The Reynolds Number and Flow Regime Change

The Reynolds Number and Flow Regime Change

Introduction

     Flows are normal occurrences that occur and are encountered in day-to-day activities. These flows can be natural or not. But whichever form it is, all flows can basically be classified into the following:
a) Flow through open channels (such as falling film) 
b) Flow through circular ducts; or 
c) Convective transport of heat 
In any case it may follow, it is essential in Chemical Engineering, Mechanical Engineering, and other fields to work with the understanding of the regime of flow at an instant across a section of channel(s) or flow path/space. The Reynolds number has, thus, become a determining factor in designs having to do with flow processes.

Objectives of the Experiment

The objectives of the experiment are to 
i. observe the transition of the flow from laminar to turbulent; 
ii. evaluate the Reynolds Number at which it occurs, and 
iii. repetitively verify the results in order to obtain a range with the changing flow speed. 

Experimental Setup of Apparatus

The Reynolds number and flow regime change apparatus demonstrates the kind of experiment conducted to show the dependence of flow on Reynolds Number. The device used in the experiment, shown in Figure 1, enables the observation of the flow transformation from laminar to turbulent in different velocities.

The Reynolds' Apparatus
The Reynolds' Apparatus

Theory

The Reynolds Number (Re) is defined as the ratio of inertia force to viscous force. The flow characteristics do not change instantly since the fluid shows reluctance to change from one condition to another. This reluctance causes the hysteresis shown in the Figure 2 and it is expected to be observed around 2300 value of Re number for tubular ducts. When the velocity is increased, there is a transition between the points A and B, and it occurs between points C and D for decreasing flow. The point D, being the most well-defined and accepted as the starts of the transitional flow, the experiment is to observe this transitional area in the graph.

Variation of head loss with velocity for flow along a pipe

The formulations to be used in the calculation throughout the experiment are as follow where ρ is the fluid density, d is the characteristic length, u is the free stream velocity and 𝜇 is the dynamic viscosity;
Re = ρud/μ

Procedure

1. Set up the apparatus 

2. Turn on the water supply and partially open the discharge valve at the base of the apparatus

3. Record the temperature of the tap water 

4. Adjust the water supply until the level in the constant head tank is just above the overflow pipe and keep it at this level by small flow down the overflow pipe 

5. Open and adjust the die injector and maintain a fine filament of die in the flow down to the glass tube, achieve a laminar flow condition for die filament 

6. Record two different data of the flow rate when the flow observed is laminar 

7. Increase the flow rate by opening the discharge valve until the observable disturbance occurs which is the transition point and should be noted 

8. Record the one flow rate sample when the flow is in the transition region 

9. Increase the flow rate by opening the discharge valve until the transition to turbulent passing occurs, record one more data 

10. Increase the water supply furthermore to maintain constant head conditions in turbulent region 

11. Record two different data of the flow rate when the flow observed turbulent 

12. Increase the flow rate until the disturbances such that die filament becomes fully turbulent which is the onset of fully turbulent flow, record temperature and the flow rate as defined in the previous steps

13. Decrease the flow rate slowly until the die returns to steady laminar filament and then again record the temperature and the flow rate in the same procedure. Seven data should be recorded. (2 turbulent, 3 transition, 2 laminar) 
Laminar flow, transition and fully turbulent characteristics are shown in the Figure 3 below. In the experiment this patterns will be observed and recorded independently. 
Velocity calculations will be handled as follow:

Where:
Q is the discharged volume (200 x 10-6 m-3), 
r is the inner radius of the pipe (6 x 10-3m), and 
t is the time.

Effect of Varying Viscosity

Viscosity of water varies with the temperature as shown in the Figure 4 below. Viscosity should be read from Figure 4 corresponding to the measured temperature value. 
Datasheet is given in Table 1

Kinematic viscosity of water at various temperature

Results and Calculations

• Calculate velocity u [m/s] for each raw
• Calculate kinematic viscosity [m2s-1] for each raw 
• Calculate the Re Number for each raw 
• Recording all the results in the table above. 
• Tabulate Re Number for each data point and the corresponding friction factor 

Discussions and Conclusions

• Discuss the transition region passing points located on the graph for laminar to turbulent transition and turbulent to laminar transition 
• Discuss the results and compare with the existing theory

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