@article{oai:mie-u.repo.nii.ac.jp:00006414,
 author = {加治佐, 隆光 and Kajisa, Takamitsu},
 journal = {三重大學農學部學術報告 = The bulletin of the Faculty of Agriculture, Mie University},
 month = {Dec},
 note = {application/pdf, 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 α obtained 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, 
X=w₀x/4µ₀, T=w₀²t/4µ₀ 
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), w₀: velocity of hydraulic　bore(m/sec), µ:equivalent to(hv)/2i, (hv): discharge per unit wise of channel, suffix 0 shows uniform flow and i: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, α≃1 and α≫1, 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. 
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) 
in which, the folowing indexes were introduced to evaluate the conditions of response with the operation. (1)KQ=0.1 is the beginning index of the response. 
(2)KQ=2/3 is the progressive state index.
(3)KQ＝0.9 is the ending index of the response.
KQ:Discharge represented non-dimensionally, equivalent to (Q－Qb)/(Qb－Qb), Q:discharge (m³/sec), suffix b shows the uniform flow just before the operation and suffix e 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 Tc(sec) in the indicial response of flow in an open-channel under various conditions. 
D+Tⅽ=l/w₀ …(C) 
w₀l/4µb-w₀²D/4µb =√w₀²D/4µb …(D)
Equation(C) was derived from the condition of continuity and  Eq.(D) was derived from Eq.(B). 
The mathematical model for evaluting dead time D and time constant Tc 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.},
 pages = {11--38},
 title = {用水システムの運用操作における流量の応答遅れ},
 volume = {75},
 year = {1987}
}