Verification Case 67
PRODUCT: AFT Fathom
TITLE: FthVerify67.fth
REFERENCE: Roland Jeppson, Analysis of Flow in Pipe Networks, 1976, Publisher Ann Arbor Science, Page 95-98
FLUID: Water
ASSUMPTIONS: Assume water at 60 deg. F.
RESULTS:
| Pipe Flow Rate (ft3/sec) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 2.94 | -1.76 | -0.54 | 1.74 | 0.88 | -2.55 | -3.35 | 2.17 |
| AFT Fathom | 2.94 | -1.76 | -0.54 | 1.74 | 0.88 | -2.56 | -3.36 | 2.18 |
| Pipe Flow Rate (ft3/sec) | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Jeppson | 3.07 | -0.44 | -0.58 | 0.64 | 0.73 | 1.32 | 1.18 | 0.80 |
| AFT Fathom | 3.07 | -0.44 | -0.58 | 0.64 | 0.73 | 1.32 | -1.19 | 0.80 |
| Pipe Flow Rate (ft3/sec) | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| Jeppson | -2.29 | -0.17 | 0.09 | 3.27 | 2.45 | -0.04 | 1.15 | -0.41 |
| AFT Fathom | -2.29 | -0.17 | 0.09 | 3.28 | 2.46 | -0.04 | 1.15 | -0.42 |
| Pipe Flow Rate (ft3/sec) | 25 | 26 | 27 | 28 |
| Jeppson | 6.84 | 6.01 | 3.35 | -2.39 |
| AFT Fathom | 6.85 | 6.02 | 3.34 | -2.40 |
| Pipe Head Loss (feet) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 6.41 | 11.85 | 0.62 | 9.10 | 10.76 | 30.20 | 45.50 | 51.10 |
| AFT Fathom | 6.38 | -11.80 | -0.61 | 9.02 | 10.62 | -30.11 | -45.32 | 50.87 |
| Pipe Head Loss (feet) | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Jeppson | 43.90 | 7.92 | 9.90 | 8.20 | 9.38 | 59.00 | 29.60 | 23.40 |
| AFT Fathom | 43.73 | -7.87 | -9.86 | 8.15 | 9.29 | 58.74 | -29.47 | 23.28 |
| Pipe Head Loss (feet) | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| Jeppson | 7.86 | 1.37 | 0.28 | 37.60 | 30.70 | 0.01 | 6.90 | 6.91 |
| AFT Fathom | -7.82 | -1.32 | 0.27 | 37.46 | 30.56 | -0.01 | 6.89 | -6.90 |
| Pipe Head Loss (feet) | 25 | 26 | 27 | 28 |
| Jeppson | 30.6 | 0.91 | 0.31 | 8.43 |
| AFT Fathom | *30.517 | *0.90 | *0.304 | -8.437 |
| Node EGL (feet) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 1365 | 1359 | 1347 | 1348 | 1357 | 1346 | 1316 | 1270 |
| AFT Fathom | 1365.2 | 1358.8 | 1347.0 | 1347.7 | 1356.7 | 1346.1 | 1315.9 | 1270.6 |
| Node EGL (feet) | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Jeppson | 1321 | 1329 | 1339 | 1347 | 1392 | 1354 | 1361 | 1354 |
| AFT Fathom | 1321.5 | 1329.4 | 1339.2 | 1347.4 | 1392.0 | 1354.5 | 1361.4 | 1354.5 |
* 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 three pumps in the example, there are three additional pipes in the AFT Fathom model. AFT Fathom pipes 25 and 29 together represent Jeppson pipe 25. Similarly, AFT Fathom pipes 26 and 31 represent Jeppson pipe 26, and AFT Fathom pipes 27 and 30 represent Jeppson pipe 27.
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.
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.
Results for AFT Fathom vary somewhat from previous versions of AFT Fathom (prior to version 7) because the equation used to convert the Hazen-Williams factor to the Darcy-Weisbach friction factor was modified to use the traditional formula, as given in the AFT Fathom help file.
