Objectives
The aim of this experiment is to study the laminar, transitional and turbulent flow of water in a pipe. This is achieved by observing the flow of colored dye introduced in the pipe, which can be altered by manipulating the flow control valve. Using the observed volume flow rate, the average velocity is computed, and used to calculate the Reynolds number for each case. The visual observations and the Reynolds numbers are then compared to analyze the extent of agreement between theory and experimental results.
Apparatus
- Osborne Reynolds Apparatus – This is the set-up required to observe the flow of water and colored dye, as shown in Figure 1.
- Digital Flow meter – Used to accurately measure volume flow rate.
- Thermometer – The kinematic viscosity of water depends on temperature, which needs to be measured.
- Purple vegetable dye – Colored dye that will make it easy to visualize the flow.
- Hydraulics bench
Figure 1: Osborne Reynolds Apparatus
Results
Formulas
Re=UDρµ
Where Re is the Reynolds number, U is the average velocity of fluid in m/s, D is the inner diameter of pipe in m, ρ is the fluid density in kg/m3, and µ is the dynamic viscosity of fluid in Pas. Further µρ=ν is the kinematic viscosity of the fluid in m2/s. The measured volume flow rate V (m3/s) is then related to the Reynolds number as:
Re=4VπDν
The measured temperature is 293 K; the corresponding ν is 100.3 x 10-8 m2/s; and D = 0.01 m.
Calculations
Conclusions
Analysis of observations
According to theory, Re < 2300 implies laminar flow, 2300 < Re < 4000 implies transitional flow, and Re > 4000 implies turbulent flow. From the experimental results, the Reynolds number for laminar flow is 1523, for transitional flow is 4671, and turbulent flow is 12694. It is evident that while the observations for turbulent and laminar flows match with predictions, in the case of transitional flow, there is a mismatch between theory and experimental result. However, it is important to note that the boundary of 4000 is not strictly fixed, and depends on a number of factors.
Possible Sources of Error
It is interesting to note that for each case, there is a wide range of values allowed. Therefore, even if there were some experimental errors, the final results may still be within the permitted range. Consequently, it is wise to analyze possible sources of error/hidden factors and the accuracy of the results obtained. For example, pipe friction is an important factor to be considered. Further, the temperature of the fluid is related to the flow rate. Therefore, the initial temperature measured need not be a constant, which may result in error. Finally, the introduction of the coloring dye may in itself alter the assumed properties of the fluid; for example, density and kinematic viscosity may vary.
Sketches of Observed Conditions of Dye
Figure 2: Observed laminar flow
Figure 3: Observed transitional flow
Figure 3: Observed turbulent flow
