The author gives here a series of improved formul〓 for the manometric head and impelling horse power, of centrifugal pumps having spacially formed impellers which may widely be applied in practice. Notation : a=intermediate constant to be substituted by..+1.1,+1.0,+.9....or..-1.1,-1.0,-.9....in the formula. b=constant. [numerical formula] g=32.2ft. sec. sec. h=manometric head in ft. i=axial opening of entrance of impeller÷inner radius of impeller. k=constant. m=constant. n=the power due to form of vane. q_2=relative velocity in ft. sec. of water particles at the exit of impeller. r=distance in ft. between a point p on the impelling surface of vane and the centre of impeller. r_1=inner radius in ft. of impeller. r_2=outer radios in ft. of impeller. A=constant in ft. sec. B=mean radial velocity in ft. sec. of flow at the entrance of impeller. H=impelling horse power. M=constant due to the form of vane. N=ditto. Q=volume in cub. ft. per sec. of flow. R=B÷ωr_1. α=angle between the tangent at a point p on the vane curve and the opposite direction of rotation of impeller. α_1=angle of entrance of vane. α_2=angle of exit of vane. β=angle between the line o p connecting p mentioned above to centre o and os connecting the entrance tip of vane s to centre o. β_2=embraced angle of vane. γ_2=embraced angle of entrance of impeller. δ=number of vanes. σ=r÷r_1 σ_2=r_2÷r_1. ω=angular velocity in radians per sec. of impeller. ρ=weight in lbs. per cub. ft. of water or 62.4 lbs. [numerical formula] Σ=axial opening of impeller at point p mentioned above÷axial opening of impeller at entrance. The well known theory is shown as H=[numerical formula]……(a) The author recommends a general formula cot α=Mσ^n+N……(b) for vane curve, being the inner radius of impeller the unit ; and [numerical formula]……(c) to draw the curve. If σ_2,α_1,α_2,and β_2 are given, we can find M, N and n by following equations : [numerical formula]……(d) cot α_1=M+N……(e) cot α_2=M^n+N……(f) And find A/B, B/A and c by substituting...+1.1,+1.0,+.9...or...-1.1,-1.0,-.9....into a of following equations : [numerical formula]……(g) [numerical formula]……(h) [numerical formula]……(i) Also get Γ_2 by equation (j), [numerical formula]……(j) Now we can find the value of R due to the shape of impeller disc, by equations (k)〜(n), Case I. Parallel disc impeller and its modification ; i.e. the axial opening of impeller is constant or Σ=1. [numerical formula]=0……(k) Case II. Conical disc impeller and its modification ; i.e. the axial opening of impeller changes linearly as radius of impeller or Σ=kσ+b. [numerical formula]……(l) Case III. Hyperbolic disc impeller and its modification ; i.e. the axial opening of impeller varies reciprocally as radius of impeller or σΣ=1. [numerical formula]……(m) Case IV. Curved disc impeller shown by (σ-b)^mΣ=(1-b)^m. [numerical formula]……(n) Where the value of R in each case must neither be negative nor much beyond tan α_1. Finallv H, Q and h can be shown as follows : [numerical formula] Ilis principle of solution can be extended on the other machines such as water turbines and centrifugal compressors ; and also the discussion on the cases affected by friction or viscosity of water may be intended. [figure]
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