{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Rect, Trap & Tri Gates","Circular Gate","Analytical Calculations"],"not_rendered":{"charts":0,"images":2,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Rect, Trap & Tri Gates","index":0,"n_rows":33,"n_cols":10,"rows_kept":33,"cut":false,"hidden":false,"merged":[[7,7,7,8],[10,3,10,4],[10,5,10,6],[4,1,4,2],[4,3,4,4],[4,5,4,6],[7,1,7,2],[10,1,10,2],[7,3,7,4],[7,5,7,6]]}
[null,"Forces on Submerged Gates (Rectangular, Trapezoidal and Triangular Gates)"]
[null,"Choose values for the four variables in the orange boxes, and the spreadsheet will display in the green boxes the net force (F), moment (M) and center of pressure (D) for the submerged gate "]
[null,"The calculated center of pressure is shown with a \"*\""]
[]
[null,"Density of Water (kg/m3)",null,"Gravitation Acceleration (m/s2)",null,"Specific Weight (N/m3)"]
[null,"ρ =",1000,"g =",9.81,"γ =",{"$f":"C6*E6","v":9810}]
[]
[null,"Depth of Top of Gate (m)",null,"Gate Height (m)",null,"Upper Width of Gate (m)",null,"Bottom Width of Gate (m)"]
[null,"D1 =",0.1,"D2 =",0.5,"W1 =",0.2,"W2 =",0.4]
[]
[null,"Net force (N)",null,"Net moment (N·m)",null,"Center of Pressure (m)"]
[null,"F =",{"$f":"G6*E9*(G9/2*(2*C9+E9)+(I9-G9)/6*(3*C9+2*E9))","v":555.9},"M =",{"$f":"G6*E9*(G9/3*(3*C9^2+3*C9*E9+E9^2)+(I9-G9)/12/E9*(6*C9^2*E9+8*C9*E9^2+3*E9^3))","v":239.52750000000003},"D =",{"$f":"E12/C12","v":0.43088235294117655}]
[]
[]
[null,null,null,null,"The force (F), moment (M) and center of pressure (D) reported in Row 10, above, are calculated using formulas "]
[null,null,null,null,"shown on the Calculations tab. F and M can also be determined by numerical integration, "]
[null,null,null,null,"as in the following table:"]
[]
[null,null,null,null,"Scaled position","D","P(D)","W(D)","dF","dM"]
[null,null,null,null,0.05,{"$f":"C$9+E20*E$9","v":0.125},{"$f":"F20*G$6","v":1226.25},{"$f":"G$9+(I$9-G$9)*(F20-C$9)/E$9","v":0.21000000000000002},{"$f":"G20*H20*(E$9/10)","v":12.875625000000003},{"$f":"F20*G20*H20*(E$9/10)","v":1.6094531250000004}]
[null,null,null,null,0.15,{"$f":"C$9+E21*E$9","v":0.17499999999999999},{"$f":"F21*G$6","v":1716.75},{"$f":"G$9+(I$9-G$9)*(F21-C$9)/E$9","v":0.23},{"$f":"G21*H21*(E$9/10)","v":19.742625000000004},{"$f":"F21*G21*H21*(E$9/10)","v":3.4549593750000001}]
[null,null,null,null,0.25,0.22500000000000001,2207.25,0.25,27.590625000000003,6.207890625000001]
[null,null,null,null,0.35,0.27500000000000002,2697.75,0.27,36.419625000000003,10.015396875]
[null,null,null,null,0.45,0.32500000000000001,3188.25,0.29000000000000004,46.229625000000006,15.024628125000005]
[null,null,null,null,0.55000000000000004,0.375,3678.75,0.31000000000000005,57.02062500000001,21.382734375000005]
[null,null,null,null,0.65,0.42500000000000004,4169.25,0.33000000000000007,68.792625000000015,29.236865625000007]
[null,null,null,null,0.75,0.47499999999999998,4659.75,0.35000000000000003,81.545625000000015,38.734171875000008]
[null,null,null,null,0.85,0.52500000000000002,5150.25,0.37000000000000005,95.27962500000001,50.021803125000005]
[null,null,null,null,0.95,0.57499999999999996,5640.75,0.39,109.994625,63.246909375000001]
[null,null,null,null,null,null,null,null,{"$f":"SUM(I20:I29)","v":555.49125000000004},{"$f":"SUM(J20:J29)","v":238.93481250000005}]
[null,null,null,null,null,null,null,null,"F = ↗","M = ↗"]
[null,null,null,null,null,null,null,null,{"$f":"J30/I30","v":0.4301324503311259}]
[null,null,null,null,null,null,null,null,"D-bar =  ↗"]

{"sheet":"Circular Gate","index":1,"n_rows":43,"n_cols":10,"rows_kept":43,"cut":false,"hidden":false,"merged":[[10,1,10,2],[10,3,10,4],[10,5,10,6],[4,1,4,2],[4,3,4,4],[4,5,4,6],[7,1,7,2],[7,3,7,4]]}
[null,"Forces on Submerged Gates (Circular Gates)"]
[null,"Choose values for the two variables in the orange boxes, and the spreadsheet will display in the green boxes the net force (F), moment (M) and center of pressure (D) for the submerged gate "]
[null,"The calculated center of pressure is shown with a \"*\""]
[]
[null,"Density of Water (kg/m3)",null,"Gravitation Acceleration (m/s2)",null,"Specific Weight (N/m3)"]
