Reynold\'s Number Laboratory Report PDF

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Summary

1 ObjectiveTo investigate Reynolds number for water using Reynolds Number apparatus.2 Introduction and TheoryLiquid or gas flow through pipes and duct is commonly used in heating and cooling applicationsand fluids distribution networks. The fluid in such application is forced to flow by a fan or pum...

Description

1.0 Objective To investigate Reynolds number for water using Reynolds Number apparatus.

2.0

Introduction and Theory

Liquid or gas flow through pipes and duct is commonly used in heating and cooling applications and fluids distribution networks. The fluid in such application is forced to flow by a fan or pump through a flow section. Whenever a fluid is flowing through a pipe, the flow is either laminar or turbulent. The existence of these two types was first demonstrated by Osborn Reynolds. The transition from laminar to turbulent flow depends on the various parameters such as diameter of circular pipe (D), flow rate (Q), velocity (V), and temperature of the fluid and type of fluid. After exhaustive experiment in 1880s, Osborne Reynolds discovered that the flow regime depended mainly on the ratio of the inertial forces to viscous forces in the fluid. This ratio is called Reynolds number and is expressed for internal flow in a circular pipe. The Reynolds number (Re) is expressed by:

Viscous forces

Re = Inertial forces = V D ν μ

=

ρVD

Where V = flow velocity, m/s D = diameter of tube, m ν = kinematics viscosity of the fluid, m2/s (μ/ρ) μ = viscosity of fluid, Ns/m2 (kg/m.s) ρ = density of water, kg/m3

The water velocity (V) is determined by:

V= Flowrate (m3/s) Cross section area (m2) A

=

Q

(m/s)

Where, flow rate (Q) is given by:

Q = Water volume (m3) Time (s)

= Q t

(m3/s)

Laminar flow ● ● ● ● ● ●

Re < 2300 'low' velocity Dye does not mix with water Fluid particles move in straight lines Simple mathematical analysis possible Rare in practice in water systems

Transitional flow ● ● ●

2300 < Re < 4000 'medium' velocity Dye stream wavers in water - mixes slightly.

Turbulent flow ● ● ●

● ● ●

Re > 4000 'high' velocity Dye mixes rapidly and completely ● Particle paths completely irregular ● Average motion is in the direction of the flow Cannot be seen by the naked eye Changes/fluctuations are very difficult to detect. Must use laser. Mathematical analysis very difficult so experimental measures are used

Table 2.1 The illustration and information of the Reynolds Number

In this experiment, the Reynolds Number apparatus will be used. This apparatus consists of a constant head supply tank supplied with water. This tank is provided with a bell mouth outlet to which a transparent tube is fitted. At outlet of the tube, a regulating valve is provided. A dye tank containing coloured dye is fitted above the supply tank. Water flow through pipe and dye is injected at the centre of the pipe.

At a lower velocity, the dye remains in the form of straight filament, indicating that the existence of laminar flow. As the increasing velocity, a transitional flow is reached, resulting in an irregular and waves of the dye. Further increase of velocity shows that the dye filament becomes more irregular and ultimately the dye diffuses over the entire cross section of the tube. At this stage, the turbulent flow is developed with an extremely irregular water flow pattern

3.0 Equipment and Apparatus

Figure 3.1 Equipment and apparatus arrangement

4.0 Procedure 1.

Fully open by-pass valve.

2.

Fully close flow control valve.

3.

Start the pump. Wait until water is discharged from by-pass valve.

4.

Slowly close the by-pass valve. The water will be pumped into supply tank. Control the by-pass valve until the water start filling the transparent tube. At the same time, control the by-pass valve so that water level in supply tank remains constant at 70% of supply tank capacity.

5.

Slowly open the flow control valve to remove all air bubble inside transparent tube. Then close the flow control valve. Ensure the water level in supply tank remains constant at 70% of supply tank capacity by control by-pass valve.

6.

Start the dye injection. Then, slowly open flow control valve. Wait for some time. A steady line of dye will be observed. Adjust dye flow, if required.

7.

During steady line phase (laminar region), take the time for 135 ml of water.

8.

Slowly open the flow control valve, the water flow will increase. In the same time ensure water level in supply tank remains constant. As the increasing of the water flow, dye line will be disturbed. Measure this flow rate.

9.

Further increase the flow by open the flow control valve. The disturbances of dye line will increase and at certain flow; the dye line diffuses over the entire cross section. Measure this flow rate.

10.

Slightly increase the flow and then slowly reduce the flow. Measure the flow rate at which diffused dye tends to become steady, (the beginning of transition zone while reducing velocity.)

11.

Further reduce the flow and measure the flow rate at which dye line becomes straight and steady.

12.

Record your observation in Table 5.1. Calculate Reynolds Number of each the flow.

5.0 Data and Results No.

Flow type

Table 5.1 Experimental observation data Time (s) for Sketch the flow in 135 ml water

1

Laminar

12

2

Laminar

7

3

Laminar

5

4

Laminar

3

5

Laminar

1

Transparent Tube

Table 5.2 Result analysis No.

