Part 19

EX.—Find the bursting pressure of a cylindrical boiler shell 7 ft. 6 in. in diameter, with plates ½in. thick, assuming an ultimate strength of 50,000 lb. per square inch.

Set 90 on C to 1·0 on D, and under 50,000 on C find 555 lb. on D.

To find working pressure for Fox’s corrugated furnaces by Board of Trade rule.

Set the least outside diameter in inches on C to 14,000 on D, and under thickness in inches on C read working pressure on D in lb. per square inch.

To find diameter d in inches, of round steel for safety valve springs by Board of Trade rule.

Set 8000 on C to load on spring in lb. on D, and under the mean diameter of the spring in inches on C read d^3 on D. Then extract the cube root as per rule.

SPEED RATIOS OF PULLEYS, ETC.

Given the diameter of a pulley and its number of revolutions per minute, to find the circumferential velocity of the pulley or the speed of ropes, belts, etc., driven thereby.

Set diameter of pulley in inches on C to 3·82 on D, and over revolutions per minute on D read speed in feet per minute on C.

EX.—Find the speed of a belt driven by a pulley 53 in. in diameter and running at 180 revolutions per minute.

Set 53 on C to 3·82 on D, and over 180 on D read 2500 ft. per minute on C.

EX.—Find the speed of the pitch line of a spur wheel 3 ft. 6 in. in diameter running at 60 revolutions per minute.

Set 42 in. on C to 3·82 on D, and over 60 on D read 660 ft. per minute on C.

Given diameter and number of revolutions per minute of a driving pulley, and the diameter of the driven pulley, to find the number of revolutions of the latter.

Invert the slide and set diameter of driving pulley on Ɔ to given number of its revolutions on D; then opposite diameter of any driven pulley on Ɔ read its number of revolutions on D.

EX.—Diameter of driving pulley 10 ft.; revolutions per minute 55; diameter of driven pulley 2 ft. 9 in. Find number of revolutions per minute of latter.

Set 10 on Ɔ to 55 on D, and opposite 2·75 on Ɔ read 200 revolutions on D.

BELTS AND ROPES.

To find the ratio of tensions in the two sides of a belt, given the coefficient of friction between belt and pulley μ and the number of degrees θ in the arc of contact (log. R = (μθ)/(132)).

Set 132 on C to the coefficient of friction on D, and read off the value found on D under the number of degrees in the arc of contact on C. Place this value on the scale of equal parts on the back of the slide, to the index mark in the aperture, and read the required ratio on D under the L.H. index of C.

EX.—Find the tension ratio in a belt, assuming a coefficient of friction of 0·3 and an arc of contact of 120 degrees.

Set 132 on C to 0·3 on D, and under 120 on C read 0·273. Place this on the scale to the index on the back of the rule, and under the L.H. index C read 1·875 on D, the required ratio.

Given belt velocity and horse-power to be transmitted, to find the requisite width of belt, taking the effective tension at 50 lb. per inch of width.

Set 660 on C to velocity in feet per minute on D, and opposite horse-power on D find width of belt in inches on C.

Given velocity and width of belt, to find horse-power transmitted.

Set 660 on C to velocity on D, and under width on C find horse-power transmitted on D.

(N.B.—For any other effective tension, instead of 660 use as a gauge point:—33,000 ÷ tension.)

Given speed and diameter of a cotton driving rope, to find power transmitted, disregarding centrifugal action, and assuming an effective working tension of 200 lb. per square inch of rope.