[null,"ρ =",1000,"g =",9.81,"γ =",{"$f":"C6*E6","v":9810}]
[]
[null,"Depth of Top of Gate (m)",null,"Gate Diameter (m)"]
[null,"D1 =",0.2,"D2 =",0.8]
[]
[null,"Net force (N)",null,"Net moment (N·m)",null,"Center of Pressure (m)"]
[null,"F =",{"$f":"PI()*G6*(C9+E9/2)*(E9/2)^2","v":2958.6262974447245},"M =",{"$f":"PI()*G6*E9^2/64*(16*C9^2+ 16*C9*E9+5*E9^2)","v":1972.4175316298165},"x̅ =",{"$f":"E12/C12","v":0.66666666666666674}]
[]
[]
[null,null,null,null,"The force (F), moment (M) and center of pressure (D) reported in Row 10, above, are calculated using formulas "]
[null,null,null,null,"shown on the Calculations tab. F and M can also be determined by numerical integration, "]
[null,null,null,null,"as in the following table:"]
[]
[null,null,null,null,"scaled position","D","P(D)","W(D)","dF","dM"]
[null,null,null,null,2.5000000000000001E-2,{"$f":"C$9+E20*E$9","v":0.22000000000000003},{"$f":"F20*G$6","v":2158.2000000000003},{"$f":"2*SQRT((E$9/2)^2-(C$9+E$9/2-F20)^2)","v":0.24979991993593573},{"$f":"G20*H20*E$9/20","v":21.564727488229465},{"$f":"F20*G20*H20*E$9/20","v":4.7442400474104831}]
[null,null,null,null,7.4999999999999997E-2,{"$f":"C$9+E21*E$9","v":0.26},2550.6,0.42142615011410944,{"$f":"G21*H21*E$9/20","v":42.995581539241904},{"$f":"F21*G21*H21*E$9/20","v":11.178851200202894}]
[null,null,null,null,0.125,0.30000000000000004,2943.0000000000005,0.52915026221291817,62.291568867704747,18.687470660311426]
[null,null,null,null,0.17499999999999999,0.33999999999999997,3335.3999999999996,0.60794736614282641,81.109905801311328,27.577367972445849]
[null,null,null,null,0.22500000000000001,0.38,3727.8,0.6681317235396026,99.626457560437231,37.858053872966153]
[null,null,null,null,0.27500000000000002,0.42000000000000004,4120.2000000000007,0.71442284397967015,117.7426000706015,49.45189202965264]
[null,null,null,null,0.32500000000000001,0.46,4512.6000000000004,0.74939975980780782,135.26965424434857,62.224040952400344]
[null,null,null,null,0.375,0.5,4905,0.7745966692414834,151.97586650517906,75.987933252589528]
[null,null,null,null,0.42499999999999999,0.54,5297.4000000000005,0.79094879733140755,167.59888635933595,90.503398634041417]
[null,null,null,null,0.47499999999999998,0.58000000000000007,5689.8000000000011,0.7989993742175272,181.84586557691551,105.47060203461101]
[null,null,null,null,0.52500000000000002,{"$f":"C$9+E30*E$9","v":0.62000000000000011},{"$f":"F30*G$6","v":6082.2000000000007},{"$f":"2*SQRT((E$9/2)^2-(C$9+E$9/2-F30)^2)","v":0.7989993742175272},194.38695975463378,120.51991504787297]
[null,null,null,null,0.57499999999999996,0.65999999999999992,6474.5999999999995,0.79094879733140766,204.84308332807728,135.19643499653097]
[null,null,null,null,0.625,0.7,6867,0.77459666924148352,212.76621310725073,148.93634917507546]
[null,null,null,null,0.67500000000000004,0.74,7259.4,0.74939975980780793,217.60770465395203,161.02970144392447]
[null,null,null,null,0.72499999999999998,0.78,7651.8,0.71442284397967015,218.66482870254563,170.55856638798559]
[null,null,null,null,0.77500000000000002,0.82000000000000006,8044.2000000000007,0.66813172353960271,214.98340841989094,176.28639490431061]
[null,null,null,null,0.82499999999999996,0.8600000000000001,8436.6,0.60794736614282663,205.16034996802287,176.43790097249968]
[null,null,null,null,0.875,0.90000000000000013,8829.0000000000018,0.52915026221291817,186.87470660311422,168.18723594280283]
[null,null,null,null,0.92500000000000004,0.94000000000000017,9221.4000000000015,0.42142615011410944,155.44556402648999,146.11883018490062]
[null,null,null,null,0.97499999999999998,0.98,9613.7999999999993,0.24979991993593684,96.06105881120439,94.139837634980296]
[null,null,null,null,null,null,null,null,{"$f":"SUM(I20:I39)","v":2968.8149913884868},{"$f":"SUM(J20:J39)","v":1981.0950173475151}]
[null,null,null,null,null,null,null,null,"F = ↗","M = ↗"]
[null,null,null,null,null,null,null,null,{"$f":"J40/I40","v":0.66730160791224502}]
[null,null,null,null,null,null,null,null,"D-bar =  ↗"]

{"sheet":"Analytical Calculations","index":2,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}