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l = length of crest; H - x = depth of water on crest: Then v= sqrt(2gx) where 2g = 64.32 feet; ∴ Q = v (H - x) l=l (H -x) √(2gx). This must be a maximum, hence the derivative of Q with respect to x must be zero; hence- 0=l √2g[(H-x)/(2x½)-x½],∴x=⅓H,there4;Q=cl H3/2;. In the case of the Austin dam, l = 1091, ∴ Q = 3362 H*frac3/2;.

The formula generally used to find the flow over crests is Q=cl H (3/2). With a view to testing the reliability of this formula and finding the coefficint c, in January and March, 1900, measurements of velocity were taken, with a small Price electric meter, by Mr. E. E. Howard, a senior in the engineering department of the University of Texas. The dam broke before the investigations were completed, but the following values of the coefficient c were found:

Depth of water on crest.