Water-power; an outline of the development and application of the energy of flowing water . of sag and tension are comparatively simple ;but these methods become inapplicable when, as most com-monly occurs, the two pulle\s are not in the same horizontalline. In this case we must regard the curxe as forming a partof a more extended catenary whose suspension points are onthe same level, viz., the level of the higher point. In Fig. CASE OF ONE PULLEY HIGHER THAN THE OTHER. 439 .210, c/and e are two pulleys at different elevations, connectedby a wire rope with lower side tight. This side is to ber
Water-power; an outline of the development and application of the energy of flowing water . of sag and tension are comparatively simple ;but these methods become inapplicable when, as most com-monly occurs, the two pulle\s are not in the same horizontalline. In this case we must regard the curxe as forming a partof a more extended catenary whose suspension points are onthe same level, viz., the level of the higher point. In Fig. CASE OF ONE PULLEY HIGHER THAN THE OTHER. 439 .210, c/and e are two pulleys at different elevations, connectedby a wire rope with lower side tight. This side is to beregarded as a part of the catenary A CB, and the elements ofthis catenary are to be arrived at by a laborious process of trialand error. We will state without demonstration some proper-ties of the curve, referring the reader who is desirous of fullerinformation to the discussion of the catenary in treatises on thecalculus. Let CH be a horizontal line through the lowestpoint of the catenary; let x and / be the coordinates of anypoint r of the curve. When x z=^ a, the semispan, y = h, the. Fig. 210. sag of the rope. At the point r, if a tangent be drawn to thecurve, it forms with the horizontal and \ertical througli C atriangle such that if6ybe taken to represent the tension onthe lowest part of the curve, y/ will represent the tension at /-,and Ck the weight of the rope Cr. l^.xpressing these severaltensions in equivalent lengths of rope, we put /„ for the tensionat Cy /j for that at r, and /„ for that at B. The quantity in column 4 of the table, corresponding to in the first, is twice the tangent of the angle Cfk. As a basis of computation,suppose the pulleys to be 300 feet apart horizontally, 50 feetvertically. We know within narrow limits what tension /^ we 440 TJ^ OF POWER. require at r. say /^ = 3600. We know that /^ is but little lessthan /, say /, = 3480. To find a we proceed thus: Assumea value of a, and find by equation (61) the corresponding valueof//. T
Size: 2132px × 1172px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjecthydraulicengineering
