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Figure-1. Diagram x-t for the basic version of the simple pipeline. below, we will analyze the simple pipeline system shown in Figure-1 [4], [5], [6].

Figure 1 -1. Diagram x-t for the basic version of the simple pipeline. below, we will analyze the simple pipeline system shown in Figure-1 [4], [5], [6].

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In the analysis of the changes of velocity and the piezometric head, which are constant during the stationary flow, the overall L length of the pipeline divide into n equals pieces, with 4x=L/n, and, by equation (2), we also choose the time step of Integration, At=Ax/c. The positional diagram for the given situation is shown in Figure-2 (1. Reservoir, 2.Pipeline, 3.Valve) [8], [9], [10]. The equations (1) and (2) will become [1], [2],
In the analysis of the changes of velocity and the piezometric head, which are constant during the stationary flow, the overall L length of the pipeline divide into n equals pieces, with 4x=L/n, and, by equation (2), we also choose the time step of Integration, At=Ax/c. The positional diagram for the given situation is shown in Figure-2 (1. Reservoir, 2.Pipeline, 3.Valve) [8], [9], [10]. The equations (1) and (2) will become [1], [2],
Figure-3. Time shifting of the pressure in front of the valve depending on the closing time T),,. Lack of friction, It makes the speed to be equated withvy. At this moment, the disorder front is again occurring from the left, but with pressure po (the difference of piezometric head converted to kinetic energy of the Opposite stream), when the fluid is still under increased pressure from its right [5].
Figure-3. Time shifting of the pressure in front of the valve depending on the closing time T),,. Lack of friction, It makes the speed to be equated withvy. At this moment, the disorder front is again occurring from the left, but with pressure po (the difference of piezometric head converted to kinetic energy of the Opposite stream), when the fluid is still under increased pressure from its right [5].
Similar analysis can also be used for pressure t-hange curves for other timing closure models.
Similar analysis can also be used for pressure t-hange curves for other timing closure models.
Table-1. Simulation results according to the WH Program - transient state of calculation. Changing spatial and temporal steps during integration
Table-1. Simulation results according to the WH Program - transient state of calculation. Changing spatial and temporal steps during integration
Figure-4. Linear valve closure.
Figure-4. Linear valve closure.
Figure-5. Suddenly closing of the valve. Assuming non-viscous fluid (A=0), — th integration time is accepted 36 s. For transient fluid flow regimes, using the method of characteristics, and the Hardy Cross program in FORTRAN, the WH program (WH - water hammer program) was developed [6], [13]. Testing the WH program for the analysis of stationary working regimes in stationary state maintenance is carried out with fully open valves throughout the entire integration time. This means that, in the input file, for all integration time steps, the product C, A, is the same as that of the moment t=0 sec; thus, the start time of the valve closure is greater than the integration times T;,> 36 sec, as shown in Table-1, [14], [15].
Figure-5. Suddenly closing of the valve. Assuming non-viscous fluid (A=0), — th integration time is accepted 36 s. For transient fluid flow regimes, using the method of characteristics, and the Hardy Cross program in FORTRAN, the WH program (WH - water hammer program) was developed [6], [13]. Testing the WH program for the analysis of stationary working regimes in stationary state maintenance is carried out with fully open valves throughout the entire integration time. This means that, in the input file, for all integration time steps, the product C, A, is the same as that of the moment t=0 sec; thus, the start time of the valve closure is greater than the integration times T;,> 36 sec, as shown in Table-1, [14], [15].
Figure-6(b). Influence of the fluid flow in the pipeline. From these figures, Figure-6.a and Figure-6.b, it is concluded that in element 5, the maximum pressure is reached after eight seconds from the closing of the valve. Further, we have the beginning of the amortization of hydraulic shoc k. For its part, the striking return wave will be more active after about 14 and 30 seconds. These results prove that, with increased distance from the power source, the hyd raulic shock is more likely.
Figure-6(b). Influence of the fluid flow in the pipeline. From these figures, Figure-6.a and Figure-6.b, it is concluded that in element 5, the maximum pressure is reached after eight seconds from the closing of the valve. Further, we have the beginning of the amortization of hydraulic shoc k. For its part, the striking return wave will be more active after about 14 and 30 seconds. These results prove that, with increased distance from the power source, the hyd raulic shock is more likely.
Figure-6(a). Influence of the fluid energy in the pipeline.
Figure-6(a). Influence of the fluid energy in the pipeline.
Figure-7(b). The fluid flow in the node, depending on the closing valve time, after t = 12 s. Figure-8(a). The pressure head in the node, depending on the closing valve time, after t = 24 s.
Figure-7(b). The fluid flow in the node, depending on the closing valve time, after t = 12 s. Figure-8(a). The pressure head in the node, depending on the closing valve time, after t = 24 s.
Figure-7(a). The pressure head in the node, depending on the closing valve time, after t = 12 s.
Figure-7(a). The pressure head in the node, depending on the closing valve time, after t = 12 s.
Figure-9(a). The pressure head in the node, depending on the closing valve time, after t = 36 s. Even the sudden closing and opening of the valve in synchronized mode is shown in the following figures, Figure-10(a) to Figure-11(b).
Figure-9(a). The pressure head in the node, depending on the closing valve time, after t = 36 s. Even the sudden closing and opening of the valve in synchronized mode is shown in the following figures, Figure-10(a) to Figure-11(b).
Figure-8(b). The fluid flow in the node, depending on the closing valve time, after t = 24 s.
Figure-8(b). The fluid flow in the node, depending on the closing valve time, after t = 24 s.
Figure-10(b). The fluid flow in the node, depending on the closing and opening valve time, each t = 6s. Figure-10(a). The pressure head in the node, depending on the closing and opening valve time, each t = 6 s.
Figure-10(b). The fluid flow in the node, depending on the closing and opening valve time, each t = 6s. Figure-10(a). The pressure head in the node, depending on the closing and opening valve time, each t = 6 s.
Figure-9(b). The fluid flow in the node, depending on the closing valve time, after t = 36 s.
Figure-9(b). The fluid flow in the node, depending on the closing valve time, after t = 36 s.
Figure-11(a). The pressure head in the node, depending on the closing and opening valve time, each t = 18 s.
Figure-11(a). The pressure head in the node, depending on the closing and opening valve time, each t = 18 s.
REFERENCES Figure-11(b). The fluid flow in the node, depending on the closing and opening valve time, each t = 18 s.
REFERENCES Figure-11(b). The fluid flow in the node, depending on the closing and opening valve time, each t = 18 s.
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