298 



THE IRRIGATION AGE. 



THE PRIMER OF HYDRAULICS* 



By FREDERICK A. SMITH, C. E. 



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

 1,600, .025, J = .00062. (Fig. 103.) 



Depth. Area. W.P. r. Mr. C. 



56 

 65 

 70 

 73 

 76 

 78 

 81 



11. Trapezoidal ditch, base 3 ft., slope 1 in 1, grade 1 in 

 400, M .025, j = .0025. (Fig. 101.) 



Gals. 



Depth. Area. IV. P. 

 2' 10.0 8.6 

 4' 28.0 14.2 

 6' 54.0 19.8 

 8' 88.0 25.4 



12. Trapezoidal ditch, base 10 ft., slope 1 to 1, grade 1 

 in 1,600, n = .025, s .00(162. (Fig. 101.) 



Gals. 



l.S.'i 

 2.76 

 3.24 

 3.75 



4.48 



Cfs. 



43.92 

 154.55 

 311.04 

 540.110 

 897.00 



mm. 



19,711 



69.366 



139.577 



242,352 



402.573 



12' 



264.0 40.8 6.47 



81 



5.06 1335.84 559.52") 



13. Advantage of Lined Ditches. 



When conducting water through ditches many things 

 must be considered, such as the maximum and minimum 

 flow to be expected and the resulting velocities. Small flows 

 of moderate velocities can be accommodated by any ditch 

 cut into the natural soil so long as the mean velocity remains 

 below 2 ft. per second. But as the velocity grows, which is 

 always a natural consequence of increased volume, there ap- 

 pears the danger of erosion or the water cutting into the 

 wetted surface of the ditch. Hence in designing a ditch the 

 maximum quantity of water to be dealt with roust be carefully 

 determined and also the maximum velocity ; if it is found 

 that such maximum velocity would cause the cutting away 

 of the bed in the ditch then it will be better to line the 

 ditch with masonry, brick, concrete, lumber, metal, etc. In 

 adopting this course the coefficient of roughness n is greatly 

 reduced according to the material used, which increases the 

 factor C in proportion so that the dimensions of the ditch 

 may be decreased, or else the slope made smaller, which 

 results in a saving in the required head. Thus an irrigation 

 ditch, for instance, lined with concrete will be able to stand 

 a velocity of 6 ft. per second without injury, while a plain 

 ditch cut through the soil would fail with a current of 

 2 ft. per second or more. Another advantage of the lined 

 ditch is that there are no losses due to seepage and the loss 

 due to evaporation is much smaller than in the rough ditch. 



As the scouring takes place in the bottom of the ditch 

 or water course, the bottom velocity, or the velocity along 

 the wetted perimeter, must be considered, not the mean 

 velocity which is greater than the bottom velocity. By many 

 experiments made for this purpose Kutter found that the 

 bottom velocity is equal to the mean velocity divided by 1.31 ; 

 thus if v = 2.0 ft. per second the velocity on the bottom and 

 sides of the ditch is 2 -=- 1.31 = 1.527 ft. It is the bottom 

 velocities which must be considered in finding the limiting 

 value of velocities permissible in a water course cut in soil. 



The following table shows velocities just necessary to 

 move the various substances lying loose on the bed : 



Mean Bottom 



Velocity Velocity 



Mud and fine clay 0.33 fs. 0.25 fs. 



Fine sand 0.46 fs. 0.35 fs. 



Clay loam and sand 0.66 f s. 0.50 f s. 



Common river sand 0.92 fs. 0.70 fs. 



Gravel 2.62 fs. 2.00 fs. 



Pebbles, 1 in. in diameter 2.79 fs. 2.13 fs. 



Coarse gravel 3.93 f s. 3.00 f s. 



Angular broken stone: 5.24 fs. 4.00 fs. 



Soft slate, shingle stone 6.55 fs. 5.00 fs. 



Stratified rock 7.86 fs. 6.00 fs. 



Hard rock 13.12 fs. 10.00 fs. 



It is seen from this table that it requires but a moderate 

 velocity to move such loose particles as clay or loam, whereas 

 a ditch lined with concrete, for instance, can withstand a 

 bottom velocity of 6 ft. per second, or a mean velocity of 

 7.86 ft. per second. 



The above velocities are just sufficient to move particles 

 as indicated. The resistance of soils to erosion is greater as 

 the cohesion in the material has to be overcome ; the limiting 

 velocities as to erosion are as follows : 



Feet per 

 Second 

 Channel in pure sand, bottom velocity 1.1 



Channel in sandy soil, 

 Channel in sandy loam, 

 Channel in loamy soil, 

 Channel in clay loam, 

 Channel in soil clay, 

 Channel in pure clay, 



15% clay...- 1.2 



40% clay 1.8 



65% clay 3.0 



85% clay 4.8 



95% clay 6.2 



100% clay 7.C 



It is, however, not good policy to permit velocities as 

 high as these unless the water is perfectly clear, since par- 

 ticles in suspension, such as grains of sand and gravel will 

 cut into the walls of the channels. 



14. Flumes. 



Flumes may be considered lined ditches and as such what 

 has been said about ditches applies also to flumes. The 

 essentials of a flume is its form and the material of which it 

 is built, which determines the factor of roughness, the hy- 

 draulic radius and the slope. In the building of open flumes 

 it is important to plan the whole work so that the inclination 

 of the slope of the flume is on the same angle as the average 

 hydraulic grade line, taking a mean between high and low 

 water stages. In many irrigation projects it is important to 

 use the smallest slope possible in order to increase the acre- 

 age available for irrigation. In order to do this and at the 

 same time to obtain the largest amount of water practicable 

 it is essential to build a flume in which the coefficient of 

 roughness is as small as possible consistent with good eco- 

 nomic practice. 



For instance, let it be required to design a flume capable 

 of carrying 40 second feet of water a distance of three miles 

 on a grade of 18 in. per mile. 



Analysis Let the size of the flume be 3 ft. by 4 ft. and 

 the flow area be 3 X 4 12 sq. ft. when delivering 40 second 

 feet ; then "V = 40 -r- 12 = 3.333 fps. ; then, according to the 

 fundamental formula: v = CVrs, we know all the quantities 

 except C, hence by transposition : 



C v 2 /r f o- C VrVrvr. 



The hydraulic radius is 12 -j- 10 = 1.2 and Vr = 1.09. 



Substitute given quantities and make computations : 



C = V3.333V1.2 X .00028 = Vll.ll/.000336 = V.33065 = 

 181.8. Hence the factor C is 182 for a hydraulic radius of 1.2 

 and sine of slope of .0003, which indicates by consulting Tables 

 A and I that the coefficient must lie between .008 and .009. 

 which means that the flume requires to be almost perfect, 

 and as a consequence it would be cheaper to either enlarge 

 the flume or increase the sine of the slope. As a usual 

 thing this latter alternative is not practicable, so the size of 

 the flume must be increased to reduce the velocity. By 

 making the size of the flume 4x4 gives a flow area of 16 ft. ; 

 divide this into 40 gives ^ = 2.5; the hydraulic radius is 

 16 -=- 12 = 1.33 ; Vr=1.16 and j = .00028, and by substituting 

 values in the formula : C = Mif/rs we obtain : 



C = V6.25/1.333 X .00028 = V 16756 = 129.4. 



This value of C is considerably lower, and looking in 



