258 



THE IRRIGATION AGE. 



THE PRIMER OF HYDRAULICS* 



By FREDERICK A. SMITH, C. E. 



1.5 d 



Fig. 102. 



XX. Ditch Tables and Their Application. 

 1. How to Use Them. 

 The following tables v /<f , 

 relate to a number of 

 ditches with their hydrau- 

 lic properties worked out; 

 the factor n = .025 and 

 the grades are shown at 

 the head of the various 

 tables. Since the mean velocity varies as the Ms, everything 

 else being equal, it is easy to form other tables from these 



given, for any 

 "^ slope desired ; 

 for instance, a 

 grade in one of 

 the given ta- 

 bles is 1 in 200, 

 and it is de- 

 1 in 300, then the 



sired to prepare a 



relation exists : V 



V 



Fig. 103. 



table for a grade of 



v = M 1 :200 : V 1 ::tOO 

 v = M .005 : M .0033. 

 v = .07071 : .05746 ; hence 



V 



.05746Z/ 

 .07071 

 d 



This gives the rule to 

 find the mean velocity for 

 any required grade ; take 

 the square root of this re- 

 quired grade and multiply 

 with the given velocity ; 

 then divide by the square 

 root of the given grade. 



2. Table of Capacity of a Triangular Ditch, slope_l to 1, 

 see Fig. 96, and grade 1 in 400, n = .025, .r = .0025, Ms = .05. 

 Depth 





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 and it is safe to predict that under his conservation and 

 careful conduct the coming Land Shows will eclipse all others 

 in the point of success. These exhibitions, which were 

 founded in 1909 by the Chicago Tribune, have done a great 

 deal of good in promoting the interest and development of 

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 continue to do so in a greater degree under the management 

 of Mr. Cross. 



4. Rectangular ditch, with 4-ft. base, grade 1 in 200, n 

 = .025, J = .005. (Fig. 99.) 



Gals. 



Depth Flow per 



flow. area. W. P. r. M~ C. v. Cfs. min. 



6" 2.0 5.0 .40 .63 42 1.85 3.70 1,660 



12" 4.0 6.0 .67 .82 49 2.70 10.80 4,845 



18" 6.0 7.0 .86 .93 53 3.45 20.70 9,290 



24" 8.0 8.0 1.00 1.00 55 3.85 30.80 13,821 



36" 12.0 10.0 1.20 1.10 57 4.39 52.68 23,643 



48* 16.0 12.0 1.33 1.15 58 4.67 74.72 33,534 



72" 24.0 16.0 1.50 1.22 61 5.20 124.80 44,662 



96" 32.0 20.0 1.60 1.26 62 5.47 175.04 78,558 



120" 40.0 24.0 1.67 1.29 63 5.69 227.60 102,148 



5. Trapezoidal ditch, 1-ft. base, side slopes */2 to 1, grade 

 1 in 200, = .025, s .005. (Fig. 100.) 



Gals. 



Depth. Area. r. Vr. W.P. C. v. Cfs. min. 



6" .63 .29 .54 . 2.12 38 1.44 .91 408 



12" 1.5 .48 .69 3.12 45 2.17 3.25 1,458 



18" 2.625 .60 .77 4.36 47 2.53 6.65 2,984 



24" 4.00 .91 .95 5.48 53 3.53 14.12 6,337 

 36" 7.50 .97 .98 7.72 55 3.77 28.28 12,692 

 48" 12.00 1.20 1.10 9.96 57 4.39 52.67 23,638 

 72" 24.00 1.66 1.29 14.44 62 5.60 134.4 60,319 

 96" 40.00 2.11 1.45 18.92 65 6.60 264.0 113,990 



120" 60.00 2.56 1.60 23.40 69 7.73 463.8 208,153 



6. Trapezoidal ditch, base 1 ft., slope 1 to 1, grade 1 in 

 800, -n = .025, s = .00125. (Fig. 101.) 



Gals. 



Depth. Area. r. Mr. W.P. C. v. Cfs. min. 



6" .75 .31 .56 2.41 38 .75 .56 251 



12" 2.00 .53 .73 3.82 46 1.18 2.35 1,055 



18" 3.75 .72 .85 5.23 50 1.49 5.58 2,491 



24" 6.00 .91 .95 6.64 53 1.79 10.74 4,820 



36" 12.00 1.26 1.12 9.46 57 2.24 26.84 12,046 

 48" 20.00 1.63 1.28 12.28 62 2.78 55.50 24,908 

 72" 42.00 2.34 1.53 17.92 67 3.59 150.78 69,685 

 96" 72.00 3.06 1.75 23.56 71 4.35 313.20 140,563 



120" 110.00 3.77 1.94 29.20 74 5.02 552.20 247,827 



7. Trapezoidal ditch, base 1 ft., slope \ l / 2 to 1, grade 1 

 in 200, n = .025, j = .005. (Fig.102.) 



Gals. 



Depth. Area. r. Mr. W.P. C. v. Cfs. min. 



6" .88 .31 .56 2.80 38 1.43 1.25 561 



12" 2.50 .54 .73 4.61 46 2.35 5.88 2,639 



18" 4.87 .76 .87 6.41 50 3.05 14.85 6,661 

 24" 8.0 .98 .99 8.21 55 3.81 30.48 13,679 

 36" 16.5 1.39 1.18 11.83 60 4.96 81.90 36,756 

 48" 28.0 1.81 1.35 15.44 63 5.95 166.60 74,771 

 72" 60.0 2.64 1.62 22.66 70 7.94 476.40 213,809 

 96" 104.0 3.48 1.87 29.88 73 9.56 994.24 446,214 



120" 160.0 4.31 2.08 37.10 75 10.92 1747.2 784,144 



8. Trapezoidal ditch, width of base 4 ft., slope \ l /2 to 1, 

 grade 1 in 400, n .025, .s = .0025. (Fig. 102.) 



Gals. 



Depth. Area. W.P. r. Mr. C. v. Cfs. min. 



2' 14.0 11.2 1.25 1.1 57 3.14 43.96 19,727 

 4' 40.0 18.4 2.17 1.5 67 5.02 200.80 90,059 

 6' 78.0 25.6 3.05 1.75 70 6.12 477.36 214,218 

 8' 128.0 32.8 3.89 1.97 75 7.48 957.44 429,678 



9. Trapezoidal ditch, base 1 ft., slope 2 to 1, grade 1 in 

 SOO, n = .025, s = .00125. (Fig. 103.) 



Gals. 



Depth. Area. r. Mr. W.P. C. v. Cfs. min. 



6' 1.0 .34 .58 3.24 40 .81 .81 363 



12' 3.0 .55 .74 5.48 46 1.19 3.57 1,602 



18' 6.0 .77 .88 7.72 52 1.60 9.60 4,308 



24' 10.0 1.00 1.00 9.96 56 1.96 19.60 8,796 



36' 21.0 1.57 1.25 13.44 61 2.67 56.07 25,156 

 48' 36.0 1.90 1.38 18.92 64 3.08 111.06 49,844 

 72' 78.0 2.79 1.67 27.88 79 4.09 319.02 143,161 

 96' 136.0 3.69 1.92 36.84 74 4.97 675.92 303,362 



120' 210.0 4.58 2.14 45.80 76 5.69 1194.9 536,571 



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