LAB REPORT ENERGY LOSSES DUE TO FRICTION IN A CYLINDRICAL PIPE
INTRODUCTION
The flow of fluid in a pipe is i s accompanied by the loss of energies as a result of the interaction between the fluid and the viscous stresses on the wall of the pipe. The energy loss may be in the form of pressure loss in the system due to friction, pipe bend or connections etc. This experiment will focus on the energy losses due to friction in the pipe, the relationship between head loss (loss in pressure), friction factor, flow rate and Reynolds number for both laminar and turbulent flow in a smooth pipe will also be investigated. AIM AND OBJECTIVE
The aim and objective of this experiment was to determine experimentally the head loss in a smooth cylindrical pipe and to establish its relationship with the fluid flow rate in the pipe. Furthermore, the dimensionless groups (Reynolds number and friction factor) were determined from the results generated in the experiment using their relationships with other parameters for the purpose of analysis. From the values obtained for the Reynolds number, the flow was classified as either laminar or turbulent with a transition region existing between the two flows.
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BACKGROUND READING
The concept of energy loss is crucial for effective design of pipe works and other channels where the fluid flows. This is because, an Engineer or the designer is interested in knowing the actual pressure force which is required to convey the fluid in a channel irrespective of the smoothness or roughness of the pipe. Failure to understand the sources of losses in pressure energy as the fluid flows from one region to the other may adversely affect the efficiency of the system. Some experimental and analytical methods has been developed to model the relationship between the head loss , the friction factor , the average velocity of flow and other parameters as given by Darcy-Weibach equation ; hf = f (L/D) x (v2/2g), (W Darcy, 2008 p.379) where; hf = head loss (m) f = friction factor L = length of pipe work (m) d = inner diameter of pipe work (m) v = velocity of fluid (m/s) g = acceleration due to gravity (m/s²) It is also necessary to consider the theoretical relationship between the friction factor and Reynolds number (Re) for a smooth pipe using the Hagen-Poiseullie equation for a laminar flow, f = 64/Re
where ;
which can be derived from dimensional analysis.
For turbulent flow, f = 0.316/Re0.25
……
(Blasius equation).
For the purpose of distingushing the various regions of flow, the Reynold number is extremely important as argued by B, Webber, (1982), which states that for a laminar flow,
< 2000 For turbulent flow, 2000 – 4000.
> 4000, and the transition zones ranges from
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EXPERIMENTAL
SET UP
U-Tube Manometer
Reservoir
1m
Measuring cylinder
Control Valve
Large diameter pipe (17.2mm) Small diameter pipe(4.5m Figure 1: A schematic diagram of the experiment set up
The apparatus was set up as shown above with a Control valve for regulating the flow rate, Manometer for reading the pressure drop or loss between the two pipes, Reservoir for the fluid storage and a stop watch for recording the time at each setting. The apparatus works by pumping water from the reservoir into the pipes. The volume of water for each test is usually measured in the reservoir. There are many valves in the apparatus; behind the apparatus is a valve which helps to control the fluid flow. The pressures were measured by connecting a manometer to the pressure taps on either sides of each pipe.
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PROCEDURE AND INSTRUMENTATION
The following procedures were followed to obtain the readings used for the evaluation of the important parameter in this experiment. 1) The water temperature before the flow was recorded as 20oc using the
thermometer 2) The volume of water for each flow test was measured and recorded 3) The air in the large pipe was removed by setting the flow rate to the maximum 4) The reading for the maximum flow rate was taken 5) The flow rate was reduced to a point where readings for the pressure drop were measured each time and the value was recorded 6) Average reading for the procedure was taken 7) Step 1-6 were repeated for the small diameter pipe and the readings were
taken accordingly.
ERROR ANALYSIS
From this experiment, some values of friction factor for two pipes were determined. Considering the results obtained for the laminar, turbulent and transition regions of flow, it could be observed clearly that there was some deviation in the values which were obtained for the experimental and theoretical values for the friction factor especially for the small diameter pipe. From the table (figure 2), the friction factor has a percentage error of + _ 11.5% for the laminar flow in the 4.5 diameter pipe. This error may have resulted from poor pressure difference readings in the scale which may have compounded the overall error. Between the laminar and transition (Transition) zones, the variation in temperature may have contributed to some of the discrepancies in these results. This is because, the change in temperature can affect the viscosity, density and other parameters used in the calculation. The variation may have been from changes in the temperature of the surrounding which was not taken into consideration. Another source of error in the experiment could be the presence of bubbles in the pipes during the time of the experiment. The air bubbles may have interrupted the 4
fluid flow rate during the initial readings. Similarly, poor readings from the manometer scales may have affected the accuracy of the results.
