【正文】 cally, as was possible in the simpler cases of parallel pipes. A practical procedure is the method of successive approximations, introduced by Cross. It consists of the following elements, in order: 1. By careful inspection assume the most reasonable distribution of flows that satisfies condition 1. 2. Write condition 2 for each pipe in the form hL = KQn () where K is a constant for each pipe. For example, the standard pipefriction equation would yield K = 1/C2 and n = 2 for constant f. Minor losses within any circuit may be included, but minor losses at the junction points are neglected. 3. To investigate condition 3, pute the algebraic sum of the head losses around each elementary circuit. ∑ hL = ∑ KQn. Consider losses from clockwise flows as positive, counterclockwise negative. Only by good luck will these add to zero on the first trial. 4. Adjust the flow in each circuit by a correction, ΔQ, to balance the head in that circuit and give ∑ KQn = 0. The heart of this method lies in the determination of ΔQ. For any pipe we may write Q = Q0 ＋ ΔQ where Q is the correct discharge and Q0 is the assumed discharge. Then, for a circuit 0100 / Qhn hQKn QKQLLn n ? ?? ?? ???? ? () It must be emphasized again that the numerator of Eq. () is to be summed algebraically, with due account of sign, while the denominator is summed arithmetically. The negative sign in Eq. () indicates that when there is an excess of head loss around a loop in the clockwise direction, the ΔQ must be subtracted from clockwise Q0’s and added to counterclockwise ones. The reverse is true if there is a deficiency of head loss around a loop in the clockwise direction. 5. After each circuit is given a first correction, the losses will still not balance because of the interaction of one circuit upon another (pipes which are mon to two circuits receive two independent corrections, one for each circuit). The procedure is repeated, arriving at a second correction, and so on, until the corrections bee negligible. Either form of Eq. () may be used to find ΔQ. As values of K appear in both numerator and denominator of the first form, values proportional to the actual K may be used to find the distribution. The second form will be found most convenient for use with pipefriction diagrams for water pipes. An attractive feature of the approximation method is that errors in putation have the same effect as errors in judgment and will eventually be corrected by the process. The pipeworks problem lends itself well to solution by use of a digital puter. Programming takes time and care, but once set up, there is great flexibility and many manhours of labor can be saved. The Future of Plastic Pipe at Higher Pressures Participants in an AGA meeting panel on plastic pipe discussed the possibility of using polyethylene gas pipe at higher pressures. Topics included the design equation, including work being done by ISO on an updated version, and the evaluation of rapid crack propagation in a PE pipe resin. This is of critical importance because as pipe is used at higher pressure and in larger diameters, the possibility of RCP increases. Several years ago, AGA’s Plastic Pipe Design Equation Task Group reviewed the design equation to determine if higher operating pressures could be used in plastic piping systems. Members felt the performance of our pipe resins was not truly reflected by the design equation. It was generally accepted that the longterm properties of modern resins far surpassed those of older resins. Major considerations were new equations being developed and selection of an appropriate design factor. Improved pipe performance Many utilities monitored the performance of plastic pipe resins. Here are some of the longterm tests used and the kinds of performance change they have shown for typical gas pipe resins. Elevated temperature burst test They used tests like the Elevated Temperature Burst Test, in which the longterm performance of the pipe is checked by measuring the time required for formation of brittle cracks in the pipe wall under high temperatures and pressures (often 80 degrees C and around 4 to 5MPa hoop stress). At Consumers Gas we expected early resins to last at least 170 hrs. at 80 degrees C and a hoop stress of 3 MPa.