University of Florida
Department of Mechanical Engineering
Pipe Loss Lab
EML 4304C
Written by: Christian Schneider
Date: 10/8/2006
ABSTRACT
The purpose of this lab was to measure the pressure drop across a series of PVC pipes
and measure the head loss, friction factor and loss coefficient. This was done by pumping
water through a system of valves and small pipes and then measuring difference in head
pressure using H2O manometers. The flow was measured using a rotometer. The friction
factors determined by the calculations were then compared against the theoretical
calculations for smooth pipe. It was found that the measured values for the friction
coefficient where several hundred percent above the theoretical smooth values. The loss
coefficient for the elbow section was calculated to be approximately 0.618.
INTRODUCTION / OBJECTIVE
The purpose of this lab was to demonstrate the concepts of major and minor losses in
hydronic pipe systems. Water with a known density was pumped through a system of
varying size pipes and the relative absolute pressures were measured at known
increments around the system. These measurements where then used to calculate the
subsequent head losses, friction factors and the loss coefficient of the elbow segment.
The friction factors of the straight segments of pipe where compared to those of the
theoretical smooth pipes.
APPARATUS / PROCEDUE
The system as given by the instructor consisted of 2 separate hydronic circuits each fed
by a common pump source. The measurements included a segment of small diameter
pipe, a segment of large diameter pipe, and a segment of small diameter pipe which
included a proprietary 90 deg elbow joint. The gauge pressure at each point were
measured by piezometers. The volume flow rate of the system was measured using a
rotometer positioned before the flow was separated between each circuit of the system.
Necessary Constants:
The pipe length: 914.4 mm
The pipe diameter of the smaller pipe: 13.6 mm.
The pipe diameter of the larger pipe: 26.2 mm.
H20 Density: 1000 kg /m^3
Viscosity of H20: 0.001
90 elbow
(1)
Pipe length between (1) and (2) is 914.4mm
(2)
Main valve
V2
V1
26.4 mm straight pipe (914.4mm)
(8)
(9)
(3)
(4)
13.6 mm straight pipe (914.4mm)
FIGURE 1: Layout of pipe circuits
TECHNICAL APPROACH (THEORY / ANALYSIS)
The head loss for each segment of piping was calculated by the following formulas where
delta H is the difference in the piezometers in mm of H20 and the density is assumed as
1000 kg / m^3
p  H * 9.774
hL 
p

The friction factor of the segment was then calculated by using:
f 
p
1
L
   v2 
2
D
This would provide the friction factors for both the large diameter and small diameter
pipes circuits.
To compare the measured values of the friction coefficient to a pipe which was
considered smooth the following formula was used to determine the friction coefficient
for a smooth pipe.
f smooth  0.316
Re 0.25
To determine the loss coefficient of the proprietary elbow the following formula was
used. The value of the head loss used in the calculation is the difference between the head
loss from the straight segment of small diameter pipe and that of the segment of pipe
including the elbow.
KL 
2  hL
v2
RESULTS / DISCUSSION
The moody charts for both the small and large diameter segments of pipe can be
seen in Figures 2 and 3. As expected the friction factor declines as the flow decreases and
the Reynolds number increases. The over all trend of the values follows the theoretical
values in overall scope but the measured values seem to be decreasing faster as the
Reynolds number increases as opposed to the theoretical values which will reach a
azimuth. This is likely caused by the fact that the errors in the measurements tend to
increase as the volume flow rate decreases. When the rotometer reaches values below 10
L/s the stability and accuracy of the rotometer come into serious question. The possible
error values are not held constant as the equations assume but the error will increase as
flow decreases.
Aside from the difference in trends between the measured and theoretical friction
factors the measured were significantly higher than the theoretical. The trends can be
explained as an error in the measurement at low flows, but the general bias error of the
measurements must stem from some systematic error within the measurements them
selves. This error could have come from many sources but the likely error lie with the
measurement of the pressure difference in the piezometers. When we were performing
the experiment we were having errors within the measurements which sometimes
included the downstream pressure to be higher than the upstream pressure. Some of these
errors were eliminated by the removal of air bubbles within the system but other large
problems with the system still existed. I believe that if the experimental setup were to be
thoroughly checked before the beginning of the experiment and all measurement devices
properly calibrated then the experimental results would like much closer to the theoretical
values.
From the displayed values the straight pipes can not be viewed as smooth as their
friction factors vary from about 175% to over 300% difference. The exact values can be
seen in table 1.
Flow Rate (L/s)
% Diff of f (small)
%Diff of f (large)
14
312
177
12
300
189
11
309
196
10
309
201
8
316
159
6
333
221
4
251
155
Table 1: % difference between measured and smooth pipe friction factors
The loss coefficient for the proprietary 90 elbow was found to be approximately 0.618.
This value is an average of the loss coefficient for the flow rates which were measured.
The range of these values was determined to be 0.315.
