View Model Problem Statement
PRODUCT: AFT Fathom
TITLE: FthVerify69.fth
REFERENCE: Roland Jeppson, Analysis of Flow in Pipe Networks, 1976, Publisher Ann Arbor Science, Page 102-105
FLUID: Water
ASSUMPTIONS: Assume water at 70 deg. F.
RESULTS:
| Pipe Flow Rate (ft3/sec) |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
| Jeppson |
11.61 |
3.18 |
2.18 |
1.5 |
2.22 |
-1.19 |
0.3 |
-0.68 |
| AFT Fathom |
11.506 |
3.175 |
2.175 |
1.498 |
2.201 |
-1.123 |
0.380 |
-0.670 |
| Pipe Flow Rate (ft3/sec) |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
| Jeppson |
0.49 |
-1.43 |
2.63 |
2.06 |
10 |
0.93 |
1.49 |
1.89 |
| AFT Fathom |
0.570 |
-1.400 |
2.520 |
1.987 |
9.937 |
1.074 |
1.535 |
1.821 |
| Pipe Flow Rate (ft3/sec) |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
| Jeppson |
1.54 |
1.47 |
2.75 |
2.71 |
-0.26 |
-1.45 |
-1.77 |
-1.71 |
| AFT Fathom |
1.322 |
1.396 |
2.480 |
2.461 |
-0.189 |
-1.271 |
-1.558 |
-1.543 |
| Pipe Flow Rate (ft3/sec) |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
| Jeppson |
0.58 |
2.09 |
-2.1 |
0.07 |
1.18 |
2.73 |
1.14 |
-0.92 |
| AFT Fathom |
0.551 |
1.973 |
1.980 |
-0.065 |
1.055 |
2.561 |
1.089 |
-0.754 |
| Pipe Flow Rate (ft3/sec) |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
40 |
| Jeppson |
4.72 |
3.51 |
0.71 |
-1.95 |
-2.72 |
0.88 |
-0.43 |
-3.72 |
| AFT Fathom |
4.632 |
3.298 |
0.642 |
-1.748 |
-2.439 |
0.815 |
-0.182 |
-3.344 |
| Pipe Flow Rate (ft3/sec) |
41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
| Jeppson |
1.05 |
-1 |
-0.86 |
-0.5 |
-0.4 |
1.45 |
1.43 |
0.35 |
| AFT Fathom |
0.867 |
-0.893 |
-0.514 |
0.505 |
-0.444 |
1.307 |
1.307 |
0.361 |
| Pipe Flow Rate (ft3/sec) |
49 |
50 |
51 |
52 |
53 |
54 |
55 |
56 |
| Jeppson |
2.55 |
1.45 |
4.25 |
9.03 |
1.24 |
-3.02 |
3.27 |
-1.21 |
| AFT Fathom |
2.462 |
1.387 |
4.125 |
8.950 |
1.582 |
-2.890 |
3.472 |
-1.600 |
| Pipe Flow Rate (ft3/sec) |
57 |
58 |
59 |
60 |
61 |
62 |
63 |
64 |
| Jeppson |
-0.22 |
-1.22 |
0.92 |
-0.8 |
1.8 |
6.25 |
-5.14 |
2.8 |
| AFT Fathom |
-0.487 |
-1.141 |
0.903 |
-0.738 |
1.738 |
6.044 |
-3.950 |
2.667 |
| Pipe Flow Rate (ft3/sec) |
65 |
| Jeppson |
7 |
| AFT Fathom |
6.263 |
| Pipe Head Loss (feet) |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
| Jeppson |
82.15 |
14.2 |
9.23 |
23.43 |
26.31 |
2.87 |
0.18 |
3.6 |
| AFT Fathom |
*80.43 |
14.15 |
9.18 |
23.32 |
25.86 |
**-2.54 |
0.27 |
**-3.51 |
| Pipe Head Loss (feet) |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
| Jeppson |
0.73 |
3.42 |
7.68 |
11.1 |
25.67 |
1.89 |
5.33 |
11.07 |
| AFT Fathom |
0.97 |
**-3.24 |
7.01 |
10.25 |
*26.74 |
2.48 |
5.58 |
10.27 |
| Pipe Head Loss (feet) |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
| Jeppson |
3.78 |
3.44 |
7.22 |
7.04 |
0.18 |
4.21 |
4.03 |
5.74 |
| AFT Fathom |
2.78 |
3.09 |
5.87 |
5.78 |
**-0.09 |
**-3.22 |
**-3.13 |
**-4.69 |
| Pipe Head Loss (feet) |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
| Jeppson |
1.71 |
19.84 |
18.13 |
0.02 |
3.26 |
21.37 |
20.22 |
1.88 |
| AFT Fathom |
1.56 |
17.70 |
16.14 |
**-0.02 |
2.62 |
18.78 |
18.49 |
**-1.26 |
| Pipe Head Loss (feet) |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
40 |
| Jeppson |
28.18 |
28.34 |
8.01 |
22.3 |
14.28 |
0.85 |
0.13 |
21.31 |
| AFT Fathom |
27.12 |
24.95 |
6.46 |
**-17.95 |
**-11.49 |
0.73 |
**-0.03 |
**-17.20 |
| Pipe Head Loss (feet) |
41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
| Jeppson |
2.4 |
4.25 |
1.63 |
90 |
0.9 |
4.75 |
4.87 |
0.79 |
| AFT Fathom |
1.64 |
**-3.37 |
**-0.61 |
1.70 |
**-1.06 |
3.85 |
4.08 |
0.84 |
| Pipe Head Loss (feet) |
49 |
50 |
51 |
52 |
53 |
54 |
55 |
56 |
| Jeppson |
17.59 |
4.21 |
13.38 |
26.61 |
3.32 |
24.63 |
18.65 |
1.55 |
