Reynolds Experiments - Lab Report Example

Reynolds Experiments Name Institution of Affiliation Date Introduction In most engineering and its related applications, one of the most important things that should be understood is the behavior of flowing fluids. This is because fluids, and principally water, are used in all manner of applications. These range from construction activities; irrigating farmlands, and even for household needs. It is therefore necessary to have an extensive understanding of how it will behave under certain conditions. With such knowledge, the engineers can be able to effectively design the distribution systems that will satisfy all conditions of flow. In fluid mechanics, there are essentially three modes of flow: Laminar, transitional and turbulent. In laminar flow, all the streamlines in a moving fluid are parallel to one another. One the other hand, turbulent flow is characterized by the formation of eddies and dissipation of energy as the streamlines do not move in parallel lines but cross into one another. As the name suggests, transitional/transient flow occurs when the type of flow is shifting from laminar to turbulent or the other way round. Since these different types of flow exhibit different characteristics, they also have different flow parameters. The concept of the Reynolds Number (Re) is one of the most useful flow parameters in determining the type of flow. Popularized by Osborne Reynolds in the 17th century, it is a dimensionless ratio of viscous and inertia forces. It is also dependent on the velocity of flow and the critical Re is achieved when the flow changes from laminar to turbulent. The unit can be used in determining the type of flow based on the following: laminar when Re < 2300 transient when 2300 < Re < 4000 turbulent when Re> 4000 The aims of this experiment were to: 1. Determine the Re for the different types of flow 2. Estimate the Critical Re 3. Show the relation between the Re and flow velocity Apparatus and Set up 1. Reynolds number measurement device 2. Thermometer 3. Stop watch 4. Flow meter For purposes of this experiment, the Reynolds Number measuring device was utilized. The figure below illustrates its set up: Fig 1:Re measuring device During the experiments, water at a controlled temperature is supplied to a 12mm tube from the constant head tank. The velocity of this water can be varied and hence by injecting fine dye filament, the nature of flow can be observed. The set-up is supported by adjustable feet and hence it can be shifted from point to point as the situation demands. Method Depending on certain flow conditions such as the velocity of water, the pipe diameter and the viscosity of water at the given temperature; the Reynolds number can be estimated and hence the type of flow determined. The following procedure was followed to determine these flow conditions: 5. The apparatus was set up as shown in Fig.1 above and the water supply opened with the discharge control valve partially open 6. The supply of water was varied until its height at the constant head tank was right above the overflow pipe. It was maintained at this level throughout the experiment by water flowing from the overflow pipe 7. The dye injector was opened and adjusted until a fine dye filament flowed down the glass tube. This was also done by continuously varying the flow rate until at that point where the dye flowed without any disturbance through the entire length of the tube, indicating laminar flow 8. The flow rate was slowly and continuously raised by opening the discharge valve. It was done until disturbances in the dye filament set in. This was taken to be the beginning of transient flow. The water supply was also increased so as to maintain the constant head conditions 9. Using the thermometer, the water temperature was measured and recorded. The flow meter was then used to measure the flow rate. Alternatively, this can be done by timing the period it takes for a known collected amount of water to flow 10. The flow rate was increased further until the dye filament is entirely diffused in the water. This marks turbulent flow and some eddies may be observed at this point. The temperature and flow rate were then measured and recorded again. 11. Next, the flow rate was decreased continuously up to the point where the dye returned to a steady filament indicating the onset of laminar flow again. The flow rate and temperature were taken and recorded. Results and Calculations Tube diameter D = 12mm = 0.012 m Water Temperature, T = 27OC (Constant throughout the experiment) Kinematic Viscosity of water at 27OC , ϑ = 0.8539 x 10-6 m2/s All the data that was collected during the experiment was recorded in the table below: Volume (l) Time (s) Flow Rate (l/s) Velocity in The pipe (m/s) Re Type of Flow 0.6 24 0.025 0.21 2952 Transition 0.6 32 0.019 0.17 2390 Transition 0.4 37 0.011 0.15 2108 Transition 0.4 72 0.006 0.11 1545 Laminar 0.2 73 0.002 0.07 984 Laminar 0.4 57 0.007 0.05 703 Laminar 0.6 21 0.029 0.29 4075 Turbulent 0.6 20 0.03 0.31 4356 Turbulent 0.6 39 0.015 0.3 4215 Turbulent Table 1: Experimental Results Tube area, A = πD2/4 = (π*0.012*0.012)/4 = 1.13 x 10-4 m2 Using the obtained time and volumes, the flow rates, F, in l/s can be calculated as follows: Flow Rate = Volume/Time. This was done for all the values and the results tabulated in Table 1 above. Thereafter, the velocity of flow was calculated in the pipe. This can be done by first converting the flow rate into discharge (m3/s) by dividing it using 1000 and then dividing the discharge with the pipe area. Therefore; Velocity, V = (F/1000)/A Therefore, the velocity for each flow rate was obtained and populated in Table 1 above. The Reynolds number is a function of the flow velocity, diameter of the tube and the kinematic viscosity at the given temperature. And since it is a dimensionless ration, it can be obtained by the following formula: Re = (Velocity*Diameter)/ Viscosity Re = VD/ ϑ Change of Re with Velocity The Re for each velocity was then calculated and recorded in Table 1 above. To determine the relationship between velocity and the