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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. 1897 Excerpt: ...by the velocity Vi. Its value is most readily found by computing the lost energy. This ost energy consists of (a) that corresponding to T.he frictional loss of head k(v2/2g), and (b) the kinetic energy due to the velocity V2. That is, for W lbs. of water we have Available energy = WVr/3g; Lost energy = (W/2g)(kv + v) = n'/2g, if m'2 = kv + The value of m' is founa graphically as the hypothenuse of a right-angled triaugle of which the sides are equal to V2 and v2"/k; that is, to Kfci (Fig.. 23D) and IJ (Fig. 23C). The construction need not be shown. The energy imparted to the motor is L = (A/2g)(V12-m'2), and the hydraulic efficiency is the ratio of this to nVi./2g, or e = (V?-m,2)/V2.. In Fig. 23E a circular quadrant is drawn with Q as center and radius QR = Vi.; A semicircle is drawn with diameter QV, its length being some convenient number of equal parts, as 100. Take QS = a', and draw SR parallel to QV and QR intersecting the semicircular arc at T. Draw TU perpendicular to QV; then it may be shown that the efficiency is equal to the ratio of QU to QV. Thus, from similar triangles, QU/QT = ES/RQ; QT/QV = RS/RQ. Multiplying these equations member by member, QD/QV = (RS)2/(RQ)2 = (V2-m,2)/V? = e. 56. Determination of Eest Wheel-Velocity and Highest Efficiency.-The general problem may be solved by repeating the constructions described in Zrt.. 55 for a number of different values of tne wheel-velocity, and drawing a curve showing the relation between efficiency and velocity of rotation.. The conctruction may be conveniently arranged as in Fig. 24. Lay off AB to represent V. and ACi, AC2,.., to represent several values of u; the corresponding values of v. are C±B, C23,.., From A draw a perpendiculai to ACj, and locate Di, D2,, in such a way that C1D1...
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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. 1897 Excerpt: ...by the velocity Vi. Its value is most readily found by computing the lost energy. This ost energy consists of (a) that corresponding to T.he frictional loss of head k(v2/2g), and (b) the kinetic energy due to the velocity V2. That is, for W lbs. of water we have Available energy = WVr/3g; Lost energy = (W/2g)(kv + v) = n'/2g, if m'2 = kv + The value of m' is founa graphically as the hypothenuse of a right-angled triaugle of which the sides are equal to V2 and v2"/k; that is, to Kfci (Fig.. 23D) and IJ (Fig. 23C). The construction need not be shown. The energy imparted to the motor is L = (A/2g)(V12-m'2), and the hydraulic efficiency is the ratio of this to nVi./2g, or e = (V?-m,2)/V2.. In Fig. 23E a circular quadrant is drawn with Q as center and radius QR = Vi.; A semicircle is drawn with diameter QV, its length being some convenient number of equal parts, as 100. Take QS = a', and draw SR parallel to QV and QR intersecting the semicircular arc at T. Draw TU perpendicular to QV; then it may be shown that the efficiency is equal to the ratio of QU to QV. Thus, from similar triangles, QU/QT = ES/RQ; QT/QV = RS/RQ. Multiplying these equations member by member, QD/QV = (RS)2/(RQ)2 = (V2-m,2)/V? = e. 56. Determination of Eest Wheel-Velocity and Highest Efficiency.-The general problem may be solved by repeating the constructions described in Zrt.. 55 for a number of different values of tne wheel-velocity, and drawing a curve showing the relation between efficiency and velocity of rotation.. The conctruction may be conveniently arranged as in Fig. 24. Lay off AB to represent V. and ACi, AC2,.., to represent several values of u; the corresponding values of v. are C±B, C23,.., From A draw a perpendiculai to ACj, and locate Di, D2,, in such a way that C1D1...
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