158 



THE IRRIGATION AGE. 



In streams of rapid descent a shorter 

 cut or tunnel will suffice to reach the 

 same depth, and in draining the founda- 

 tions for a submerged dam less pumping 

 will be required, as short drain cuts or 

 tunnels can be employed. 



PROBA.BLE VOLUME OF UNDERFLOW. 



We have already seen how the existence 

 of an underflow can be determined by the 

 natural characteristics of the watershed 

 and channel of a stream. By the same 

 means the volume of the underflow can 

 also be judged. That is to say it can be 

 determined whether it is probable that the 

 underflow is quite considerable, or whether 

 it is small and unimportant. It is impos- 

 sible, however, to determine the exact 

 amount of the underflow from any obser- 

 vations in regard to the channel and water- 

 shed of a stream. In fact it can be seen 

 very readily that it is a difficult matter to 

 ascertain the volume of H stream of water 

 flowing by underground percolation 

 through sand and gravel. Some experi- 

 ments covering the velocity of water per- 

 colating through such materials as usually 

 comprise the beds of rivers have been 

 made by engineers. From these experi- 

 ments the following laws have been de- 

 duced: The velocity of percolating water 

 varies directly as the density and character 

 of the stratum through which it percolates, 

 and as the square root of the one-hun- 

 dredth part of the product of the slope and 

 depth of the percolating stratum. The 

 quantity of water percolating through any 

 formation depends upon the mean velocity 

 of percolation and the area of cross-section 

 of the stratum of percolating water. 



By plotting the results of such experi- 

 ments as have been made with varying 

 grades, depths and classes of material they 

 have all been found to follow quite closely 

 the following formulae: 



v = O.lm 



and 



Q a (0. 1m V Tirir, in which the let- 

 ters denote the following factors: 



v = the mean velocity of the percolating 

 water in feet per second. 



Q = the number of cubic feet of perco- 

 lating water per second. 



a = area of cross-section occupied by 

 water in the deposit containing the perco- 

 lating watery in square feet. 



d = mean depth in feet of the deposit 

 containing the percolating water. 



s = mean fall or inclination per foot of 

 the deposit containing the percolating 

 water, in feet. 



m = a variable factor. 

 The value of the factor m depends on 

 the density of the deposit of materials 

 through which the underflow percolates. 

 A deposit in which a large portion' of the 

 mass consists of voids affords an easy out- 

 let to percolating water, while one with 

 less voids makes percolation more slow and 

 difficult. 



The following values for the factor m 

 have been deduced from such experiments 

 as have been made and recorded: 



For coarse boulders of nearly uniform 

 size, m 1.0. 



For coarse boulders with some gravel, 

 m= 0.9. 



For boulders with considerable gravel, 

 m = 0.8. 



For coarse gravel, m = 0.1. 

 For coarse gravel with some sand, m 

 = 0.6. 



For coarse river sand with some gravel, 

 t = 0.5. 



For ordinary sharp river sand with very 

 little gravel, m = 0.4. 



For coarse quicksand, m 0.3. 

 For medium quicksand, m 0.2. 

 For fine quicksand, m = 0.1. 

 For intermediate cases between those 

 enumerated above the values of in can be 

 approximated from those given. 



While it is not believed that the formulae 

 given above will produce results which are 

 entirely exact, yet, if the true conditions 

 are arrived at, employing the formulae will 

 give as close results as are required for all 

 practical purposes. The best method for 

 determining the depth and area of cross- 

 section of an underflow is by making bor- 

 ings at intervals across the stream from 

 the top to the bottom of the water-bearing 

 formation. If the expense of making such 

 borings cannot be incurred, the only way 

 to determine these things is by approxi- 

 mation from such characteristics of the 

 stream as are observable. The slope of 

 the river bed, the proximity of bed rock at 

 the sides of the channel, the dip or angle 

 of the materials comprising the sides of 

 the river bed, the width of the channel, 

 the distance from the surface flow to the 

 top of the underflow and other things of a 

 like nature are often guides, which help to 

 determine the probable depth and sec- 

 tional area of the underflow. 