| AFT Fathom |
16.38 |
3.82 |
12.57 |
*26.06 |
5.25 |
**-22.45 |
*20.90 |
**-0.26 |
| Pipe Head Loss (feet) |
57 |
58 |
59 |
60 |
61 |
62 |
63 |
64 |
| Jeppson |
0.08 |
3.78 |
1.17 |
1.15 |
4.23 |
12.87 |
19.47 |
16.8 |
| AFT Fathom |
**-0.343 |
**-3.312 |
1.111 |
**-0.981 |
3.946 |
*12.006 |
**-29.681 |
15.549 |
| Pipe Head Loss (feet) |
65 |
| Jeppson |
23.88 |
| AFT Fathom |
23.043 |
| Node EGL (feet) |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
| Jeppson |
390.2 |
376 |
366.7 |
363.9 |
366.6 |
363.1 |
374.2 |
372.3 |
| AFT Fathom |
393.20 |
379.10 |
369.90 |
367.40 |
369.60 |
366.40 |
376.70 |
374.20 |
| Node EGL (feet) |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
| Jeppson |
376.1 |
369.1 |
368.9 |
363.2 |
345 |
341.8 |
362 |
333.8 |
| AFT Fathom |
377.00 |
371.20 |
371.10 |
366.40 |
350.20 |
347.60 |
366.10 |
341.20 |
| Node EGL (feet) |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
| Jeppson |
340.9 |
343.3 |
348.1 |
364.9 |
351.5 |
347.3 |
342.4 |
340.8 |
| AFT Fathom |
346.90 |
348.50 |
352.40 |
367.90 |
355.40 |
351.60 |
347.50 |
346.90 |
| Node EGL (feet) |
25 |
26 |
27 |
28 |
29 |
| Jeppson |
319.5 |
316.1 |
342.3 |
346.1 |
347.3 |
| AFT Fathom |
329.70 |
324.40 |
347.10 |
350.50 |
351.40 |
* AFT Fathom results combine two pipes, as discussed below
** Note that AFT Fathom represents head loss on pipes with reverse flow as a negative. Jeppson represents it as positive regardless of the direction.
DISCUSSION:
Jeppson's method of applying pump data is to lump it into a pipe, whereas AFT Fathom's method is to place pumps at boundaries between pipes. Pumps are therefore a specific node (or junction) in AFT Fathom. To accommodate Jeppson's method, the pipe which contains the pump is split into two equivalent pipes in AFT Fathom. Where the split is made will have no impact on the results.
Because there are five pumps in the example, there are five additional pipes in the AFT Fathom model. AFT Fathom pipes 1 and 71 together represent Jeppson pipe 1. Similarly, AFT Fathom pipes 13 and 72 represent Jeppson pipe 13, AFT Fathom pipes 52 and 73 represent Jeppson pipe 52, AFT Fathom pipes 55 and 75 represent Jeppson pipe 55, and AFT Fathom pipes 62 and 74 represent Jeppson pipe 62.
Jeppson presents results in terms of HGL. However, Jeppson's method assumes EGL and HGL are essentially the same because of minimal velocity. Therefore, Jeppson results are presented in the results shown above as EGL.
Results differ slightly between AFT Fathom and Jeppson for a few reasons. First, Jeppson represents pump curves differently than AFT Fathom. Jeppson typically uses an exponential formula (see page 82), while AFT Fathom uses a polynomial based on a least squares curve fit. Second, the head loss formula used by Jeppson differs from AFT Fathom. Jeppson's formula is more common to the water industry, and assumes the head loss is proportional to flow rate to some power near but less than 2. AFT Fathom assumes it always proportional to flow rate to the power of 2. These differences affect the results to some degree. Third, this system is highly networked which may cause some individual pipes, especially those with lower flow rates, to differ quite a bit from AFT Fathom. Looking at the system as a whole, the agreement is quite good between Jeppson and AFT Fathom.
Slight differences in property and calculation constants that were assumed, as well as potential differences from Jeppson's solution tolerances, which are not known, may also contribute to differences in the solution results. Examples are the specific value of water density and gravitational constant.
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