Reynolds Number

REYNOLDS NUMBER Page 1 TABLE OF CONTENTS TABLE OF CONTENT 1 OBJECTIVE 2 ABSTRACT 2 AIM 3 PROBLEM STATEMENT 3 EQUIPMENT 4 PROCEDURE 5 RESULT 6 CALCULATION 7 DISCUSSION 8 CONCLUSION 9 PRE-LAB QUESTION 10 REFERENCE 11

REYNOLDS NUMBER Page 2 EXPERIMENT 3

REYNOLDS NUMBERS OBJECTIVES

The objectives of the experiment are:

1. Arrange work procedure accordingly. 2. Execute safety and health procedure. 3. Handle the given task correctly. 4. Identify the data needed.

5. Accomplish the task within a time frame given. 6. To document the task and produce the report.

INTRODUCTION

Fluid flow can be classified to three regimes which is laminar, transitional and turbulent regime. Laminar regime is a regime where the flow is characterized by smooth streamlines and highly ordered motion. Turbulent is a regime where flow is characterized by velocity fluctuations and highly disordered motion. Transitional regime is where the flow fluctuates between laminar and turbulent before it becomes fully turbulent.

The transitional from laminar to turbulent flow depends on geometry, surface roughness, flow velocity, surface temperature, and type of fluid. However, Osborne Reynolds discovered that the flow regime mainly depends on the ratio of inertial forces to viscous forces. This ratio is what we called as Reynolds number.

At small or moderate Reynolds numbers the viscous forces are large enough to suppress theses fluctuations and to keep the fluid “in line”. Thus, the flow is streamlined and in ordered motion. However, at large Reynolds numbers, the inertial forces, which are proportional to the fluid density and the square of the fluid velocity, are large relative to the viscous force. As the results, the viscous force cannot prevent the random and rapid fluctuations of the fluid. Thus, the flow will be in disordered motion.

The boundary of Reynolds number for laminar, transitional and turbulent regime varies by geometries and flow condition. For example, flow in a circular pipe is laminar for Reynolds number less than 2300, turbulent for Reynolds number larger than 4000 and transitional in between. However, we will have other boundaries if the pipe cross sectional area is a square.

REYNOLDS NUMBER Page 3 This experiment is to visualize the laminar, transitional and turbulent flow in a pipe and to

determine the boundary of Reynolds number for flow in the pipe.

First by controlling the flow rate, establish the laminar flow. Then by slowly increase the flow rate observe what happened to the dye streak. Record the flow pattern change and it volumetric flow rate reading. Determine the boundary of Reynolds number of laminar, transitional and turbulent regine.

AIM

To transitional from laminar to turbulent flow depends on geometry, surface roughness, flow velocity, surface temperature, and type of fluid.

PROBLEM STATEMENT

To determine transitional from laminar to turbulent flow depends on geometry, surface roughness, flow velocity, surface temperature, and type of fluid.

REYNOLDS NUMBER Page 4 EQUIPMENT

Hydraulic Bench.

Reynolds experiment apparatus.

REYNOLDS NUMBER Page 5 PROCEDURE

1. Fill the water tank with water and allow it to stand for some time so that the water comes to rest.

2. Partially open the outlet valve of the glass tube and allow the flow to take place at a very low rate.

3. Allow the flow to stabilize then open the valves at the inlet of the dye injector and allow the dye to move through the tube. Observe the nature of the filament.

4. Record the data to the table.

5. Observed the regime, then sketch the flow of the dye.

6. Measure the discharge by collecting water in the graduated cylinder for a certain interval of time.

REYNOLDS NUMBER Page 6 RESULT

i.

Pipe diameter , d 0.01 M

Cross section area , A 78.53 x 10-3 m2 Kinematic viscosity , v 1x 10-6 m2/s

ii.

Flow type Reynolds no. (Re) 0.0004 69.68 5.741x 10-6 7.311 x10-5 Laminar flow 0.731 0.0004 20.53 1.948 x10-4 2.481 x10-3 Transitional flow 24.810 0.0004 7.06 5.666 x10-4 7.215 x10-3 Turbulent flow 72.15

REYNOLDS NUMBER Page 7 SAMPLE CALCULATION

Example For Table 1

Cross section area, A 78.53 x10-3 Flow rate , Q (m3/s) V/T 5.741 x10-6 Velocity (m/s) Q/A 5.741 x10-6 / 78.53 x10-3 7.311 x105

Reynolds no. (Re)

= 0.731

REYNOLDS NUMBER Page 8 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/m³, the area of glass tube is 78.53 x 10-3 m², while the viscosity of water is1x 10-6 m2/s, 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 it’s not occurs suddenly.

REYNOLDS NUMBER Page 9 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

REYNOLDS NUMBER Page 10 PRE-LAB QUESTIONS

1) What is Reynolds Number?

the Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.

2) Explain what is the meaning is if one say “ The flow has low Reynolds Number”? For small Reynolds number, on the other hand, the flow will always be laminar. For pipe flow, the critical Reynolds number above which turbulence may exist 3) Draw velocity profile for fully develop turbulent flow.

REYNOLDS NUMBER Page 11 REFERENCE

Guderley, G.; and Hantsch, E.: Beste Formen Für Achsensymmetrische

Uberschallschubdusen. Zeitschrift für Flugwissenschaften, Brauschweig, Sept. 1955. Rao, G.V.R.: Exhaust Nozzle Contour for Maximum Thrust. Jet Propulsion, vol. 28, June 1958, pp. 377-382.

Candler, G.; and Perkins, J.: Effects of Vibrational Nonequilibrium on Axisymmetric

Hypersonic Nozzle Design. AIAA Paper 91-0297, Jan. 1991.

Kim, S.: Calculations of Low Reynolds Number Rocket Nozzles. AIAA Paper 93-0888, Jan. 1993.

Korte, J. J.; Kumar, A.;Singh, D. J.; and White, J. A.: CAN-DO - CFD-Based

Aerodynamic Nozzle Design & Optimization Program for Supersonic/Hypersonic Wind Tunnels. AIAA Paper 92-4009, July 1992.