Flow Rate
Loss Coefficent (K)
Average
Range:
14
12
11
10
8
6
4
0.68995 0.709342 0.601629 0.404197 0.660023 0.547266 0.719207
0.618802
0.31501
CONCLUSION
The results of this experiment showed the general form and process for determining the
friction factor of a straight pipe and the loss coefficient of an elbow section. The values
of the determined friction coefficient where much higher than expected. The friction
factors followed the projected reality in that they decreased as the flow was decreased
and the Reynolds number was increased. The lab could be greatly improved by obtaining
a more precise set of measuring devices. The errors show a constant bias to a greatly
increased pressure drop between the measuring points. This could be eliminated by using
a digital measuring system for both the flow measurements and the pressure
measurements. Also the system needs to be checked for mineral or other solid mater
build ups within the piping system.
APPENDIX
Darcy Friction Factor (f)
Small Pipe Moody Chart
0.16008
0.14008
0.12008
0.10008
0.08008
0.06008
0.04008
0.02008
0.00008
5000
Measured
Smooth
Poly. (Measured)
Poly. (Smooth)
10000
15000
20000
Reynolds # (Re)
FIGURE 2: Moody chart of small pipe segment
Moody Chart Large Pipe
Darcy Friction Factor (f)
0.14
0.12
Measured Values
0.1
Smooth Flow
0.08
0.06
Poly. (Measured
Values)
0.04
Poly. (Smooth Flow)
0.02
0
3000
5000
7000
Reynolds # (Re)
FIGURE 3: Moody chart for large pipe segment
9000
Pipe Loss
Reading Accuracies
Q±
Length of Pipe ±
Diameter ±
3.6
5
1
Constants:
Density:
Viscosity
(l/m)
mm
mm
1000
0.001
±
0.02
Uncertainty Del p
Small Pipe (3 and 4)
Length
Diameter
Area:
0.9144
0.0136
0.0001453
±
±
m^2
Flow Rate
Corrected Flow
High Level
Low Level
Delta H
Head loss
Flow Rate (m^3/s)
Velocity
14
12.2906
800
45
755
7.398547
0.0002048
1.4101137
12
10.6464
680
110
570
5.585658
0.0001774
1.2214729
11
9.8243
637
130
507
4.9682958
0.0001637
1.1271525
10
9.0022
590
155
435
4.262739
0.00015
1.0328321
8
7.358
506
195
311
3.0476134
0.0001226
0.8441912
6
5.7138
435
227
208
2.0382752
9.523E-05
0.6555504
4
4.0696
355
262
93
0.9113442
6.783E-05
0.4669096
Friction Factor
Reynolds Number
Smooth
Uncertainty V
Uncertainty del P
% Difference of f
0.1106804
19177.547
0.0268528
0.0705057
0.1479709
312.17536
0.1113626
16612.031
0.0278344
0.0610736
0.1117132
300.09025
0.1163255
15329.274
0.0283992
0.0563576
0.0993659
309.6077
0.1188672
14046.516
0.0290265
0.0516416
0.0852548
309.51242
0.127207
11481.001
0.0305276
0.0422096
0.0609523
316.69544
0.1410858
8915.4854
0.03252
0.0327775
0.0407655
333.84291
0.1243511
6349.9702
0.0353993
0.0233455
0.0182269
251.2816
Small Pipe Uncertainty
(df/dL)*δL
6.052E-07
(df/dd)*δd
8.138E-06
(df/dρ)*δρ
2.214E-09
(df/dv)*δv
1.107E-05
(df/dΔp)*δΔp
2.214E-06
6.089E-07
8.188E-06
2.227E-09
1.114E-05
2.227E-06
6.361E-07
8.553E-06
2.327E-09
1.163E-05
2.327E-06
6.5E-07
8.74E-06
2.377E-09
1.189E-05
2.377E-06
6.956E-07
9.353E-06
2.544E-09
1.272E-05
2.544E-06
7.715E-07
1.037E-05
2.822E-09
1.411E-05
2.822E-06
6.8E-07
9.143E-06
2.487E-09
1.244E-05
2.487E-06
δf=sum(uncertainties)
Root Sum Square
2.203E-05
1.393E-05
2.216E-05
1.401E-05
2.315E-05
1.464E-05
2.366E-05
1.496E-05
2.532E-05
1.601E-05
2.808E-05
1.775E-05
2.475E-05
1.565E-05
Large Pipe
Length:
Diameter
Area:
0.9144
0.0262
0.0005391
±
±
m^2
7
6.5359
221
