The lab is aimed at investigating the relation between the head loss and the mean velocity in the pipes either during the laminar and turbulent flow regimes. The experimental data will be collected from two type of pipes, i.e. a small smooth pipe in both laminar and turbulent regimes and large sand roughened interior pipe under the turbulent flow. The lab will also endeavour to determine the lower critical velocity and coefficient of viscosity of water for the small pipe.
Introduction
The experiment undertaken in this study is to characterize the flow regimes in pipes and the factors affecting laminar and turbulent flow regimes. The experiment is typically done via the use of two pipes of known diameters with water being pumped from a tank (Marusic et al., 2007). The lab exercise will entail the measurement of water and the time taken to determine the flow rate and the velocity of the fluid in the two pipes. The parameters will be utilized in the calculation of the flow rate, friction factor and Reynolds number. The primary purpose of the process is to analyse and identify the region of laminar and turbulent flow in the smaller smooth pipe.
Theory
The following fundamental equations will be used to analyse the data that was collected in the experiment.
Poiseuille equation:
Head loss along the pipe
The kinematic viscosity can be calculated using the following equation
Alternatively, the velocity of the fluid can be determined empirically using the temperature:
The friction factor f can be calculated using the formula
Procedure
Part 1: Small Pipe Test
The red valve P was also fully opened then the water will be allowed to flow over the weir in the constant head tank.
Valve C was opened fully to allow maximum flow. The flow rate will be recorded from the rotameter mm scale. The manometer was read after the stream steadies.
The discharge was decreased by 2 to 3 mm on the rotameter scale by closing valve C. The manometer and rotameter scales were recorded, as before and exercise moved to the next value. Once done valve C and red valves were fully closed.
Part 2: Large Pipe Test
Valve D and F were fully opened, and then the manometer valves E were opened.
The manometer scale was read and the volumetric flow rate on the rotameter scale record. The flow rate was reduced in six steps of 25 litres/minute from the approximate value of 47.5 l/m to 35 l/m and the manometer scales for the different flow rate. Once the second part was completed, the manometer valve E was closed, and then the valves D and F closed.
Results
Figure 1: The graph of head loss against the velocity
Figure 2: The Graph of log hf against the log (V)
Reynolds number can be calculated as
Thus, the Reynolds number becomes
Where
is the density of the fluid
is the diameter of the pipe
is the velocity of the fluid
is the viscosity of the fluid
Laminar Flow
The Reynold Number
815.78 < 2000
Turbulent Flow
The Reynold Number
6003.6461 > 2000
Discussion
The results illustrate that the head loss in the pipes increased with an increase in the velocity of the fluid. The head losses were higher in the turbulent flow than the laminar flow (Riveros " Riveros-Rosas, 2010). The Reynolds number in the experiment fell within the expected defined bounds for the laminar and turbulent flows. The value of the Re for the laminar flow was 815.78 which is lower than the set boundary of 2000. Additionally, the value of the turbulent flow was 6003.6461 which was higher than the set limit of 4000 (Gupta et al., n.d.). The Reynolds number values illustrate an increase in the head losses hence the trend is changing from laminar to turbulent. The flow rate increased with the increase in the velocity subsequently decreasing the pressure in the pipes. The results illustrate that the flow rate in the pipes is directly related to the Reynolds number. The variation in the Reynolds number was caused by numerous reasons such as parallax in data collection and inaccuracies in the measurement methods.
Conclusion
The lab provided the relationship between the head losses and the mean velocity of the fluid. The data characterizing the relation was compared for the laminar and the turbulent flow regimes. The Reynolds number was used to describe the different regimes. The lab introduced the Reynolds number which was used to quantify the flow regimes in the experiment.
Reference
Gupta, N., Hmurcik, L., Joshi, M. " Dharmadhikari, B., n.d. On the Analysis of the Laminar to Turbulent Flow Patterns in the Treatment of a Patient Receiving Oxygen. International Journal of Applied Sciences, 1(2), pp. 23-29.
Marusic, I., Joseph, D. D. " Mahesh, K., 2007. Laminar and turbulent comparisons for channel flow and flow control. Journal of Fluid Mechanics, Volume 570, pp. 467-477.
Riveros, H. G. " Riveros-Rosas, D., 2010. Laminar and turbulent flow in water. Physics Education, 45(3), pp. 288-291.
