Verification Case 64
PRODUCT: AFT Fathom
TITLE: FthVerify64.fth
REFERENCE: Roland Jeppson, Analysis of Flow in Pipe Networks, 1976, Publisher Ann Arbor Science, Page 109-110
FLUID: Water
ASSUMPTIONS: Assume water at 70 deg. F.
RESULTS:
| Pipe Flow Rate (ft3/sec) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 2.56 | -0.32 | 2.44 | 0.73 | 0.88 | 1.12 | 1.83 | 3.17 |
| AFT Fathom | 2.53 | -0.38 | 2.47 | 0.72 | 0.92 | 1.08 | 1.81 | 3.19 |
| Pipe Head Loss (feet) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 130.61 | 1.89 | 119.67 | 8.75 | 18.42 | 24.12 | 6.33 | 17.88 |
| AFT Fathom | *128.35 | **-2.66 | 122.19 | 8.50 | *19.98 | 22.64 | 6.25 | 17.75 |
| PRV EGL (feet) | Up | Down |
| Jeppson | 53.8 | 50.0 |
| AFT Fathom | 49.9 | 49.9 |
* 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 and PRV data is to lump it into a pipe, whereas AFT Fathom's method is to place pumps and PRVs at boundaries between pipes. Pumps and PRVs are therefore a specific node (or junction) in AFT Fathom. To accommodate Jeppson's method, the pipe which contains the pump or PRV is split into two equivalent pipes in AFT Fathom. In the case of the pump, where the split is made will have no impact on the results. 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 is one pump and one PRV in the example, there are two additional pipes in the AFT Fathom model. AFT Fathom pipes 1 and 10 together represent Jeppson pipe 1. Similarly, AFT Fathom pipes 5 and 9 represent Jeppson pipe 5.
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's 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 pipe head loss formula used by Jeppson differs from AFT Fathom. Jeppson's Hazen-Williams formula is given in his book and does not agree exactly with the accepted formula as used in AFT Fathom. 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 also 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.
Because of the slight differences in calculations between AFT Fathom and Jeppson, there is slightly less pressure head available across the PRV than the 50 feet specified in the problem statement. Thus, there is a warning message generated in AFT Fathom that the control valve is unable to control, and has failed open. Results are displayed above for the failed open 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.