Reynolds Number, a graph of Re against V was plotted. This is shown in Fig 2 below. Fig. 2: Re against V Based on the values for Re obtained, the different flow states could therefore be identified. It was noted that the flow began at the transitional state and gradually moved to laminar before turbulence set in and eventually went back to the original transient state. From the curve of Re against V, it can be observed that the two are directly proportional and hence Re increases with velocity. It means that at lower velocities, the flow is laminar and enters the transient state as the velocity increases (Streeter, 1962). Finally, turbulence sets in once the critical velocity is attained. Fig. 3: Types of flow These phenomena can be explained by the fact that the motion of a fluid is determined by the viscous forces and inertia forces. Initially when the water is flowing at a low velocity, the viscous forces are more dominant (Batchelor, 1967). The streamlines therefore move in parallel lines and hence the flow is laminar. Since the inertia forces are a product of mass and velocity, they tend to increase as the velocity is raised. As such, they gradually rise over the transient state until at the critical velocity where they become the dominant forces. Turbulence therefore begins and eddies are formed. If the velocity increases further, then turbulence will increase and more eddies will be formed. Likewise, a reduction in the velocity leads to a reduction in the inertia forces and hence the flow becomes transient again before laminar flow is finally achieved at much lower velocities ((Patel, Rodi, & Scheuerer, 1985)). The type of flow affects the energy state of any fluid, regardless of other flow parameters. This is mostly observed in the form of energy dissipation during turbulent flow. It requires a significant amount of energy for eddies to be formed during this sate of flow. Such dissipation of energy reduces the velocity head of the fluid. It is therefore a common occurrence for the velocity of a fluid to gradually start decreasing after turbulent flow due to the reduction in the internal energy. It is this concept that is used in applications such as hydraulic jumps which dissipate great amounts of energy to prevent water from causing damage. They do so by providing a barrier which abruptly raises the inertia forces in water and hence leading to the formation of eddies and consequently a reduction in the velocity head (Batchelor, 1967). Critical Reynolds Number From the results, it is also evident that there is a point where the flow begins to transit from laminar to turbulent. In this experiment, it was observed to be at the stage where the Reynolds number is 2107 and is referred to as the Critical Reynolds number. Other similar experiments suggest that the Critical Reynolds number is nearly equal for all kinds of fluids and is in the region of 2100 (Streeter, 1962). Hence, is possible to determine at which point the flow will begin to transit from laminar to turbulent. Therefore, it can be established that the Critical Re for water at 27OC is 2107. As it has been observed with water, the critical Re is not exactly 2100 and may vary depending on a number of flow factors (Patel, et. al., 1985). These include the temperature of the flowing fluid; the physical characteristics of the path it is flowing in; and the viscosity of the fluid. Although these values will all tend towards 2100, it is important to note that they may vary due to the mentioned parameters. From this value of the Critical Re, it can be noted that the critical velocity is 0.15 m/s. This means that the flow below this velocity is mostly laminar and once it is attained the flow stars to become turbulent. Errors in the Lab In most experiments, there are errors which occur. The observed values are therefore more often than not different from the theoretical values. In the course of this experiment, there are some errors which might have occurred. Some of these include: 1. Errors in the equipment There are different apparatus that were used during this experiment. These include the stopwatch and Reynolds number measuring device. These pieces of equipment may not have been accurately calibrated before the experiment and hence could have yielded some errors. 2. Operation and Observation Errors The people who were operating the apparatus may have made mistakes at one point or another. These include things such as involuntarily varying the flow rate faster that it should. Errors might also have been introduced when making the observations such as not timing the flow accurately or reading the incorrect values on the thermometer due to parallax. 3. Calculation errors The values obtained from this experiment yielded some decimal numbers during calculations. The used ones were therefore truncated or rounded off. These were the calculation errors and they affected the final outcome as they did not represent the true picture of what was really observed. Conclusions Summing up, it is suffice to state that the Reynolds experiments are necessary in order to understand the behavior of fluids under different flow conditions. Such experiments, as has been observed, reveal that there are three states of flow: laminar, transient and turbulent. The values of the Reynolds number vary from one type of flow to another and generally increase with velocity. It can also be conclude that the transition from one state to another occurs at a critical Reynolds that is estimated to be around 2100 for most fluids. This value is also affected by different flow parameters but is for most cases observed to tend towards the Re of 2100. When conducting such experiments, the sources of errors like those mentioned above should be minimized so as to get the most accurate set of data. By doing so, the Re can be precisely obtained. References Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press. Patel, V. C.; Rodi, W.; Scheuerer, G. (1985). "Turbulence Models for Near-Wall and Low Reynolds Number Flows—A Review". AIAA Journal 23 (9) Streeter, V. L. (1962). Fluid Mechanics (3rd ed.). McGraw-Hil Read More

