THE IKKIGATION AGE. 



1107 



Channels to be grouped under n = .010 : 



Glass pipe, lead pipe, tin pipe, straight and regular ; 

 wrought iron pipe, galvanized pipe, straight and regular; 

 very hard wood, surfaced, straight and regular. 



= .011: 



Cast iron pipe (new), neat cement channel, straight 

 and regular: glazed tiling; very smooth planed plank chan- 

 nels of uniform section. 



n = .012 : 



Used cast iron pipe, channels formed of two-thirds ce- 

 ment and one-third fine sand, planed boards in flumes of 

 regular section. 



n = .013 : 



Very smooth brick work plastered with cement, planed 

 common boards of slightly varying cross-section, hard brick, 

 smooth surface with clean joints, concrete channels, very 

 regular and smoothly plastered. 



n =.014: 



Channels formed of regular masonry, regular brick 

 work with slight variations in cross-section straight line, 

 concrete channels fairly smooth or fairly well plastered. 



n = .015 : 



Rough brick work, Ashlar masonry channels, small irregu- 

 larities in cross-section and line; also channels of very rough 

 concrete. 



n = .017 : 



Channels of very rough brick work, or very rough ma- 

 sonry, very good ditches of uniform cross-section and smooth, 

 paved channels. 



= .020 : 



Channels and rivers with paved banks and bed of fine 

 sand (Ohio river, Point Pleasant, .021), ditches cut fairly 

 smooth and uniform. 



= .025 : 



River beds, side walls of good Rubble masonry, channels 

 of fair line and fairly regular cross-section, ditches of irregu- 

 lar section, (not too much so), with some small detritus or 

 light growth of aquatic plants. 



n = .030 : 



River bed with embankment walls, detritus in small 

 quantities, pebbles and small boulders in bed, channels and 

 ditches of irregular outline and grade channels with heavy 

 growth of aquatic plants. 



= .035 : 



Channels, rivers and ditches with irregular bed and irregu- 

 lar side walls, boulders, heavy detritus, great variation in 

 the slope and cross-sections. 



n .040 : 



Rivers, canals and ditches with irregular beds, coarse 

 detritus, irregular cross-section, irregular slopes. 



n = .050 : 



Rivers of very irregular beds, very coarse detritus, very 

 irregular cross-section with large obstructions and very steep 

 grades. 



It is to be understood that the character of a channel 

 has a great deal to do with the flow of water and it may be 

 that the flow conditions of one kind of cast iron pipe may be 

 covered by = .010, while another may require n = .012. 

 Similar variations must be looked for in brick, mason and 

 concrete work, and the observant hydraulic engineer or irri- 

 gator must judge for himself what coefficient will be suited 

 best for his particular work. Here is where enters the per- 

 sonal equation of the practical side, which cannot be covered 

 in the book, but which each engineer must solve for himself. 

 The foregoing list of different materials and channels are 

 cited merely for an approximate guide. 



"Article XI. How to Calculate "n". 



It is evidently of importance to be able to compute the 

 coefficient n for any case where proper gaugings and observa- 

 tions have been made so as to define more clearly the different 

 degrees of roughness. By an intricate transmutation of the 

 general formula for C, given in the beginning of this article, 

 the quantity n may be developed, and here follows the formula 

 which results : 



, 



r 



C-B 



" 



In this formula r is the hydraulic radius 

 j = slope 



.00281 

 B = 41.6 + - 



s 



C = v -r- \/rs 

 v = mean velocity. 



Following is an application of this formula, illustrated 

 upon a practical problem : A brick conduit 4 feet in diam- 

 eter is flowing full ; the sine of slope = .0004 and the observed 

 mean velocity = 2 feet ; find n. 



Solution. r=:l and -\/r=l; \/s = .02; hence: 

 C = 2 ~ .02 = 100. 



B = 41.6 + .00281 -4- 0004 = 41.6 -f 7.02 = 48.62. 

 Substitute these quantities in above equation : 



4S.62y.100 



1_ / 100-4S.a\ 2 _ l_flOO 4S.62\ 



Executing operations : 



n = V 1 - 811 -J- 4863 + 54 (-01056 )" l / 2 (.01056) 



= V- 000376 + -0000279 .00528 



n = V .0004039 .00528 



n .0201 .00528 = .0148. 



In this case take n = .015. 



By the aid of the tables prepared by the author which 

 are embodied in this work this cumbersome operation could 

 have been avoided in the following manner : Since r, v and .s 

 are given, C is obtained from the formula v=C\/rs, from 

 which we first obtain: C = v---\/rs. This operation exe- 

 cuted in the case under consideration gives C = 100. 



Now look through the different tables for the place when 

 C is nearest to 100, when \/r = l, and for slope .0004. The 

 table for it = .013 shows C= 119.25 and the table for n = .015 

 shows C = 97.96; thus it is seen that the coefficient of rough- 

 ness should be .015. If absolute accuracy is wanted it may be 

 found by interpolation ; thus the coefficient n will be less than 

 .015 and more than .013, in the same ratio as 100 lies between 

 97.96 and 119.25; difference between these two numbers is 

 21.29 ; hence as C decreases 21.29, n advanced from .013 to 

 .015, or at the rate of .0001 per unit ; as 97.96 is nearly 

 equal to 98, multiply this by 2 and subtract from .015 = .0148, 

 which is the number as found above. 



Hence the determination of the coefficient n is quite read- 

 ily done by the use of the tables with very little work. 

 Article XII.. Explanation of the "C" Tables. 



This book contains 13 tables giving the factor C for 13 

 different degrees of roughness and for 29 different hydraulic 

 radii, each for six different slopes. These were carefully 

 selected for the purpose of providing sufficient data for all 

 practical problems which might present themselves. 



The author made the computations for the square root 

 of the hydraulic radii (\/r), which still further increases 

 the range of the tables, so that they cover pipes from J^-inch 

 diameter to conduits of 3,600 ft. diameter or rivers or canals of 

 equivalent cross-section. The slopes shown vary from .001 

 to .000025, which covers practically all cases ever arising. 



With these tables calculated ready for use, the solution 

 of hydraulic problems becomes an easy matter, especially if 

 use is made of the tables of hydraulic radii, wetted peri- 

 meters, areas of circular segments, and the many other 

 original auxiliary tables, such as square roots, cube roots, etc. 



A DAM THAT SEEMS IN DEMAND. 



The Ambursen Hydraulic Construction Co. reports a 

 contract with the Auglaize Construction Co. for the con- 

 struction of Development No. 1 on the Auglaize River 

 near Defiance, Ohio,. The dam is 28 feet high and the 

 total length of the concrete structure, including the power 

 house, is 555 feet. 



The Ambursen type of dam has been adopted by the 

 War Department of the U. S. government for the dam 

 which they are about to build across the Mississippi River 

 between Minneapolis and St. Paul. As the dam will be 

 built directly by the government on force account, the 

 contract with the Ambursen company takes the form of 

 an adequate royalty. 



The Ambursen Co. is also building two dams for the 

 Department of Irrigation in Porto Rico. One on the 

 Jacaguas River near Guayabal is 115 feet high and 1,200 

 feet long, and the other on the Coamo River is 62 feet 

 high and 600 feet long. These two, in connection with the 

 125-foot dam for the Porto Rico Railways Co., near San 

 Juan, makes three heavy pieces of work now under con- 

 struction in Porto Rico bv the Ambursen Company. The 

 plans for still a fourth dam are now in preparation. 



