用水システムの運用操作における流量の応答遅れ
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The operation of discharge and delay of response in a open-channel irrigation system were discussed with mathematical analyses and experimental evalualions. Analytical treatments were made based on the linearized diffusion analog model. [1] It was clarified that parameter αobtained as a result of the analyses was an effective factor to describe the response of the operation, and α was denoted as α=√X=√T …(A) in which, <special>X=w0x/4µ0</special>, <special>T=w02t/4µ0</special> X : Distance represented non-dimensionally, T : time represented non-dimensionally, x : distance from the upside end of open-channel (m), t : time from the change of discharge(sec), <special>w0</special> : velocity of hydraulic bore(m/sec), µ : equivalent to<special>(hv)/2i</special>, <special>(hv)</special> discharge per unit wise of channel, suffix 0 shows uniform flow and <special>i</special> ; bottom slope. Also, the phenomena of the response in the operations were transferred to down stream as dynamic, dynamic~kinematic and kinematic waves for α≪1, ユ,<special>α=1 and α≫1</special>, respectively. [2] A simple and useful equation was derived as a result of solving the linearized diffusion analog model with in the effective range of X. <special>X-T/√T= {1.0(KQ=0.1, 0.1≦X≦10.0) 0.0(KQ=2/3, 0.1≦X≦10.0) -0.6(KQ=0.9, X≒1.0)</special> in which, the folowing indexes were introduced to evaluate the conditions of response with the operation. (1) <special>KQ</special>=0.1is the beginning index of the response. (2) <special>KQ</special>=2/3 is the progressive state index. (3) <special>KQ</special>=0.9 is the ending index of the response. <special>KQ</special> : Discharge represented non-dimensionally, equivalent to <special>(Q-Qb)/(Qb-Qb)</special>, Q : discharge<special>(m3/sec)</special>, suffix b shows the uniform flow just before the operation and suffix <special>e</special> shows the uniform flow at the end of the response. The validity of Eq. (B) was confirmed in the transition range of the dynamic and kinematic waves. [3] The Eqs. (C) and (D) were applied to evaluate dead time D(sec) and time constant <special>Tc</special>(sec) in the indicial response of flow in an open-channel under various conditions. <special>D+TC=l/w0</special> …(C) <special>w0l/4µb-w02D/4µb =√w02D/4µb</special> …(D) Equation (C) was derived from the condion of continuity and Eq. (D) was derived from Eq. (B). The mathematical model fo revaluting deal time D and time constant <special>Tc</special> of the flow in an open-channel with step works in series was presented and checked using a numerical analysis. The validity of this model was confirmed within about 10 step works in a open-channel.
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