Enhancements and Modifications to the Full Equations (FEQ) Model, March 1995 to August 1999
Note: This document is separate from the U.S. Geological Survey report by Franz and Melching (1997). This description of enhancements and modifications to the Full Equations Utilities Model has not been approved by the Director of the U.S. Geological Survey.

Input description update for section 13.6, Network-Matrix Control Block-- Network-Matrix Table, Code5 (Two-node head-discharge relations), Franz and Melching (1997a), p. 174

To RELEASE.TXT

If TYPE3 (Variable-speed variable-head pump):

N(5) is the flow direction: 1 means pumping from upstream node to downstream node; -1 means pumping from downstream node to upstream node. The node from which water is being drawn is called the source node and the node to which water is being pumped is called the destination node.

N(6) is the table number of table giving the flow through the pump for each head, that is, a pump performance curve. The speed of the pump used to define this curve is the base speed to which all speeds are relative. This should be the highest speed for the pump so that all other speeds are smaller. For example, if a pump has a speed range from 0 to 1800 revolutions per minute (rpm), then 1800 rpm should be used to define the head across the pump. A relative speed of 0.5 then means that the pump is operating at 900 rpm. The relationship between flow through the pump and head must be unique. Pumps exist for which this is not true, that is, they have ranges of flow for which the head increases as the flow increases followed by a decreasing head with increasing flow. For a given head, there are two different flows. These pumps could prove to be unstable if used for pumping in an open channel network. They could also prove unstable in simulation using FEQ and therefore, the representation of the pump performance in FEQ requires that their pump curve be modified to render them stable when used in an open channel network.

N(7) is the table number of table giving the sum of the entrance losses at the inlet, friction losses in the inlet conduit, and friction losses in the outlet conduit. The sum is expressed in terms of head as a function of flow through the pump. FEQ assumes that these losses will increase with flow. This table is optional and if omitted, the losses are assumed to be included in the pump performance curve table given in N(5).

N(8) is the table number of table giving the exit loss coefficient on the velocity head difference between the end of the outlet conduit and the destination node. This coefficient is given as a function of the depth of submergence of the outlet conduit. The loss coefficient must be 1.0 at zero submergence. If this table is omitted, FEQ uses an exit loss coefficient of 1.0 for all levels of submergence.

N(9)0 gives the table number for the table specifying the pump speed as a function of time. N(9)0 gives the operation block number controlling the pump. N(9)0 keeps the pump running at its base speed all the time. Water will not be pumped if the water-surface elevation at the source node is below the inlet elevation. If N(9)0 and N(9)the maximum number of operation blocks, then FEQ treats the value of N(9) as a table number for selection of the operation block. This permits FEQ to model operation rules that vary with the season of the year. The operation-block selection table is a time-series table of type 7. The function value is a block number. Block numbers are integers but the table treats them as real numbers in its operations. The result of a table-lookup is rounded to the nearest integer to yield the current operation block number for control of the structure. The maximum number of operation blocks is contained in the value MNBLK in the file ARSIZE.PRM. Its value is also printed near the top of the output file from FEQ. This number is typically 50 so that any table number greater than 50 will be treated as if it were an operation-block selection table.

N(10) is the optional name for the pump. The name can be four alpha-numeric character at most. The first character should be alphabetic. A name given for the pump permits having its state printed in the Special Output file by giving the name in the field as for an exterior node in the Special Output Block. In this case the state of the pump includes its relative speed, and the nature of flow: NO H2O-denotes that the pump is on but the inlet is above water; FP-denotes free flow out of the pump outlet; SP-denotes submerged flow out of the pump outlet; and OFF-denotes that the pump is currently not running.

F(1) is the elevation of the outlet conduit. Point of reference for submergence of the outlet. If the water surface elevation at the destination node is below this elevation, FEQ assumes that the exit velocity head from the outlet conduit is a loss. If the water surface elevation at the destination node is greater than this elevation, FEQ looks up a loss coefficient in the table in N(8), if it exists, or takes 1.0 if it does not, and uses the loss coefficient to compute the fraction of the velocity head difference between the exit and the destination node to use as an exit loss. The argument to the table is the depth of submergence computed relative to the elevation of the outlet conduit.

F(2) is the area of the outlet conduit when flowing full. FEQ assumes that the pump will keep the outlet conduit flowing full at all pump speeds.

F(3) is the elevation of the inlet conduit. Pump flow is zero if the water-surface elevation is below the inlet.

F(4) is the factor on the velocity head at the source node. Usually 0 or 1 to exclude or include the velocity head at the source node. FEQ will force this factor to 0 if the source node is a free node.

F(5) is the factor on velocity head at the destination node. Usually 0 or 1 to exclude or include the velocity at the destination node. FEQ will force this factor to 0 if the destination node is a free node.

Discussion: This network-matrix control option is designed to represent a variable-speed variable-head pump. If the head on the pump exceeds its cutoff head, the flow through the pump will reverse if a check valve of some kind does not exist in the outflow conduit. The pump characteristic table determines if reverse flow is to be allowed. In most cases check valves are provided, and reverse flows are not allowed. If this is the case, the table given in N(6), must be extended to a head higher, and sometimes much higher, than any expected with flow through the pump set to zero in the extension.