= se Pi ae as | ae = ee se MMIVINNIII THESIS Ctl CSM eh ty ee a Seem Te CS Se ee Me eB OUT RMEISOR CT home. —M a, THESIS 01706 Pl Lf SUPPLEMENTARY MATER:AL iN BACK OF BOOK A Study of the Rainfall and Floods at East Lansing, Michigan. A Thesis Submitted to The Faculty of The Michigan Agricultural College wo ~ rae George R. Hayes Raymond J. DeMonéd Candidates for the degree of Bachelor of Science May, 1918. THESIS INTRODUCTION Phe purpose of this thesis is twofold;:- le Fo Gevelop a formale which can be used by practicing engineers in the design of sterm water earriers. 2. To enable forcaste to be made of the rise in the Red Cedar River at Bast Lansing and the Grand River at Lensing for various rainfalls likely to produce flcods. In view of the annual destructive floods in this vioinity this ietter information is of particular value in warning riperian owners of the likelihsod of fleod so that they may take necessary means to insure themselves and pro- perty against loss. 4014775 i. INTENSITY OF PRECIPITATION. For the design of sewers or storm water carriers, the intensity of precipitation is very important. The annual, monthly, daily and hourly rates are useful chiefly in problems of water supply, but useless in sewer design. The short, sharp shower taxes the capacity of the sewer ané forms a *“fiood wave" parallel to the fluctuation in intensity of the storm at a time sufficiently subsequent thereto to allow the water to veach the sewer from pavements, yards and roofs. Until recent years no considerable amount of trust-~ worthy information on intensity of preaipitetion was availabie, Since all rainfall records inoluded little more than the total precipitation in each storm. Moreover not until the establish- ment ef self-recording rein-gages became somewhat general and not until these had been maintained for a mufficient period was there sufficient information on which to predicate definite statements as to the relation of intensity of rainfall to the length of time during which the rein might fall continuously at any given rate. Kuiokling in 1689 investigating the rainfall in Rechester, HN. Y., studied mch records as were available and expressed formulae, from the date, for storms of periodea leas than one hour and for storms grester then one hour. Prof. Talbot in 18692 analysed in detail the rainfall records reported by the U. S. Weather Bureau. The greater part of them were records of ordinary rain gages, dut in a few cases were those of self-recoraing gages. Thus he devised formulae for intensity of storms in certain parts of the U. 58. But these formulae are generel and do not fit any partionlar eity. Recently with the inoreasing use of automatic rain gages ané with the greater use of the rational method of de- eign emong sewer engineers, the reecrds of automatic rain gages in the more important cities have been separately analyzed in detail, and onurves have been prepared which have been used as a basis of design in those cities. This is whet the writers have done in Curve III. We Plotted the points, time in minutes ae abscisase and the rate of rainfall per hour as ordinate. Then we drew in a smooth curve which would take in most of these pointe but not all of the severe storms which is never done in any case. It is sone sidered a waste in money to put in big sewers to carry off the water for those storms which happen once in ten years, or onse in fifteen. Hence for Hast Lansing we have a curve which could be used for sewer design. For any short period of time, say ten minutes, follow up until the curve is struck and we read 3.5 inches of rainfall. That is, for ten minutes the maximus rate of vainfell whieh is likely to ocour here will be at the rate of 3.6 inches per hour, except those unusual storms which Coaur onee in ten or fifteen years. It is customary in designing olty sewers to express the Felationship between time and intensity of rainfall in the form of an equation. We derived the equation of the time and in- tensity eurve for this locality hy plotting the curve inked in black as shown in Curve III. We took values from this curve ané plotted them on log-arithmetic paper. The points were founa to lie nearly on a straight line whieh indicates that the curve was of the form Y=ax". Determining the con- stents from the empirical date we have Y= 12.5 x ~ °5%8 , Prof. Hoad, of Michigan, in working on the design of sewers for Flint, devised a modification of the Talbot formals whieh is more easily adapted to local conditions I = 2 ; 2 where "R* © maximum rete for one hour, “t" is the duration in minutes and "I" is the intensity in inehes. By substitution in the equation of the time and intensity curve, we find that rer 2 which is adapted to this locelity. he FUTURE BSTIMA?TES. Where rainfall records of only a few years mst be mete the basis of engineering computations, it becomes important to inquire how reliable such records may be. Alex. Ae Binnie, memoer of the Institute of G. Ee draws geome conclusions in the Soolety Proceedings, Vole 109, Pe 89 172. He says “Dependence can be placed on any good reeord of twenty five years duration to give a mean rainfall correstily within two per cent of the truth". Mr. Rafter reviewing the paper says, “For records from twenty to thirty five years in length the error may be expected to vary from 5.25 down to two per cent and that for shorter periods the variation of the error is slightly higher". Mr. Henry has drawn the following conclusion. For a ten year period the following variations from the normal have eoooured ; New Bedford — +16 per cent - ili per cent Oineinnati + 20 per cent ~- iY per cent St. Lokhis + 17 per cent - 15 per cent Fe. Leavenworth + 16 per cent - i168 per eent San Fraeneisce « 9% per cent - 10 per cent fr. Henry found for a total 40 year period that the average variation was + or ~- 3 per cent. But it ie a facet that the rainfall for a particular locality may average considerably below the mean for many years after which may follow, perhaps, 5 | 1 an equally long period of surplus.