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The aim of this lab report "Minor Losses in Bends and Fittings" is the determination of k values through experiments for the various pipe fittings and what was obtained then being compared with theoretical values obtained for books and other authentic sources…
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Extract of sample "Minor Losses in Bends and Fittings"
MINOR LOSSES in bends and fittings
Introduction
Fluids going through pipes results to brings about loss of pressure that is stated in terms of of equivalent head loss, HL of the fluid passing through the pipe. The pressure (P) and head (H) are related by equation. The loss in pressure is as a result of fluid viscosity why the viscosity is measured by value of coefficient of fluid friction. Just as in the case of friction occurrence in moving solids, shear resistance happening in fluids that have high viscosity are to transform kinetic energy to heat energy that is a representation of loss of energy that is in flowing fluid. The bulk of this energy is changed to heat that brings about warming of fluid while some proportion is lost through radiation and conduction. There can be prediction of pipe work head losses by having separate computation of head losses that comes about as a result of friction between the fluid layers and the inner walls of pipes and then head losses attributable to minor losses, linked to fittings. Minor losses relative to magnitude of head losses as loss coefficient K.
Apparatus
Figure 1
Procedure
This experiment involved measurement of pressure drop across the pipe features by use of piezometer tappings located upstream and downstream of the target fitting. There was connection to multitude manometer, as can be seen in figure 1 , such that pressure drop across each of the fitting was a differential piezometer reading, with the value being expressed in mm. The rate of flow was varied by use of flow control valves, such that the maximum possible flow was registered but taking care that the maximum flow did not reach to a point it became impossible for the manometer menisci could not be seen. There was recording of readings associated with various flow rates with the measurement of Q being in kg/s. Table 1 gives the results from experiment and further calculation have been done to come up with table 2.
Calculations
In cases that involve bends and fittings in pipes the energy losses incurred is expressed in terms of the equivalent head loss HL (m) that is given by the equation
HL =
Where K gives the loss coefficient that is dimensionless, g is the gravitational acceleration which is supposed to be constant given in (m/s2) with V being the velocity of the fluid in m/s.
For each type of connection there is to be a unique K which is determined experimentally. The aim of this experiment was the determination of k values through experiment for the various pipe fittings and what was obtained then being compared with theoretical values obtained for books and other authentic sources.
The pipe diameter of 22.5mm is used in the calculation of velocity in the pipe line.
Area of pipeline = 397.61mm2
= 0.0003976m2
Figure 2
Results
Table 2 gives the results that were calculated in excel. With the units of V2/2g being in m K will be unitless remembering that HL is in m something that can also be achieved through division of units of V2 by units of g
Thus m2/s2 m/s2 = m
The plots of H vs V2/2g the fittings are as shown in figure 3 and figure 4. The K values are obtained from the equation on the graphs and are as shown in table 1.
Figure 3
Figure 4
Table 1: Comparison on Ks
Type of loss
K Experimental
K from books
Mitre
1.617
1.38
Elbow
1.126
1.5
Large bend
0.66
0.46
Enlargement
1.141
5
Contraction
0.307
0.5
Table 2
H2
Q
Q
Area(1)
Area(2)
Velocity1
Velocity2
Mitre
(mm)
(m3/s)
(m3/s)
(m/s)
154
0.154
0.554
0.000554
0.0003976
0.0006881
1.393360161
1.941452538
1.39336
1.941453
0.098953
0.098953
148
0.148
0.524
0.000524
0.0003976
0.0006881
1.317907445
