Surveys of the distribution of average dye concentration 

 across-stream in the vertical plane were made at distances down- 

 stream of 1/2, 3/4, 1, and 1 1/2 in„ 



ANALYSIS OF RESULTS 



In Figures 4 and 5 are plotted the points obtained from 

 these surveys at the various stations downstream from the injector. 

 Note that the y~eoordinate in these figures is measured from a 

 displaced origin, not from the axis of symmetry A smooth curve 

 has been faired through each set of data The ordinates give the 

 ratio of the concentration of the measured sample to the concentra- 

 tion of the original solution,, These curves will be called con- 

 centration curves. Actually, they are traces in a vertical plane 

 of a concentration surface,, Although it was not verified, it 

 will be assumed that these surfaces are axially symmetric so that 

 the surface could be generated by revolving the measured curve 

 about its symmetry axis 



Measurements of other experimenters indicate that one can 

 expect the concentration surface to be an axially symmetric 

 Gaussian error surface One would then expect the concentration 

 curves to fit an equation of the form 



where r is the distance from the axis and A and cr are constants 

 depending upon the station under consideration,, The constant A 

 gives a measure of the total amount of dye passing a given station; 

 & is a measure of the width of the dye wake, the distance from 

 the axis to the inflection of the concentration surface Actually, 

 however , the effect of the finite size of opening of the sampler 

 will be to deform this curve, the deformation being greater, the 

 greater the size of opening of the sampler relative to the 

 quantity or <, Indeed, in case the rate of flow of water entering 

 the sampler is greater than the free-stream velocity the effective 

 size of the opening is further increased „ In the present experi- 

 ments the average velocity of water in the sampler was about three 

 times the free=stream velocity,, This corresponds to an effective 

 diameter of the sampler about 1„7 times its actual diameter,, 

 Since the actual sampler diameter was o 035 in , w e shall take 

 as effective sampler diameter 0„060 in„ The effective radius 

 of the sampler will hereafter be denoted by R„ 



The chief difficulty in analyzing the data is in determining 

 from the measured, deformed curves the constants A and xf of the 

 true curveso The theory for the method of correction is developed 

 in the appendix and is based upon the assumption that the true 

 concentration surface is a circuler Gaussian surface The pro- 

 cedure for finding ©r was as follows,, First 9 the experimental 

 curves were treated as if they were Gaussian curveso In this 



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