DISCUSSION OF RESULTS
The results obtained as shown on the table and the graph of Reynolds number versus friction factor shows that the pipe flow in the 4.5mm diameter pipe behaves similarly as predicted by Hagen Poiseuille’s equation for laminar flow,(f =64/Re). The agreement in these values could be that experimental errors were minimal in this region, thus, the laminar flow region was more consistent the overall trend observed in the experiment. However, the prediction of the region of the transition was a bit more complex for analysis given that there were no empherical methods or equation to compare their behaviour with in order to interpret the trend. Furthermore, the value of the friction factor for the turbulent flow in the large diameter pipe was not much accurate when compared with standard models such as the Moody chart and the Blasius equation (f = 0.316/Re0.25 ). The probable cause of these discrepancies could be as a result of poor readings of pressure drop in the manometer which influenced most of the calculated parameters. Similarly, there was an anomalous value for a friction factor in the turbulent state (0.109) ,(see graph) which corresponds to the maximum flow rate. The measurement error at this point may be associated with an increase in temperature which may have increased the viscosity of the fluid resulting from the assumption that the fluid viscosity at 20oc was taken as 0.001 N.sm -2 giving room for errors since the external temperature in the surrounding was not considered as the experiments proceeds. The effect of this variation may have had a serious impact on the calculation of the friction factor at this point owing to the relationship of the flow rate, the friction factor and the Reynolds number in a given flow. It was observed that as the flow rate and the Reynolds number increases respectively for each test for the turbulent flow in a smooth pipe, there was a corresponding decrease in the friction factor. For the lowest flow rate, the probable measurement error could be error in pressure readings which may have affected the important calculations.
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CONCLUSION
The aim of this experiment was to determine the head loss (pressure difference), the flow rate, friction factor and some associated parameters relating to the Reynolds number. The head loss and the friction factor was determined through a 4.4mm and 17.2mm cylindrical pipes and compared with equations for friction factor, f = 64/Re and f = 0.316/Re for laminar and turbulent flow respectively. Though the experiment fulfilled most of the above relationships, no actual model was developed for determining the behaviour of fluid in the transition region. Furthermore, the direct variation of the Reynolds number and the flow rate was shown to vary inversely with the friction factor as the flow develops from one region to the other. Finally, some errors limited the overall results obtained in the experiment. To improve the reliability of subsequent experiments, conducting the experiment in a controlled environment should be considered in order to minimise the effects of variation of temperature or viscosity in the fluid system. Similarly, the manometer should be marked in such a way that readings may be taken more accurately.
REFERENCES N.B WEBBER, 1965,. Fluid Mechanics for Civil engineers, The University of Southampton, UK. F.M Frank, 2008; Fluid Mechanics, 6 th edition. McGraw Hill Companies, Americas, New York.
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S A M P L E C A L C U L AT IO N S B e l o w is t h e s a m p l e c a l c u l a t io n s f o r th e p r e s s u r e d if fe r e n c e , F l o w r a t e , M e number. LAMINAR P r e s s u r e d if f e r e n c e , a v e ra g e re a d in g s
1)
ହǤହାସǤାାସ଼ Ǥ ଷ ଵାǤ ǤଷାǤ h 2f = ଷ ሺଵ ଷǤସାଵଷǤଷାଵ ଷǤଶሺ hf 3 = ଷ
a.
h 1f =
b. c.
= 0.049m =
0 .0 7 1 m =
0.133m
2 ) F l o w r a t e (Q ) ௨ ሺ ଷሺ
Q =
் ሺ ௦ሺ
1 L i t r e = 0 .3 0 0 1 m a . Q1 = b . Q2 = c . Q3 =
Ǥ ଵ
= 4 . 3 2 5 -63 m* 31 0
ଶ ଷ Ǥଵଶ Ǥ ଵ
ଵ ଶଶǤଽ Ǥ ଵ
= 8 . 1 3 6 -67 m* 31 0 =
ଵ Ǥଽା ଼
9 . 1 0 7 -65m* 31 0 ்
3)
T h e m e a n v e= l o c i t y ῡ
ଷǤଵ ସ ଶ Ǥ ସ ହଶ W h e re A = = = = 1 . 5 9 0 4-5 m * 12 0 ସ ସ ଶ
ሺ1
=
ሺ2 =
ሺ3
=
ସǤଷଷଵାି = ଵǤହ ଽ ଵାହି
0 .2 7 2 m /s
ାǤଵ଼ ସଵାି = ଵǤହ ଽ ଵାହି
0 .5 1 2 m /s
ଽǤଵ ଵଵାି = ଵǤହ ଽ ଵାହି
0 . 5 7 3 m /s
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