This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 Excerpt: ...trial values for the unknown (these values always positive) and compute the corresponding values of the left-hand side of the equation. (3) Plot a curve with these trial values for the unknown as ordinates and the values of the left-hand member corresponding as abscissae. The ordinate corresponding to the predetermined ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 Excerpt: ...trial values for the unknown (these values always positive) and compute the corresponding values of the left-hand side of the equation. (3) Plot a curve with these trial values for the unknown as ordinates and the values of the left-hand member corresponding as abscissae. The ordinate corresponding to the predetermined value of the right-hand member will at once yield the correct value of the unknown. Illustration of Use of Equations. Condition.--Hydrostatic water pressure on back, with overtopping. Eliminating all but hydrostatic and overtopping factors in Eq. (2), above, gives, as a result, Eq. (4), following: 6H3-7Kb'H2A-H2k'b'A8VKb'(H-W) + 3k'b'-2k(b')2(7KA-gk)) + i6kk'(b')2A VKb'(H-kb') =k(b')3k(7KA-i2k)-6(k')2A (4) Eq. (4) will serve to illustrate the foregoing remarks, using the numerical-coefficients for k, k' and K, respectively, 0.89, say; 0.25; and 2.25. Substituting these values in Eq. (4) and reducing, gives an expression in terms of b', A, and H, the last, the unknown to be determined, as follows: H3-2.625b'H2A-Hb'Al V 2.2 5b'(H-0.89b') +0.06256'-(b')2(4-6725A-2.3763) +0.5933 (b')2A V 2.2 5b'(H-0.89b') = (fe')3(2.0236A-1.4099) (5) Eq. (5), then, contains Bazin's coefficients and a constant, fixing the parabolic face that will determine a cross-section presumably acceptable as to flow conditions. The conditions of stability down to the depth of water, H, on the base at that depth, is that of the "middle third limit," for the resultant pressures on the joints at and above that base. The loading conditions, for simplicity, comprise only those of horizontal static water pressure on back and "overtopping." See Table III. Assuming a head (b') on the theoretical crest of 20 feet and A = 2.24 and inserting these values in Eq. (5) g...
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