Flow Type

1

Laminar

2

Laminar

3

Laminar

4

Laminar

Flow rate, Q (m3/s)

Velocity, V (m/s)

Reynolds Number, Re

(Show your calculation)

(Show your calculation)

(Show your calculation)

0

Laminar 5

6.0 Questions 6.1

Give two errors in the experiment? Possible error in the experiment especially when expecting a turbulent flows as the velocity was increased might be possible due to a defective equipment and the instability of the area where it was situated.

6.2

Briefly discussed the laminar and turbulent flow? Laminar Where the flow is characterized by fluid particles moving in the form of lamina sliding over each other. It is a flow characterized by smooth streamlines and highly ordered motion. Turbulent Where the flow is characterized by constant agitation and intermixing of fluid particles such that their velocity changes from point to point and even at the same point from time to time. It is characterized by velocity fluctuations and highly disordered motion.

6.3

Compare Reynolds Number for laminar and turbulent flow from the experimental and Theoretical Study.

Laminar

Turbulent

•

Re < 2300

•

Re > 4000

•

'low' velocity

•

'high' velocity

•

Dye does not mix with water

•

Dye mixes rapidly and completely

•

Fluid particles move in straight

Particle paths completely

lines •

Simple mathematical analysis

irregular •

possible •

Rare in practice in water systems

Average motion is in the direction of the flow

•

Cannot be seen by the naked eye

•

Changes/fluctuations are very difficult to detect. Must use laser.

•

Mathematical analysis very difficult - so experimental measures are used

•

Based on the calculation we conclude all the calculation to find the Reynold Number is Laminar Flow. Because after we calculate to find the Velocity the answer we will get low and for the Reynold Number also we got less 2300 so we assume all this experiment is Laminar Flow.

6.4

What is transition region? •

The area in a seed-bearing plant where the vascular tissue of the root changes into the vascular tissue of the stem. In eudicotyledons, the roots have a solid cylinder of vascular tissue surrounded by cortex. The vascular tissues gradually branch apart and reorient themselves in the stem around a central pith.

•

The thin layer of the solar atmosphere that separates the chromosphere from the corona. In the transition region, temperatures increase from a relatively cool 20,000°K in the chromosphere to the 1,000,000°K and higher temperatures of the corona. Transition region chemistry involves the ionization of hydrogen and other elements; the light produced by this region comes from ionized forms of carbon, oxygen, and silicon.

6.5

What is the ‘unit’ of Reynolds number? Justify your answer. •

It is found that Reynolds numbers values have no units. Even though the inputs all have units, they divide out in the end. This can be further explained with the units cancellation methods that involved in the calculation are as below:

𝑅𝑒 =

𝑘𝑔

𝑚

× 𝑠 ×𝑚 𝜌𝑉𝐷 𝑚3 = 𝑁𝑠 𝜇 𝑚2

=

𝑘𝑔 ) 𝑚𝑠 𝑁𝑠 ( 2) 𝑚

(

𝑘𝑔

= 𝑚𝑠 × =

𝑚2

𝑁.𝑠

𝑘𝑔 𝑚 𝑁.𝑠2 𝑘𝑔 𝑚

= (𝑘𝑔 𝑚𝑠−2) ; 𝑁 = 𝑘𝑔 𝑚𝑠 −2 𝑘𝑔 𝑚

= 𝑘𝑔 𝑚 =1

 Hence, it is now proved that the Reynolds number value has no unit.

7.0

Discussions

The Reynold Number of each trial was calculated using the obtained data and the tabulated in 5.1 and 5.2. Also displayed in the aforementioned table is the type of flow as observed with the naked eye. All the five trial showed laminar and smooth flow and their Reynolds Number were both calculated to below 2100. Laminar Flow occur at low velocity, where the layers of fluid seem to slide by one another without eddies or swirls being present on the other hand, turbulent flow occur higher velocity where eddies are present giving the fluid a fluctuating nature.

8.0

Conclusions

The flow of a fluid can be characterized to be laminar, turbulent, and transitional. In laminar flow, the motion of the particles of a fluid is very orderly with particles close to a solid surfaces moving in straight lines parallel to that surface. Flow is laminar at Reynolds Number of below 2100. In turbulent flow, the motion of the particles is chaotic and there is lateral mixing. Flow is turbulent at Reynolds Number of above 4000. Between Reynolds Number of 2100 and 4000 is in transitional.

9.0

Reference

1.

Reynolds'Number.(n.d.).Retrieved https://www.sciencedirect.com/topics/engineering/reynolds-number

2.

What is the SI unit of the Reynolds number? (n.d.). Quora - A place to share knowledge and better understand the world. https://www.quora.com/What-is-the-SI-unit-oftheReynolds-number

3.

Water - Density viscosity specific weight | Engineers edge | www.engineersedge.com. (2014, May 1). Engineers Edge - Reference Data for Engineers | GD&T ASME Training | GD&T Training | DFM DFA Training|Engineering Supplies Store | Engineering Tools for productivity. https://www.engineersedge.com/physics/water density viscosity specific weight 13146.htm

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