERENCE

http://ffden-2.phys.uaf.edu/212_fall2003.web.dir/ROBERT_CASEY/typeofluid.htm http://www.engineeringtoolbox.com/laminar-transitional-turbulent-flow-d_577.html http://www.dummies.com/how-to/content/the-different-types-of-fluid-flow.html Douglas J.F., Gasiorek J.M. and Swaffield, Fluid Mechanics, 3rd edition, Longman

Singapore Publisher.

Munson B.R., Young D.F. and Okiishi T.H.(1998). Fundamentals of Fluid Mechanics, 3rd

edition, New York : Wiley and Sons.

APPENDICES

Figure 1: type of flow is laminar. Figure 2: type of flow is turbulence.

Figure 3: type of flow is turbulence