1.736880033
1.317907
1.73688
0.088526
0.088526
126
0.126
0.514
0.000514
0.0003976
0.0006881
1.292756539
1.67121947
1.292757
1.671219
0.085179
0.085179
104
0.104
0.462
0.000462
0.0003976
0.0006881
1.161971831
1.350178536
1.161972
1.350179
0.068816
0.068816
90
0.09
0.427
0.000427
0.0003976
0.0006881
1.073943662
1.153354989
1.073944
1.153355
0.058785
0.058785
75
0.075
0.392
0.000392
0.0003976
0.0006881
0.985915493
0.972029359
0.985915
0.972029
0.049543
0.049543
53
0.053
0.329
0.000329
0.0003976
0.0006881
0.827464789
0.684697977
0.827465
0.684698
0.034898
0.034898
Elbow
113
0.113
0.554
0.000554
0.0003976
0.0006881
1.393360161
1.941452538
1.39336
1.941453
0.098953
0.098953
102
0.102
0.524
0.000524
0.0003976
0.0006881
1.317907445
1.736880033
1.317907
1.73688
0.088526
0.088526
93
0.093
0.514
0.000514
0.0003976
0.0006881
1.292756539
1.67121947
1.292757
1.671219
0.085179
0.085179
77
0.077
0.462
0.000462
0.0003976
0.0006881
1.161971831
1.350178536
1.161972
1.350179
0.068816
0.068816
64
0.064
0.427
0.000427
0.0003976
0.0006881
1.073943662
1.153354989
1.073944
1.153355
0.058785
0.058785
58
0.058
0.392
0.000392
0.0003976
0.0006881
0.985915493
0.972029359
0.985915
0.972029
0.049543
0.049543
40
0.04
0.329
0.000329
0.0003976
0.0006881
0.827464789
0.684697977
0.827465
0.684698
0.034898
0.034898
Large Bend
62
0.062
0.554
0.000554
0.0003976
0.0006881
1.393360161
1.941452538
1.39336
1.941453
0.098953
0.098953
58
0.058
0.524
0.000524
0.0003976
0.0006881
1.317907445
1.736880033
1.317907
1.73688
0.088526
0.088526
55
0.055
0.514
0.000514
0.0003976
0.0006881
1.292756539
1.67121947
1.292757
1.671219
0.085179
0.085179
45
0.045
0.462
0.000462
0.0003976
0.0006881
1.161971831
1.350178536
1.161972
1.350179
0.068816
0.068816
39
0.039
0.427
0.000427
0.0003976
0.0006881
1.073943662
1.153354989
1.073944
1.153355
0.058785
0.058785
28
0.028
0.392
0.000392
0.0003976
0.0006881
0.985915493
0.972029359
0.985915
0.972029
0.049543
0.049543
22
0.022
0.329
0.000329
0.0003976
0.0006881
0.827464789
0.684697977
0.827465
0.684698
0.034898
0.034898
Enlargement
-28
-0.028
0.554
0.000554
0.0003976
0.0006881
1.393360161
1.941452538
0.805116
0.648211
0.033038
0.098953
-26
-0.026
0.524
0.000524
0.0003976
0.0006881
1.317907445
1.736880033
0.761517
0.579908
0.029557
0.088526
-25
-0.025
0.514
0.000514
0.0003976
0.0006881
1.292756539
1.67121947
0.746984
0.557986
0.02844
0.085179
-19
-0.019
0.462
0.000462
0.0003976
0.0006881
1.161971831
1.350178536
0.671414
0.450797
0.022976
0.068816
-12
-0.012
0.427
0.000427
0.0003976
0.0006881
1.073943662
1.153354989
0.620549
0.385081
0.019627
0.058785
-14
-0.014
0.392
0.000392
0.0003976
0.0006881
0.985915493
0.972029359
0.569685
0.324541
0.016541
0.049543
-10
-0.01
0.329
0.000329
0.0003976
0.0006881
0.827464789
0.684697977
0.478128
0.228607
0.011652
0.034898
Contraction
109
0.109
0.554
0.000554
0.0003976
0.0006881
0.805115536
0.648211026
1.39336
1.941453
0.098953
0.033038
100
0.1
0.524
0.000524
0.0003976
0.0006881
0.761517221
0.579908478
1.317907
1.73688
0.088526
0.029557
89
0.089
0.514
0.000514
0.0003976
0.0006881
0.74698445
0.557985768
1.292757
1.671219
0.085179
0.02844
71
0.071
0.462
0.000462
0.0003976
0.0006881
0.671414039
0.450796811
1.161972
1.350179
0.068816
0.022976
63
0.063
0.427
0.000427
0.0003976
0.0006881
0.620549339
0.385081482
1.073944
1.153355
0.058785
0.019627
52
0.052
0.392
0.000392
0.0003976
0.0006881
0.569684639
0.324540588
0.985915
0.972029
0.049543
0.016541
36
0.036
0.329
0.000329
0.0003976
0.0006881
0.478128179
0.228606556
0.827465
0.684698
0.034898
0.011652
References
F. M. White, 1999. Fluid Mechanics, McGraw-Hill.
B. R. Munson, D.F Young and T. H. Okiisshi, 1998. Fundamentals of Fluid Mechanics, John Wiley and Sons, Inc. . Y. Nakayama and R.F. Boucher, 1999.Intoduction to Fluid Mechanics, Butterworth Heinemann.
Y.A. Cengel and J. M. Cimbala, 2006. Fluid Mechanics, McGraw Hill.
J.M. McDonough, 2004. Lectures in Elementary Fluid Dynamics: Physics, Mathematics and Applications, University of Kentucky, Lexington.
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