Worksheet - Pressure Losses in Flow
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Pressure Losses in Flow Worksheet This worksheet supports Section 3 in the general Lab Manual. I.
Head Losses in Pipe and Fittings 1.
Determine the transducer voltage bias average value from the data file. Include the 95% CI for this value. 2.
Record the following data:
Value
Precision
L
small pipe
39 7/16
1/32
L
large pipe
39 3/8
1/32
L
rough pipe
39 3/8
1/32
Each team member should make an independent measurement of the diameter for each of the
three pipes. Record the readings and compute the 95% confidence intervals. Also note the manufacturer’s stated accuracy (bias) for the calipers. Reading 1
Reading 2
Reading 3
Reading 4
95% CI
Mfgr
Accuracy
D
small pipe
.427
.425
.424
.429
.42625
+/–
.004
0.001
D
Large pipe
.670
.672
.674
.674
.6725
+/–.
003
0.001
D
rough pipe
.625
.628
.627
.627
.62675
+/–
.002
0.001
3.
Complete the first four columns of Table 1 below. Use recorded data and determine the average, standard deviation of the voltage signals for each measurement, and 95% CI for each measurement. 1.
Third from top diameter length of pipe 2.
Largest length of smooth pipe 3.
Length of roughened pipe 4.
90 degree elbow (brass fitting after valve section)
5.
90 degree long radius (tubing in top right)
ME 460
1 Pressure Losses in Flow V
o
= 2.6241323+/– 2.899*10^-5
From the data file, find the average value, standard deviation and CI for each fill in Table.
ME 460
2 Pressure Losses in Flow
Table 1: Flow rate and pressure transducer voltage measurement results for various fittings and pipe configurations.
Pipe/Fitting
Flow
Rate
(GPM)
Avg
Voltage
(Volts)
St Dev (Volts)
95% CI
(Volts)
Pressure
Loss
(PSID)
3
rd
Tube from Top
9
6.2056
.0184
0.0038
6.7709
8
5.5664
.012381
0.0029
6.4012
7
4.902511
.009200
0.0032
5.9152
6
4.39717
.012705
0.0127
5.4469
5
3.922362
.01275
0.0034
4.8970
Largest Smooth Pipe
12
3.111849
0.01151
0.0026
3.5704
10
3.000707
0.05242
0.0098
3.3327
8
2.852248
0.0186008
0.0038
2.9861
6
2.708298
0.01128335
0.0029
2.6139
4
2.60758
0.01128543
0.0030
2.3290
Rough Pipe
11
5.1072575
0.03308824
0.0090
6.0786
9
4.2729534
0.03160118
0.0093
5.3148
7
3.5579196
0.03638409
0.0088
4.3753
5
3.1157204
0.03777299
0.0101
3.5784
3
2.7149301
0.04565835
0.0123
2.6319
90 deg elbow
11
3.2988303
0.01289019
0.0034
3.9343
90 deg long radius
11
2.6938629
0.01049060
0.0027
2.5743
ME 460
3 Pressure Losses in Flow
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4.
Pressure loss calculation: Use equation editor to input the relevant equation used to convert
voltage signal into pressure loss. Convert voltages in the table above and complete the table
with the pressure differential for each case. Ideal PSI=
[
R
∗
(
I
−
4
mA
)
∗
(
psid Range
R
∗
16
mA
)
]
−[
(
V
−
V
0
)
∗
(
psid Range
∆Vmax
)
]
5.
Calculate the maximum measurement precision error (95% CI) for measured pressure differential in the table above. Report your value below in green font. Compare this value to
the manufacturer’s bias for the pressure transducer. Do you need to consider the precision error in uncertainty propagation? Discuss.
P
MAX
=6.7709+.0127(max CI)=6.7836
The pressure transducer has an accuracy of .25%. This accuracy percentage would result in a range of +- .01692725. The 95% confidence interval found shows is well within the range described by the manufacturer.
6.
Use the equation editor to document in green font the equations used to calculate 1) friction factor f
D
, and 2) loss coefficient, K
, from the measured parameters (
L, D, GPM, PSI
). Include
units to demonstrate that f
D
and K
are indeed unitless.
K
=
h
f
(
2
g
c
)
V
2
¿
∗
¿
s
2
¿
2
s
2
f
D
=
h
f
(
D
)(
2
g
c
)
L
∗
V
2
¿
∗
¿
∗
¿
s
2
¿
∗
¿
2
s
2
Use your equations to compute the nominal values for f
D
and K
and insert them in the columns of Table 2.
7.
Error propagation calculations: Use equation editor to input the relevant equations used to propagate uncertainty in length, diameter, flow rate, and pressure drop into the calculated values for f
D
and K
. Note: For the pressure transducer (Omega PX2300-25DI the manufacturer states the accuracy is 0.25% FS. For the flow meter (Omega FL-75D Rotameter), the stated accuracy is
3% FS.
ME 460
4 Pressure Losses in Flow
U
Δ P
=
¿
√
Measure∆ P
2
+
.25
2
Measurement = 10/8 * (V_V0)
U
D
=
¿
.0005
U
L
=
¿
.03125
U
GPM
=
¿
√
Measured Flow rate
2
+
.03
2
U
f
D
=
¿
√
¿¿
U
K
=
¿
√
¿¿
Input the results of these calculations in Table 2.
ME 460
5 Pressure Losses in Flow
Table 2 - Friction Factor and Loss Coefficient Results
Pipe
Flow Rate
(GPM)
Friction Factor, f
D
Uncertainty, U
f
3
rd
Tube from Top
9
0.0262
0.0005
8
0.0314
0.0006
7
0.0379
0.0008
6
0.0475
0.0010
5
0.0615
0.0012
Largest Smooth Pipe
12
0.0626
0.0018
10
0.0842
0.0024
8
0.1179
0.0034
6
0.1834
0.0052
4
0.3677
0.0105
Rough Pipe
11
0.1099
0.0032
9
0.1435
0.0042
7
0.1953
0.0058
5
0.3130
0.0092
3
0.6395
0.0188
0.0262
0.0005
Fitting
Loss Coefficient, K
Uncertainty, U
K
90 deg elbow
11
2.406544
0.292145
90 deg long radius
11
1.459633
0.179879
ME 460
6 Pressure Losses in Flow
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Prepare plots showing the variation of f
D
with Reynolds number. Show measured values as data points (with no lines) and include a dashed line with corresponding theoretical values from the Swamee-Jain relation.
What value did you determine for the absolute roughness of the roughened pipe?
= .0012 feet
Discuss your results and uncertainties. This Lab provided a very easy to understand demonstration of the principles of head loss. However it appears that some of the data shown in the Reynolds number vs friction factor graph is a little off, as shown by two of the curves not following the line as expected. Aside from this instance, the results are as expected with changes accruing as expected from change in flow rate, diameter, and roughness. The largest source of error expected would be from reading the flow rate, followed by possible rounding errors when making calculations. ME 460
7 Pressure Losses in Flow
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