The apparatus was set up as shown in Fig.1 above and the water supply opened with the discharge control valve partially open 6. The supply of water was varied until its height at the constant head tank was right above the overflow pipe. It was maintained at this level throughout the experiment by water flowing from the overflow pipe 7. The dye injector was opened and adjusted until a fine dye filament flowed down the glass tube. This was also done by continuously varying the flow rate until at that point where the dye flowed without any disturbance through the entire length of the tube, indicating laminar flow 8.

The flow rate was slowly and continuously raised by opening the discharge valve. It was done until disturbances in the dye filament set in. This was taken to be the beginning of transient flow. The water supply was also increased so as to maintain the constant head conditions 9. Using the thermometer, the water temperature was measured and recorded. The flow meter was then used to measure the flow rate. Alternatively, this can be done by timing the period it takes for a known collected amount of water to flow 10.

The flow rate was increased further until the dye filament is entirely diffused in the water. This marks turbulent flow and some eddies may be observed at this point. The temperature and flow rate were then measured and recorded again. 11. Next, the flow rate was decreased continuously up to the point where the dye returned to a steady filament indicating the onset of laminar flow again. The flow rate and temperature were taken and recorded. Results and Calculations Tube diameter D = 12mm = 0.

012 m Water Temperature, T = 27OC (Constant throughout the experiment) Kinematic Viscosity of water at 27OC , ϑ = 0.8539 x 10-6 m2/s All the data that was collected during the experiment was recorded in the table below: Volume (l) Time (s) Flow Rate (l/s) Velocity in The pipe (m/s) Re Type of Flow 0.6 24 0.025 0.21 2952 Transition 0.6 32 0.019 0.17 2390 Transition 0.4 37 0.011 0.15 2108 Transition 0.4 72 0.006 0.11 1545 Laminar 0.2 73 0.002 0.07 984 Laminar 0.4 57 0.007 0.05 703 Laminar 0.6 21 0.029 0.29 4075 Turbulent 0.6 20 0.03 0.

31 4356 Turbulent 0.6 39 0.015 0.3 4215 Turbulent Table 1: Experimental Results Tube area, A = πD2/4 = (π*0.012*0.012)/4 = 1.13 x 10-4 m2 Using the obtained time and volumes, the flow rates, F, in l/s can be calculated as follows: Flow Rate = Volume/Time. This was done for all the values and the results tabulated in Table 1 above. Thereafter, the velocity of flow was calculated in the pipe. This can be done by first converting the flow rate into discharge (m3/s) by dividing it using 1000 and then dividing the discharge with the pipe area.

Therefore; Velocity, V = (F/1000)/A Therefore, the velocity for each flow rate was obtained and populated in Table 1 above. The Reynolds number is a function of the flow velocity, diameter of the tube and the kinematic viscosity at the given temperature. And since it is a dimensionless ration, it can be obtained by the following formula: Re = (Velocity*Diameter)/ Viscosity Re = VD/ ϑ Change of Re with Velocity The Re for each velocity was then calculated and recorded in Table 1 above. To determine the relationship between velocity and the Reynolds Number, a graph of Re against V was plotted.

This is shown in Fig 2 below. Fig. 2: Re against V Based on the values for Re obtained, the different flow states could therefore be identified. It was noted that the flow began at the transitional state and gradually moved to laminar before turbulence set in and eventually went back to the original transient state. From the curve of Re against V, it can be observed that the two are directly proportional and hence Re increases with velocity. It means that at lower velocities, the flow is laminar and enters the transient state as the velocity increases (Streeter, 1962).

Finally, turbulence sets in once the critical velocity is attained. Fig. 3: Types of flow These phenomena can be explained by the fact that the motion of a fluid is determined by the viscous forces and inertia forces.

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