AREA OF WATERWAYS. 625 



to the author's gaugings of flood flow from catchments, including 

 areas of 1 to 300 acres and one of 180 square miles. The values 

 assigned to the area A in the formulae vary from Af to At to A a, 

 which give results for a catchment of 100,000 acres from 5600 to 

 10,000 to 14,700 respectively. Such results surely indicate some 

 fundamental error. In spite of this great diversity of values of 

 individual factors the resulting volume determined by either one 

 of the best four formulae — Burkli Ziegler, McMath, Adams, Hawksley 

 — give fairly uniform results for a rainfall up to four inches and 

 areas up to 10,000 acres. 



The uncertainty of the results obtained by these formulae 

 induced the author to systematise his practice during the past 20 

 years, with the object of securing rational results ; and while 

 shrinking from increasing the already long list of formulae, feels 

 justified in doing so for the reasons given and in the hope that those 

 who may have the opportunity of checking it will do so to the benefit 

 not only of engineers, but the country and community at large. 



Firstly, inclusion of direct values for length and breadth of 

 catchment had to be considered, and it was decided to omit them 

 after making many calculations, and also for the following reason. 

 Assume a uniform rainfall and a strip of catchment one chain wide 

 and 100 chains long, and assume that the rain continues during 

 time taken by flood water in travelling from top of catchment to 

 outlet, then the discharge becomes equivalent to 100 times the 

 average rainfall over one square chain, i.e., is directly proportional 

 to R X A. The same result is obtained if the storm is assumed to 

 travel with the flow and at the same rate, perhaps a rare occuiTcnce, 

 but nevertheless a result which may be approximated in large areas 

 and certainly attained in small ones. 



The maximum volume of flood flow may then be accepted as 

 depending directly on the rainfall — r, the area — A, and probably 

 as the velocity of flow of water off catchment, which is inversely 

 as the square root of the average length or radius of the catchment, 



and may be represented by -j- ; and as the velocity of flow is directly 



governed by the average rainfall over the catchment, this factor 

 is assumed to indicate the percentage of run-off to maximum fall. 

 It has been found that maximum flood flow is chiefly associated 

 with a heavy general rain — not of maximum intensity — over the 

 catchment after the surface soil has become saturated by previous 

 rain. Some have accordingly suggested a reduced value for r ; 

 but to do so, whilst eliminating a co-efficient for absorption in small 

 areas would give too small results for large areas ; and it must be 

 borne in mind that the rain previously absorbed may be considered 

 as an equivalent increase in amount of actual rainfall causing 

 maximum flood flow, i.e., the value to be assigned to r becomes 

 practically equal to the maximum record. 



Adopt=Maximum rate of rainfall, in inches per hour. 



A=Area of catchment in acres. 



Q=Maximum flood discharge in cubic feet per sec. 



Q2 