214
7
0.0685958
5.5
5.30275
174
168
6
0.0587964
4
4.0696
118
115
3
0.0293982
Flow Rate
Corrected Flow
High Level
Low Level
Delta H
Head loss
13
11.4685
535
515
20
0.195988
11.5
10.23535
444
427
17
0.1665898
0.005
0.001
0.005
0.001
10
9.0022
338
324
14
0.1371916
m
m
m
m
8.5
7.76905
281
270
11
0.1077934
Flow Rate (m^3/s)
Velocity
0.0001911
0.3545381
0.0001706
0.3164164
0.00015
0.2782947
0.0001295
0.240173
0.0001089
0.2020513
8.838E-05
0.1639296
6.783E-05
0.1258079
Friction Factor
Reynolds Number
Smooth
Uncertainty V
Uncertainty del P
% Difference of f
0.0893509
9288.898
0.0321882
0.0177269
0.22937
177.58929
0.0953511
8290.1097
0.0331167
0.0158208
0.204707
187.92442
0.1015109
7291.3213
0.0341968
0.0139147
0.180044
196.84325
0.1070875
6292.5329
0.0354798
0.0120087
0.155381
201.82703
0.0962873
5293.7445
0.0370464
0.0101026
0.130718
159.90994
0.1253808
4294.9561
0.0390344
0.0081965
0.106055
221.20591
0.1064388
3296.1677
0.0417047
0.0062904
0.081392
155.22019
Large Pipe Uncertainty
(df/dL)*δL
4.886E-07
(df/dd)*δd
3.41E-06
(df/dρ)*δρ
1.787E-09
(df/dv)*δv
8.935E-06
(df/dΔp)*δΔp
0.0001046
5.214E-07
3.639E-06
1.907E-09
0.0005858
0.0001172
5.551E-07
3.874E-06
2.03E-09
0.0006661
0.0001332
5.856E-07
4.087E-06
2.142E-09
0.0007718
0.0001544
5.265E-07
3.675E-06
1.926E-09
0.0009174
0.0001835
6.856E-07
4.786E-06
2.508E-09
0.0011308
0.0002262
5.82E-07
4.063E-06
2.129E-09
0.0014734
0.0002947
δf=sum(uncertainties)
Root Sum Square
0.0007072
0.0005975
0.0008037
0.0006793
0.0009309
0.0007871
0.0011051
0.0009356
0.0013624
0.0011532
0.0017728
0.0015026
0.0001174
0.000105
Elbow Pressure (1 and 2)
Length
0.935
Diameter
0.0136
Area
0.0001453
±
±
Flow Rate
Corrected Flow
High
Low
Delta H
Head loss
Volume Flow Rate
Velocity
14
12.2906
855
30
825
8.084505
0.0002048
1.4101137
12
10.6464
700
76
624
6.1148256
0.0001774
1.2214729
11
9.8243
640
94
546
5.3504724
0.0001637
1.1271525
10
9.0022
570
113
457
4.4783258
0.00015
1.0328321
8
7.358
470
135
335
3.282799
0.0001226
0.8441912
6
5.7138
370
150
220
2.155868
9.523E-05
0.6555504
4
4.0696
265
164
101
0.9897394
6.783E-05
0.4669096
Friction Factor
Reynolds Number
Smooth
Uncertainty V
Uncertainty del P
% Difference of f
0.1182776
19177.547
0.0268528
0.0705057
0.245812
340.46726
0.2348613
16612.031
0.0278344
0.0610736
0.212928
743.78167
0.2413359
15329.274
0.0283992
0.0563576
0.196486
749.79696
0.2405755
14046.516
0.0290265
0.0516416
0.180044
728.81272
0.2639719
11481.001
0.0305276
0.0422096
0.14716
764.70017
0.2874783
8915.4854
0.03252
0.0327775
0.114276
784.004
0.2601659
6349.9702
0.0353993
0.0233455
0.081392
634.94733
Elbow Pipe Uncertainty
(df/dL)*δL
6.325E-07
(df/dd)*δd
8.697E-06
(df/dρ)*δρ
2.366E-09
(df/dv)*δv
1.183E-05
(df/dΔp)*δΔp
3.596E-06
6.376E-07
8.767E-06
2.385E-09
1.192E-05
4.152E-06
6.552E-07
9.008E-06
2.45E-09
1.225E-05
4.499E-06
6.531E-07
8.98E-06
2.443E-09
1.221E-05
4.91E-06
7.166E-07
9.853E-06
2.68E-09
1.34E-05
6.007E-06
7.804E-07
1.073E-05
2.919E-09
1.459E-05
7.736E-06
7.063E-07
9.711E-06
2.641E-09
1.321E-05
1.086E-05
δf=sum(uncertainties)
2.548E-05
2.642E-05
2.676E-05
2.998E-05
3.384E-05
3.449E-05
2.476E-05
0.005
0.001
m
m
Root Sum Square
1.513E-05
1.538E-05
1.587E-05
1.595E-05
1.77E-05
1.971E-05
1.968E-05
Loss Coefficient (K)
0.6899526
0.7093418
0.601629
0.4041967
0.660023
0.5472661
0.719207
Average
Range:
0.6188023
0.3150103