Verification Case 66
PRODUCT: AFT Fathom
TITLE: FthVerify66.fth
REFERENCE: Roland Jeppson, Analysis of Flow in Pipe Networks, 1976, Publisher Ann Arbor Science, Page 88-89
FLUID: Water
ASSUMPTIONS: Assume water at 70 deg. F.
RESULTS:
| Pipe Flow Rate (ft3/sec) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 0.5 | 0.37 | 2.16 | 3.16 | 0 | 1 | 0.25 | 0.25 |
| AFT Fathom | 0.500 | 0.374 | 2.168 | 3.168* | 0.000* | 1.000 | 0.246 | 0.254 |
| Pipe Flow Rate (ft3/sec) | 9 | 10 | 11 | 12 | 13 | 14 |
| Jeppson | 0.05 | 1 | 0.79 | 0.71 | 0.13 | 1.84 |
| AFT Fathom | 0.046 | 1.000 | 0.794 | 0.706 | 0.126 | 1.832 |
| Pipe Head Loss (feet) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Jeppson | 2.44 | 0.63 | 19.27 | 6.4 | 0 | 6.4 | 1.01 | 1.06 |
| AFT Fathom | 2.409 | 0.636 | 19.217 | 6.375* | 0.000* | 6.329 | 0.989 | 1.045 |
| Pipe Head Loss (feet) | 9 | 10 | 11 | 12 | 13 | 14 |
| Jeppson | 0.06 | 2.56 | 2.73 | 2.22 | 0.09 | 2.21 |
| AFT Fathom | 0.056 | 2.532 | 2.699 | 2.148 | 0.085 | 2.179 |
| PRV EGL (feet) | Up | Down |
| Jeppson | 417.6 | 393.04 |
| AFT Fathom | 417.6 | 393.1 |
* AFT Fathom results combine two pipes, as discussed below
** The problem statement has a typo on pipe length. It says 1000 ft., and it should only be 500 ft.
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 4 and 16 together represent Jeppson pipe 4. Similarly, AFT Fathom pipes 5 and 15 represent Jeppson pipe 5.
In both Jeppson's solution and AFT Fathom's, the PRV cannot control to its set pressure head, and it fails 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 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.
