Verification Case 65
PRODUCT: AFT Fathom
TITLE: FthVerify65.fth
REFERENCE: Roland Jeppson, Analysis of Flow in Pipe Networks, 1976, Publisher Ann Arbor Science, Page 110-111
FLUID: Water
ASSUMPTIONS: Assume water at 15 deg. C.
RESULTS:
| Pipe Flow Rate (m3/sec) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 0.6402 | 0.2857 | 0.1857 | -0.0857 | 0.2344 | -0.2402 | 0 | 0 |
| AFT Fathom | 0.651 | 0.282 | 0.182 | -0.082 | 0.249 | -0.251 | 0.000 | 0.000 |
| Pipe Flow Rate (m3/sec) | 9 | 10 |
| Jeppson | 0.12 | -0.1902 |
| AFT Fathom | 0.120 | -0.201 |
| Pipe Head Loss (m) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 6 | 16.21 | 12.32 | 1.79 | 30.32 | 11.77 | 0 | 0 |
| AFT Fathom | 6.132 | 15.664 | 11.798 | -1.662** | 29.124 | -12.640** | 0.000* | 0.000* |
| Pipe Head Loss (m) | 9 | 10 |
| Jeppson | 56.47 | 1.91 |
| AFT Fathom | 55.766 | -2.104** |
| Node EGL (meters) | 1 | 2 | 3 | 4 | 5 | 6 |
| Jeppson | 294 | 277.79 | 265.48 | 263.68 | 251.91 | 237.54 |
| AFT Fathom | 293.9 | 278.2 | 266.4 | 264.7 | 252.1 | 238.1 |
| PRV EGL (meters) | 1 Up | 1 Down | 2 Up | 2 Down |
| Jeppson | 251.91 | 237.54 | 265.48 | 237.54 |
| AFT Fathom | 252.1 | 238.1 | 266.4 | 238.1 |
* 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 PRV data is to lump it into a pipe, whereas AFT Fathom's method is to place PRVs at boundaries between pipes. PRVs are therefore a specific node (or junction) in AFT Fathom. To accommodate Jeppson's method, the pipe which contains the PRV is split into two equivalent pipes in AFT Fathom. If the PRV control pressure is specified in terms of head, the elevation of the PRV becomes important. In such cases, Jeppson specifies the elevation and AFT Fathom incorporates this.
Because there are two PRVs in the example, there are two additional pipes in the AFT Fathom model. AFT Fathom pipes 7 and 11 together represent Jeppson pipe 7. Similarly, AFT Fathom pipes 8 and 12 represent Jeppson pipe 8.
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.
In both Jeppson's solution and AFT Fathom's, the two PRVs cannot control to their set pressure head, and fail closed. Results are displayed above for the failed closed case. AFT Fathom shows warnings in the Warnings section at the top of the Output window. In addition, the Valve Summary at the top of the Output window shows the PRV status.
Results differ slightly between AFT Fathom and Jeppson. 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.
